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07070100000000000081A40000000200000002000000015D8693EF000001D4000000000000000000000000000000000000002300000000wfmath-1569100783.d0f8a54/.mailmapErik Ogenvik <erik@ogenvik.org> Erik Hjortsberg <erik.hjortsberg@iteam.se> 
Erik Ogenvik <erik@ogenvik.org> Erik Hjortsberg <erik.hjortsberg@gmail.com>
Erik Ogenvik <erik@ogenvik.org> Erik Hjortsberg <erik.hjortsberg@jayway.se>
Alistair Riddoch <alriddoch@googlemail.com> Al Riddoch <alriddoch@googlemail.com>
Alistair Riddoch <alriddoch@googlemail.com> Al Riddoch <alriddoch@localhost>
Peter Szücs <peter.szucs.dev@gmail.com> Peter Szucs <peter.szucs.dev@gmail.com>
07070100000001000081A40000000200000002000000015D8693EF00000204000000000000000000000000000000000000002200000000wfmath-1569100783.d0f8a54/AUTHORSMaintainer:
	Erik Ogenvik <erik@ogenvik.org>

Original author:
	Ron Steinke <rsteinke@w-link.net>

Other contributors:
	James Turner <james@worldforge.org>
	Michael Koch <konqueror@gmx.de>
	Dan Tomalesky <grim@xynesis.com>
	Al Riddoch <alriddoch@googlemail.com>

The Miniball code of Bernd Gaertner
<http://www.inf.ethz.ch/personal/gaertner>
is used for finding bounding spheres for
collections of points.

The Mersenne Twister code of Richard J. Wagner
<rjwagner@writeme.com> is used for random
number generation.

07070100000002000081A40000000200000002000000015D8693EF00001BD0000000000000000000000000000000000000002900000000wfmath-1569100783.d0f8a54/CMakeLists.txtcmake_minimum_required(VERSION 3.2)

project(wfmath)
set(CMAKE_CXX_STANDARD 14)
set(CMAKE_CXX_STANDARD_REQUIRED on)
include(GNUInstallDirs)
include(FindPkgConfig)

# Version setup

set(WFMATH_VERSION_MAJOR 1)
set(WFMATH_VERSION_MINOR 0)
set(WFMATH_VERSION_PATCH 3)

set(VERSION ${WFMATH_VERSION_MAJOR}.${WFMATH_VERSION_MINOR}.${WFMATH_VERSION_PATCH})
set(SUFFIX -${WFMATH_VERSION_MAJOR}.${WFMATH_VERSION_MINOR})

set(WFMATH_ABI_CURRENT 1)
set(WFMATH_ABI_REVISION 0)
set(WFMATH_ABI_AGE 0)
math(EXPR WFMATH_SOVERSION ${WFMATH_ABI_CURRENT}-${WFMATH_ABI_AGE})
set(WFMATH_ABI_VERSION ${WFMATH_SOVERSION}.${WFMATH_ABI_AGE}.${WFMATH_ABI_REVISION})

# Set compiler flags
set(WF_WARNING_FLAGS -Wall -Winit-self -Wcast-qual -Wwrite-strings -Wextra -Wundef -Wmissing-declarations -Wno-unused-parameter -Wshadow -Wno-missing-field-initializers -Wno-long-long)

include_directories("${PROJECT_SOURCE_DIR}")

# Meta data

set(DESCRIPTION "A math library for the Worldforge system.")

# This macro defines a library
macro(wf_add_library _LIB_NAME _SOURCE_FILES_VAR _HEADER_FILES_VAR)

add_library(${_LIB_NAME} SHARED ${${_SOURCE_FILES_VAR}} ${${_HEADER_FILES_VAR}})
    add_library(${_LIB_NAME}_STATIC STATIC ${${_SOURCE_FILES_VAR}} ${${_HEADER_FILES_VAR}})
    set_target_properties(${_LIB_NAME} PROPERTIES
            VERSION ${WFMATH_ABI_VERSION}
            SOVERSION ${WFMATH_SOVERSION}
            )

install(TARGETS ${_LIB_NAME}
            LIBRARY DESTINATION ${CMAKE_INSTALL_LIBDIR})

foreach (file ${${_HEADER_FILES_VAR}})
        get_filename_component(dir ${file} DIRECTORY)
        install(FILES ${file} DESTINATION include/${PROJECT_NAME}${SUFFIX}/${dir})
    endforeach ()

set(PKG_CONFIG_LIBS "-l${_LIB_NAME} ${PKG_CONFIG_LIBS}")

endmacro()

# Add a "check" target, which builds and runs the tests.
add_custom_target(check COMMAND ${CMAKE_CTEST_COMMAND})

#Macro for adding a test. The test name will be extracted from the name of the first submitted file.
#Additional files can be submitted as varargs.
macro(wf_add_test TEST_FILE)

get_filename_component(TEST_NAME ${TEST_FILE} NAME_WE)

add_executable(${TEST_NAME} EXCLUDE_FROM_ALL ${TEST_FILE} ${ARGN})
    target_link_libraries(${TEST_NAME} ${PROJECT_NAME}${SUFFIX}_STATIC)
    add_test(NAME ${TEST_NAME} COMMAND ${TEST_NAME})

add_dependencies(check ${TEST_NAME})
endmacro()

# We only need Atlas for tests
pkg_check_modules(WF atlascpp-0.7>=0.7)

if (WF_FOUND)
    wf_add_test(atlas/atlas_0_7_test.cpp)
    target_link_libraries(atlas_0_7_test ${WF_LDFLAGS})
    target_include_directories(atlas_0_7_test PUBLIC ${WF_INCLUDE_DIRS})
endif (WF_FOUND)

# Define source files for libraries

set(SOURCE_FILES
        wfmath/axisbox.cpp
        wfmath/ball.cpp
        wfmath/const.cpp
        wfmath/int_to_string.cpp
        wfmath/intersect.cpp
        wfmath/line.cpp
        wfmath/point.cpp
        wfmath/polygon.cpp
        wfmath/polygon_intersect.cpp
        wfmath/probability.cpp
        wfmath/quaternion.cpp
        wfmath/randgen.cpp
        wfmath/rotbox.cpp
        wfmath/rotmatrix.cpp
        wfmath/segment.cpp
        wfmath/stream.cpp
        wfmath/timestamp.cpp
        wfmath/vector.cpp)

set(HEADER_FILES
        wfmath/atlasconv.h
        wfmath/axisbox.h
        wfmath/axisbox_funcs.h
        wfmath/ball.h
        wfmath/ball_funcs.h
        wfmath/basis.h
        wfmath/const.h
        wfmath/error.h
        wfmath/general_test.h
        wfmath/int_to_string.h
        wfmath/intersect.h
        wfmath/intersect_decls.h
        wfmath/line.h
        wfmath/line_funcs.h
        wfmath/MersenneTwister.h
        wfmath/miniball.h
        wfmath/miniball_funcs.h
        wfmath/point.h
        wfmath/point_funcs.h
        wfmath/polygon.h
        wfmath/polygon_funcs.h
        wfmath/polygon_intersect.h
        wfmath/probability.h
        wfmath/quaternion.h
        wfmath/randgen.h
        wfmath/rotbox.h
        wfmath/rotbox_funcs.h
        wfmath/rotmatrix.h
        wfmath/rotmatrix_funcs.h
        wfmath/segment.h
        wfmath/segment_funcs.h
        wfmath/shuffle.h
        wfmath/stream.h
        wfmath/timestamp.h
        wfmath/vector.h
        wfmath/vector_funcs.h
        wfmath/wfmath.h
        wfmath/wrapped_array.h
        wfmath/zero.h)

wf_add_library(${PROJECT_NAME}${SUFFIX} SOURCE_FILES HEADER_FILES)
target_compile_options(${PROJECT_NAME}${SUFFIX} PRIVATE ${WF_WARNING_FLAGS})

# pkg-config files
configure_file(${PROJECT_NAME}.pc.in ${PROJECT_NAME}${SUFFIX}.pc @ONLY)
install(FILES ${PROJECT_BINARY_DIR}/${PROJECT_NAME}${SUFFIX}.pc DESTINATION ${CMAKE_INSTALL_LIBDIR}/pkgconfig)

# RPM spec files
#TODO: fix these
configure_file(${PROJECT_NAME}.spec.in ${PROJECT_NAME}.spec @ONLY)
#TODO: fix these
configure_file(mingw32-${PROJECT_NAME}.spec.in mingw32-${PROJECT_NAME}.spec @ONLY)

# Add test
enable_testing()

wf_add_test(wfmath/ball_test.cpp)
wf_add_test(wfmath/const_test.cpp)
wf_add_test(wfmath/intstring_test.cpp)
wf_add_test(wfmath/line_test.cpp)
wf_add_test(wfmath/point_test.cpp)
wf_add_test(wfmath/polygon_test.cpp)
wf_add_test(wfmath/probability_test.cpp)
wf_add_test(wfmath/quaternion_test.cpp)
wf_add_test(wfmath/randgen_test.cpp)
wf_add_test(wfmath/rotmatrix_test.cpp)
wf_add_test(wfmath/shape_test.cpp)
wf_add_test(wfmath/timestamp_test.cpp)
wf_add_test(wfmath/vector_test.cpp)

# Doxygen support, exports a "docs" target.

find_package(Doxygen)
configure_file(doc/Doxyfile.in Doxyfile @ONLY)

if (DOXYGEN_FOUND)

set(DOXYGEN_INPUT ${CMAKE_CURRENT_BINARY_DIR}/Doxyfile)
    set(DOXYGEN_OUTPUT doc)

add_custom_command(
            OUTPUT ${DOXYGEN_OUTPUT}
            COMMAND ${CMAKE_COMMAND} -E echo_append "Building API Documentation..."
            COMMAND ${DOXYGEN_EXECUTABLE} ${DOXYGEN_INPUT}
            COMMAND ${CMAKE_COMMAND} -E echo "Done."
            WORKING_DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR}
            DEPENDS ${DOXYGEN_INPUT}
    )

add_custom_target(docs DEPENDS ${DOXYGEN_OUTPUT})

endif (DOXYGEN_FOUND)

add_custom_command(
        OUTPUT ChangeLog
        COMMAND ${CMAKE_SOURCE_DIR}/support/generate-ChangeLog.sh ${CMAKE_SOURCE_DIR} ${CMAKE_SOURCE_DIR} 8bd480b053190ffde2afe33af66f484953036f5a
)
add_custom_target(changelog DEPENDS ChangeLog)

# Packaging (for source tarballs

set(CPACK_PACKAGE_DESCRIPTION_SUMMARY ${DESCRIPTION})
set(CPACK_PACKAGE_VENDOR "Worldforge")
set(CPACK_PACKAGE_DESCRIPTION_FILE "${PROJECT_SOURCE_DIR}/README.md")
set(CPACK_RESOURCE_FILE_LICENSE "${PROJECT_SOURCE_DIR}/COPYING")
set(CPACK_PACKAGE_VERSION_MAJOR "${WFMATH_VERSION_MAJOR}")
set(CPACK_PACKAGE_VERSION_MINOR "${WFMATH_VERSION_MINOR}")
set(CPACK_PACKAGE_VERSION_PATCH "${WFMATH_VERSION_PATCH}")
#set(CPACK_INSTALL_SCRIPT "sh ${CMAKE_SOURCE_DIR}/support/generate-ChangeLog.sh ${CMAKE_SOURCE_DIR} ${CPACK_PACKAGE_INSTALL_DIRECTORY} 8bd480b053190ffde2afe33af66f484953036f5a")

set(CPACK_SOURCE_GENERATOR TBZ2 ZIP)

set(CPACK_SOURCE_PACKAGE_FILE_NAME "${PROJECT_NAME}-${VERSION}" CACHE INTERNAL "tarball basename")

set(CPACK_SOURCE_IGNORE_FILES
        # no hidden files
        "/\\\\..+$"
        "~$"
        )

include(CPack)07070100000003000081A40000000200000002000000015D8693EF000046AC000000000000000000000000000000000000002200000000wfmath-1569100783.d0f8a54/COPYING                    GNU GENERAL PUBLIC LICENSE
                       Version 2, June 1991

Copyright (C) 1989, 1991 Free Software Foundation, Inc.,
 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
 Everyone is permitted to copy and distribute verbatim copies
 of this license document, but changing it is not allowed.

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0. This License applies to any program or other work which contains
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Also add information on how to contact you by electronic and paper mail.

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Yoyodyne, Inc., hereby disclaims all copyright interest in the program
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  Ty Coon, President of Vice

This General Public License does not permit incorporating your program into
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Public License instead of this License.
07070100000004000081A40000000200000002000000015D8693EF00000123000000000000000000000000000000000000002400000000wfmath-1569100783.d0f8a54/ChangeLogThis file is autogenerated from the Git history when a the "dist" make target is invoked. If you find this file in an official release something has gone wrong and you should contact erik@ogenvik.org. It needs to be exactly one line long in order for the ChangeLog generating script to work.07070100000005000081A40000000200000002000000015D8693EF000003F8000000000000000000000000000000000000001F00000000wfmath-1569100783.d0f8a54/NEWS2013-08-31  Erik Ogenvik  <erik@ogenvik.org>

* wfmath 1.0.2 released.

2012-10-24  Al Riddoch  <alriddoch@googlemail.com>

* wfmath 1.0.1 released.

2012-03-21  Al Riddoch  <alriddoch@googlemail.com>

* wfmath 1.0.0 released.

2012-01-18  Al Riddoch  <alriddoch@googlemail.com>

* wfmath 0.3.12 released.

2011-02-12  Al Riddoch  <alriddoch@googlemail.com>

* wfmath 0.3.11 released.

2009-12-29  Al Riddoch  <alriddoch@googlemail.com>

* wfmath 0.3.10 released.

2009-01-26  Al Riddoch  <alriddoch@googlemail.com>

* wfmath 0.3.9 released.

2008-11-15  Al Riddoch  <alriddoch@googlemail.com>

* wfmath 0.3.8 released.

2007-07-25  Al Riddoch  <alriddoch@googlemail.com>

* wfmath 0.3.7 released.

2007-07-20  Al Riddoch  <alriddoch@zepler.org>

* wfmath 0.3.6 released.

2006-08-18  Al Riddoch  <alriddoch@zepler.org>

* wfmath 0.3.5 released.

2005-06-11  Al Riddoch  <alriddoch@zepler.org>

* wfmath 0.3.4 released.

2003-04-24  Al Riddoch  <alriddoch@zepler.org>

* wfmath 0.2.11 released.

07070100000006000081A40000000200000002000000015D8693EF00000F05000000000000000000000000000000000000002400000000wfmath-1569100783.d0f8a54/README.md# WFMath

[![Join us on Gitter!](https://badges.gitter.im/Worldforge.svg)](https://gitter.im/Worldforge/Lobby)

This is the  [WorldForge](http://worldforge.org/ "The main Worldforge site") math library.
It's licensed under the GPL (see file COPYING).

The primary focus of WFMath is geometric objects. Thus,
it includes several shapes (boxes, balls, lines), in addition
to the basic math objects that are used to build these shapes
(points, vectors, matricies).

## Installation

If you intend to build this as a prerequisite for the Ember client or the Cyphesis server we strongly suggest that you 
use the [Hammer](http://wiki.worldforge.org/wiki/Hammer_Script "The Hammer script") tool to compile Ember.
This is script provided by the Worldforge project which will download and install all of the required libraries and 
components used by Worldforge.

Otherwise the library can most easily be built through the following commands.
```
mkdir build_`arch` && cd build_`arch`
cmake ..
make
make install
```

### Tests

The test suite can be built and run using the ```check``` target. For example:

```
make check
```

### API documentation

If Doxygen is available API documentation can be generated using the ```docs``` target. For example:

```
make docs
```

## Dependencies

The only library that WFMath checks for is Atlas, and it only does this
for the sake of some test functions. The only dependency on Atlas is
in the file atlasconv.h. This header file contains
some inline functions which can be used to convert the various
objects in WFMath to Atlas::Message::Object and back. This
header file will be installed whether Atlas is present or not,
but to use it you must of course have the Atlas headers installed.

## Design

Most of the library classes can be divided into two sorts. The
first kind are basic mathematical objects, whose members are all fundamental
types. The second kind are shapes, which implement the shape class
interface described in doc/shape.h. There are four classes of the first kind:

* Vector<>	A basic mathematical vector
* RotMatrix<>	An orthogonal matrix of determinant 1, useful for
		describing rotations.
* Point<>		A point in space. This basic class also implements
		the shape interface in doc/shape.h.
* Quaternion	A quaternion

The shape classes are:

* AxisBox<>	A box oriented parallel to the coordinate axes
* Ball<>		Ball<2> is a circle, Ball<3> is a sphere, etc.
* Segment<>	A line segment, defined by its endpoints
* RotBox<>	Like AxisBox<>, but it can be rotated to arbitrary
		angles
* Polygon<>	A 2 dimensional polygon contained in a (possibly)
		larger dimensional space

The library also contains some probability-related functions,
as well as wrappers for system time and random number functions.

# Contributing

Anyone interested in contributing to this project shouldl ook at the file doc/CLASS_LAYOUT, which specifies which member
functions all classes should have, and what order they should appear in.
This only applies to significant classes, not things like
ColinearVectors in error.h, which is only there to be thrown as
as exception.

## How to help

If you're interested in helping out with development you should check out these resources:

* [The main Worldforge site](http://worldforge.org/ "The main Worldforge site")
* [Bugs and feature planning on Launchpad](https://launchpad.net/wfmath "WFMath Launchpad entry")
* [Gitter conversation](https://gitter.im/Worldforge/Lobby "Gitter conversation")
* [Mailing lists](http://mail.worldforge.org/lists/listinfo/ "Mailing lists")
07070100000007000081A40000000200000002000000015D8693EF000007C7000000000000000000000000000000000000001F00000000wfmath-1569100783.d0f8a54/TODOInline in the foo.h any method in foo_funcs.h that does not require another
header, and has no loop

Re-write operators so that for a given operator O, operatorO is implemented
using operatorO= rather than the other way around which is inefficient.

Add throw(ColinearVectors) to the appropriate vector and matrix
	rotation functions
Get rid of templates as template args, use ValueType for standard
	containers instead

Intersect functions unimplemented for dim != 2,3 (extremely low priority):
	Intersect(Polygon<>, AxisBox<>, bool)
	Intersect(Polygon<>, RotBox<>, bool)
	Intersect(RotBox<>, AxisBox<>, bool)
	Intersect(RotBox<>, RotBox<>, bool)
    These will be postponed until I can think of a way to write them,
    or someone needs them, whichever comes first
Add shape tests from COAL
Write rotateInverse() functions
Look into whether miniball code can handle using float instead of double;
	if so, replace Wrapped_array with Point
Requests from Jesse: NAN, INFINITY, RADIANS_TO_DEGREES, DEGREES_TO_RADIANS
Write an API reference for the library. Find some inline documentation tool?
Deal with difficulties in making certain functions friends of the
	appropriate classes
Rearrange the functions in foo_funcs.h to match the order in the class
	in foo.h

Schedule:
0.3.0 will come out once I get around to testing the Polygon intersect functions
      and make sure they work. At that point the old Intersect()/IntersectProper()
      interface will be removed, as will support for deprecated network
      formats in atlas_conv.h. This is also an appropriate time to make changes
      that break binary compatibility.

alriddoch's TODO 2008-11-10

Clean up const.h removing all includes that it itself does not use.

<cmath>, <cassert> and <iosfwd> should go. Clean up the rest of the headers
that turn out to need this, but completely get rid of asserts from the
interface headers. This should reduce the cost of including these headers,
and stop them from polluting the namespace.
07070100000008000041ED0000000200000002000000025D8693EF00000000000000000000000000000000000000000000002000000000wfmath-1569100783.d0f8a54/atlas07070100000009000081A40000000200000002000000015D8693EF00000668000000000000000000000000000000000000003300000000wfmath-1569100783.d0f8a54/atlas/atlas_0_4_test.cpp// atlas_tests.cpp (WFMath/Atlas Message conversion test code)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-12

#include<Atlas/Message/Object.h>
#include "atlasconv.h"

using namespace WFMath;

template<class C>
void atlas_test(const C& c)
{
//  cout << c << std::endl;
  Atlas::Message::Object a = c.toAtlas();
  C out(a);
//  cout << out << std::endl;
  // Only match to string precision
  assert(Equal(c, out, FloatMax(WFMATH_EPSILON,1e-5)));
}

int main()
{
  Point<3> p(1, 0, Sqrt2);
  atlas_test(p);

Vector<3> v(1, -1, 4);
  atlas_test(v);

Quaternion q(v, 0.7);
  atlas_test(q);

AxisBox<3> b1(Point<3>().setToOrigin(), p), b2(p, p + v);
  atlas_test(b1);
  atlas_test(b2);

return 0;
}
0707010000000A000081A40000000200000002000000015D8693EF0000094F000000000000000000000000000000000000003300000000wfmath-1569100783.d0f8a54/atlas/atlas_0_7_test.cpp// atlas_tests.cpp (WFMath/Atlas Message conversion test code)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-12

#include<Atlas/Message/Element.h>
#include "wfmath/atlasconv.h"
#include "wfmath/stream.h"

using namespace WFMath;

template<class C>
void atlas_test(const C& c)
{
  std::cout << c << std::endl;
  Atlas::Message::Element a = c.toAtlas();
  C out(a);
  assert(out.isValid());
  std::cout << out << std::endl;
  // Only match to string precision
  assert(Equal(c, out, FloatMax(numeric_constants<CoordType>::epsilon(),1e-5)));
}

int main()
{
  Point<3> p(1, 0, numeric_constants<CoordType>::sqrt2());
  atlas_test(p);

Vector<3> v(1, -1, 4);
  atlas_test(v);

Quaternion q(v, 0.7);
  atlas_test(q);

AxisBox<3> b1(Point<3>().setToOrigin(), p), b2(p, p + v);
  atlas_test(b1);
  atlas_test(b2);
  
  Ball<3> ball(Point<3>(1, 2, 3), 10);
  atlas_test(ball);
  
  Polygon<2> poly;
  poly.addCorner(0, WFMath::Point<2>(0, 0));
  poly.addCorner(1, WFMath::Point<2>(10, 0));
  poly.addCorner(2, WFMath::Point<2>(10, 10));
  atlas_test(poly);
  
  Line<2> line;
  line.addCorner(0, WFMath::Point<2>(0, 0));
  line.addCorner(1, WFMath::Point<2>(10, 0));
  atlas_test(line);
  
  Line<3> line2;
  line2.addCorner(0, WFMath::Point<3>(0, 0, 0));
  line2.addCorner(1, WFMath::Point<3>(10, 0, 5));
  atlas_test(line2);
  
  RotBox<2> rotbox(Point<2>(1, 2), Vector<2>(10, 20), RotMatrix<2>().identity());
  atlas_test(rotbox);

return 0;
}
0707010000000B000041ED0000000200000002000000025D8693EF00000000000000000000000000000000000000000000001E00000000wfmath-1569100783.d0f8a54/doc0707010000000C000081A40000000200000002000000015D8693EF000008C3000000000000000000000000000000000000002B00000000wfmath-1569100783.d0f8a54/doc/CLASS_LAYOUTI'm trying to come up with a general class layout that all
(significant) classes will obey. Friend functions are included
under the corresponding section. Currently it's this:

1) Constructors and destructor

The default constructor will not initialize the object. If the default
constructor is used, the object must first be initialized with operator>>(),
FromString(), FromAtlas(), operator=(), or one of the initializer functions
given later in the class. There is no constructor from a string value, as such
construction can fail. The destructor is not virtual, nor is any other
function in the class, as this is a low-level library designed primarily
for speed.

2) operator<<() and operator>>(), toAtlas() and fromAtlas()

friend std::ostream& operator<<(std::ostream& os, const Foo& f);
friend std::istream& operator>>(std::istream& is, Foo& f);

operator>>() indicates a parse failure by setting the fail() flag on the stream.
Failure also indicates that the object is in an invalid state. The definitions
of these functions are placed in the file stream.h, so the class only needs to
include <iosfwd>. The toAtlas() and fromAtlas() functions need a forward
declaration of Atlas::Message::Object, which is done in const.h. They
are only defined for certain classes (see Atlas protocol specs (where?)
for details). The implementations of these functions belong in atlasconv.h,
and must be done inline or as templates, so that the library can be built and
used without libAtlas.

3) operator=()

4) isEqualTo() method

this function is of the form

bool C::isEqualTo(const C& c, CoordType tolerance = WFMATH_EPSILON);

5) operator==(), operator!=()

these call isEqualTo()

6) Class initializers

e.g. zero() for Vector<>, origin() for Point<>, etc.

7) operator<()

sort only, if comparison makes sense stick others here too

8) math operators

9) other operators (e.g. operator[]())

10) other functions

11) dimension-specific constructors/operators/functions

e.g. Vector(CoordType& x, CoordType& y, CoordType& z) for Vector<3>

Every class is also defines two non-member functions:
ToString() and FromString(). These functions are
automatically generated in stream.h using templates
and the operator<<() and operator>>() functions.
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#
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PROJECT_NAME           = WFMath

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OUTPUT_DIRECTORY       = doc/

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CREATE_SUBDIRS         = NO

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# The default language is English, other supported languages are:
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# Greek, Hungarian, Italian, Japanese, Japanese-en (Japanese with English
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OUTPUT_LANGUAGE        = English

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ABBREVIATE_BRIEF       =

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SHORT_NAMES            = NO

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EXTRACT_LOCAL_CLASSES  = NO

# This flag is only useful for Objective-C code. When set to YES local
# methods, which are defined in the implementation section but not in
# the interface are included in the documentation.
# If set to NO (the default) only methods in the interface are included.

EXTRACT_LOCAL_METHODS  = NO

# If this flag is set to YES, the members of anonymous namespaces will be
# extracted and appear in the documentation as a namespace called
# 'anonymous_namespace{file}', where file will be replaced with the base
# name of the file that contains the anonymous namespace. By default
# anonymous namespace are hidden.

EXTRACT_ANON_NSPACES   = NO

# If the HIDE_UNDOC_MEMBERS tag is set to YES, Doxygen will hide all
# undocumented members of documented classes, files or namespaces.
# If set to NO (the default) these members will be included in the
# various overviews, but no documentation section is generated.
# This option has no effect if EXTRACT_ALL is enabled.

HIDE_UNDOC_MEMBERS     = YES

# If the HIDE_UNDOC_CLASSES tag is set to YES, Doxygen will hide all
# undocumented classes that are normally visible in the class hierarchy.
# If set to NO (the default) these classes will be included in the various
# overviews. This option has no effect if EXTRACT_ALL is enabled.

HIDE_UNDOC_CLASSES     = YES

# If the HIDE_FRIEND_COMPOUNDS tag is set to YES, Doxygen will hide all
# friend (class|struct|union) declarations.
# If set to NO (the default) these declarations will be included in the
# documentation.

HIDE_FRIEND_COMPOUNDS  = NO

# If the HIDE_IN_BODY_DOCS tag is set to YES, Doxygen will hide any
# documentation blocks found inside the body of a function.
# If set to NO (the default) these blocks will be appended to the
# function's detailed documentation block.

HIDE_IN_BODY_DOCS      = NO

# The INTERNAL_DOCS tag determines if documentation
# that is typed after a \internal command is included. If the tag is set
# to NO (the default) then the documentation will be excluded.
# Set it to YES to include the internal documentation.

INTERNAL_DOCS          = NO

# If the CASE_SENSE_NAMES tag is set to NO then Doxygen will only generate
# file names in lower-case letters. If set to YES upper-case letters are also
# allowed. This is useful if you have classes or files whose names only differ
# in case and if your file system supports case sensitive file names. Windows
# and Mac users are advised to set this option to NO.

CASE_SENSE_NAMES       = YES

# If the HIDE_SCOPE_NAMES tag is set to NO (the default) then Doxygen
# will show members with their full class and namespace scopes in the
# documentation. If set to YES the scope will be hidden.

HIDE_SCOPE_NAMES       = NO

# If the SHOW_INCLUDE_FILES tag is set to YES (the default) then Doxygen
# will put a list of the files that are included by a file in the documentation
# of that file.

SHOW_INCLUDE_FILES     = YES

# If the FORCE_LOCAL_INCLUDES tag is set to YES then Doxygen
# will list include files with double quotes in the documentation
# rather than with sharp brackets.

FORCE_LOCAL_INCLUDES   = NO

# If the INLINE_INFO tag is set to YES (the default) then a tag [inline]
# is inserted in the documentation for inline members.

INLINE_INFO            = YES

# If the SORT_MEMBER_DOCS tag is set to YES (the default) then doxygen
# will sort the (detailed) documentation of file and class members
# alphabetically by member name. If set to NO the members will appear in
# declaration order.

SORT_MEMBER_DOCS       = YES

# If the SORT_BRIEF_DOCS tag is set to YES then doxygen will sort the
# brief documentation of file, namespace and class members alphabetically
# by member name. If set to NO (the default) the members will appear in
# declaration order.

SORT_BRIEF_DOCS        = NO

# If the SORT_MEMBERS_CTORS_1ST tag is set to YES then doxygen will sort the (brief and detailed) documentation of class members so that constructors and destructors are listed first. If set to NO (the default) the constructors will appear in the respective orders defined by SORT_MEMBER_DOCS and SORT_BRIEF_DOCS. This tag will be ignored for brief docs if SORT_BRIEF_DOCS is set to NO and ignored for detailed docs if SORT_MEMBER_DOCS is set to NO.

SORT_MEMBERS_CTORS_1ST = NO

# If the SORT_GROUP_NAMES tag is set to YES then doxygen will sort the
# hierarchy of group names into alphabetical order. If set to NO (the default)
# the group names will appear in their defined order.

SORT_GROUP_NAMES       = NO

# If the SORT_BY_SCOPE_NAME tag is set to YES, the class list will be
# sorted by fully-qualified names, including namespaces. If set to
# NO (the default), the class list will be sorted only by class name,
# not including the namespace part.
# Note: This option is not very useful if HIDE_SCOPE_NAMES is set to YES.
# Note: This option applies only to the class list, not to the
# alphabetical list.

SORT_BY_SCOPE_NAME     = NO

# The GENERATE_TODOLIST tag can be used to enable (YES) or
# disable (NO) the todo list. This list is created by putting \todo
# commands in the documentation.

GENERATE_TODOLIST      = YES

# The GENERATE_TESTLIST tag can be used to enable (YES) or
# disable (NO) the test list. This list is created by putting \test
# commands in the documentation.

GENERATE_TESTLIST      = YES

# The GENERATE_BUGLIST tag can be used to enable (YES) or
# disable (NO) the bug list. This list is created by putting \bug
# commands in the documentation.

GENERATE_BUGLIST       = YES

# The GENERATE_DEPRECATEDLIST tag can be used to enable (YES) or
# disable (NO) the deprecated list. This list is created by putting
# \deprecated commands in the documentation.

GENERATE_DEPRECATEDLIST= YES

# The ENABLED_SECTIONS tag can be used to enable conditional
# documentation sections, marked by \if sectionname ... \endif.

ENABLED_SECTIONS       =

# The MAX_INITIALIZER_LINES tag determines the maximum number of lines
# the initial value of a variable or define consists of for it to appear in
# the documentation. If the initializer consists of more lines than specified
# here it will be hidden. Use a value of 0 to hide initializers completely.
# The appearance of the initializer of individual variables and defines in the
# documentation can be controlled using \showinitializer or \hideinitializer
# command in the documentation regardless of this setting.

MAX_INITIALIZER_LINES  = 30

# Set the SHOW_USED_FILES tag to NO to disable the list of files generated
# at the bottom of the documentation of classes and structs. If set to YES the
# list will mention the files that were used to generate the documentation.

SHOW_USED_FILES        = YES

# If the sources in your project are distributed over multiple directories
# then setting the SHOW_DIRECTORIES tag to YES will show the directory hierarchy
# in the documentation. The default is NO.

SHOW_DIRECTORIES       = NO

# Set the SHOW_FILES tag to NO to disable the generation of the Files page.
# This will remove the Files entry from the Quick Index and from the
# Folder Tree View (if specified). The default is YES.

SHOW_FILES             = YES

# Set the SHOW_NAMESPACES tag to NO to disable the generation of the
# Namespaces page.
# This will remove the Namespaces entry from the Quick Index
# and from the Folder Tree View (if specified). The default is YES.

SHOW_NAMESPACES        = YES

# The FILE_VERSION_FILTER tag can be used to specify a program or script that
# doxygen should invoke to get the current version for each file (typically from
# the version control system). Doxygen will invoke the program by executing (via
# popen()) the command <command> <input-file>, where <command> is the value of
# the FILE_VERSION_FILTER tag, and <input-file> is the name of an input file
# provided by doxygen. Whatever the program writes to standard output
# is used as the file version. See the manual for examples.

FILE_VERSION_FILTER    =

# The LAYOUT_FILE tag can be used to specify a layout file which will be parsed by
# doxygen. The layout file controls the global structure of the generated output files
# in an output format independent way. The create the layout file that represents
# doxygen's defaults, run doxygen with the -l option. You can optionally specify a
# file name after the option, if omitted DoxygenLayout.xml will be used as the name
# of the layout file.

LAYOUT_FILE            =

#---------------------------------------------------------------------------
# configuration options related to warning and progress messages
#---------------------------------------------------------------------------

# The QUIET tag can be used to turn on/off the messages that are generated
# by doxygen. Possible values are YES and NO. If left blank NO is used.

QUIET                  = NO

# The WARNINGS tag can be used to turn on/off the warning messages that are
# generated by doxygen. Possible values are YES and NO. If left blank
# NO is used.

WARNINGS               = YES

# If WARN_IF_UNDOCUMENTED is set to YES, then doxygen will generate warnings
# for undocumented members. If EXTRACT_ALL is set to YES then this flag will
# automatically be disabled.

WARN_IF_UNDOCUMENTED   = YES

# If WARN_IF_DOC_ERROR is set to YES, doxygen will generate warnings for
# potential errors in the documentation, such as not documenting some
# parameters in a documented function, or documenting parameters that
# don't exist or using markup commands wrongly.

WARN_IF_DOC_ERROR      = YES

# This WARN_NO_PARAMDOC option can be abled to get warnings for
# functions that are documented, but have no documentation for their parameters
# or return value. If set to NO (the default) doxygen will only warn about
# wrong or incomplete parameter documentation, but not about the absence of
# documentation.

WARN_NO_PARAMDOC       = NO

# The WARN_FORMAT tag determines the format of the warning messages that
# doxygen can produce. The string should contain the $file, $line, and $text
# tags, which will be replaced by the file and line number from which the
# warning originated and the warning text. Optionally the format may contain
# $version, which will be replaced by the version of the file (if it could
# be obtained via FILE_VERSION_FILTER)

WARN_FORMAT            = "$file:$line: $text"

# The WARN_LOGFILE tag can be used to specify a file to which warning
# and error messages should be written. If left blank the output is written
# to stderr.

WARN_LOGFILE           =

#---------------------------------------------------------------------------
# configuration options related to the input files
#---------------------------------------------------------------------------

# The INPUT tag can be used to specify the files and/or directories that contain
# documented source files. You may enter file names like "myfile.cpp" or
# directories like "/usr/src/myproject". Separate the files or directories
# with spaces.

INPUT                  = ../wfmath \
                         shape.h

# This tag can be used to specify the character encoding of the source files
# that doxygen parses. Internally doxygen uses the UTF-8 encoding, which is
# also the default input encoding. Doxygen uses libiconv (or the iconv built
# into libc) for the transcoding. See http://www.gnu.org/software/libiconv for
# the list of possible encodings.

INPUT_ENCODING         = UTF-8

# If the value of the INPUT tag contains directories, you can use the
# FILE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp
# and *.h) to filter out the source-files in the directories. If left
# blank the following patterns are tested:
# *.c *.cc *.cxx *.cpp *.c++ *.java *.ii *.ixx *.ipp *.i++ *.inl *.h *.hh *.hxx
# *.hpp *.h++ *.idl *.odl *.cs *.php *.php3 *.inc *.m *.mm *.py *.f90

FILE_PATTERNS          = *.h

# The RECURSIVE tag can be used to turn specify whether or not subdirectories
# should be searched for input files as well. Possible values are YES and NO.
# If left blank NO is used.

RECURSIVE              = NO

# The EXCLUDE tag can be used to specify files and/or directories that should
# excluded from the INPUT source files. This way you can easily exclude a
# subdirectory from a directory tree whose root is specified with the INPUT tag.

EXCLUDE                =

# The EXCLUDE_SYMLINKS tag can be used select whether or not files or
# directories that are symbolic links (a Unix filesystem feature) are excluded
# from the input.

EXCLUDE_SYMLINKS       = NO

# If the value of the INPUT tag contains directories, you can use the
# EXCLUDE_PATTERNS tag to specify one or more wildcard patterns to exclude
# certain files from those directories. Note that the wildcards are matched
# against the file with absolute path, so to exclude all test directories
# for example use the pattern */test/*

EXCLUDE_PATTERNS       = *_test.h \
                         basis.h \
                         miniball.h \
                         miniball_funcs.h \
                         wrapped_array.h

# The EXCLUDE_SYMBOLS tag can be used to specify one or more symbol names
# (namespaces, classes, functions, etc.) that should be excluded from the
# output. The symbol name can be a fully qualified name, a word, or if the
# wildcard * is used, a substring. Examples: ANamespace, AClass,
# AClass::ANamespace, ANamespace::*Test

EXCLUDE_SYMBOLS        =

# The EXAMPLE_PATH tag can be used to specify one or more files or
# directories that contain example code fragments that are included (see
# the \include command).

EXAMPLE_PATH           =

# If the value of the EXAMPLE_PATH tag contains directories, you can use the
# EXAMPLE_PATTERNS tag to specify one or more wildcard pattern (like *.cpp
# and *.h) to filter out the source-files in the directories. If left
# blank all files are included.

EXAMPLE_PATTERNS       =

# If the EXAMPLE_RECURSIVE tag is set to YES then subdirectories will be
# searched for input files to be used with the \include or \dontinclude
# commands irrespective of the value of the RECURSIVE tag.
# Possible values are YES and NO. If left blank NO is used.

EXAMPLE_RECURSIVE      = NO

# The IMAGE_PATH tag can be used to specify one or more files or
# directories that contain image that are included in the documentation (see
# the \image command).

IMAGE_PATH             =

# The INPUT_FILTER tag can be used to specify a program that doxygen should
# invoke to filter for each input file. Doxygen will invoke the filter program
# by executing (via popen()) the command <filter> <input-file>, where <filter>
# is the value of the INPUT_FILTER tag, and <input-file> is the name of an
# input file. Doxygen will then use the output that the filter program writes
# to standard output.
# If FILTER_PATTERNS is specified, this tag will be
# ignored.

INPUT_FILTER           =

# The FILTER_PATTERNS tag can be used to specify filters on a per file pattern
# basis.
# Doxygen will compare the file name with each pattern and apply the
# filter if there is a match.
# The filters are a list of the form:
# pattern=filter (like *.cpp=my_cpp_filter). See INPUT_FILTER for further
# info on how filters are used. If FILTER_PATTERNS is empty, INPUT_FILTER
# is applied to all files.

FILTER_PATTERNS        =

# If the FILTER_SOURCE_FILES tag is set to YES, the input filter (if set using
# INPUT_FILTER) will be used to filter the input files when producing source
# files to browse (i.e. when SOURCE_BROWSER is set to YES).

FILTER_SOURCE_FILES    = NO

#---------------------------------------------------------------------------
# configuration options related to source browsing
#---------------------------------------------------------------------------

# If the SOURCE_BROWSER tag is set to YES then a list of source files will
# be generated. Documented entities will be cross-referenced with these sources.
# Note: To get rid of all source code in the generated output, make sure also
# VERBATIM_HEADERS is set to NO.

SOURCE_BROWSER         = NO

# Setting the INLINE_SOURCES tag to YES will include the body
# of functions and classes directly in the documentation.

INLINE_SOURCES         = NO

# Setting the STRIP_CODE_COMMENTS tag to YES (the default) will instruct
# doxygen to hide any special comment blocks from generated source code
# fragments. Normal C and C++ comments will always remain visible.

STRIP_CODE_COMMENTS    = YES

# If the REFERENCED_BY_RELATION tag is set to YES
# then for each documented function all documented
# functions referencing it will be listed.

REFERENCED_BY_RELATION = YES

# If the REFERENCES_RELATION tag is set to YES
# then for each documented function all documented entities
# called/used by that function will be listed.

REFERENCES_RELATION    = YES

# If the REFERENCES_LINK_SOURCE tag is set to YES (the default)
# and SOURCE_BROWSER tag is set to YES, then the hyperlinks from
# functions in REFERENCES_RELATION and REFERENCED_BY_RELATION lists will
# link to the source code.
# Otherwise they will link to the documentation.

REFERENCES_LINK_SOURCE = YES

# If the USE_HTAGS tag is set to YES then the references to source code
# will point to the HTML generated by the htags(1) tool instead of doxygen
# built-in source browser. The htags tool is part of GNU's global source
# tagging system (see http://www.gnu.org/software/global/global.html). You
# will need version 4.8.6 or higher.

USE_HTAGS              = NO

# If the VERBATIM_HEADERS tag is set to YES (the default) then Doxygen
# will generate a verbatim copy of the header file for each class for
# which an include is specified. Set to NO to disable this.

VERBATIM_HEADERS       = YES

#---------------------------------------------------------------------------
# configuration options related to the alphabetical class index
#---------------------------------------------------------------------------

# If the ALPHABETICAL_INDEX tag is set to YES, an alphabetical index
# of all compounds will be generated. Enable this if the project
# contains a lot of classes, structs, unions or interfaces.

ALPHABETICAL_INDEX     = NO

# If the alphabetical index is enabled (see ALPHABETICAL_INDEX) then
# the COLS_IN_ALPHA_INDEX tag can be used to specify the number of columns
# in which this list will be split (can be a number in the range [1..20])

COLS_IN_ALPHA_INDEX    = 5

# In case all classes in a project start with a common prefix, all
# classes will be put under the same header in the alphabetical index.
# The IGNORE_PREFIX tag can be used to specify one or more prefixes that
# should be ignored while generating the index headers.

IGNORE_PREFIX          =

#---------------------------------------------------------------------------
# configuration options related to the HTML output
#---------------------------------------------------------------------------

# If the GENERATE_HTML tag is set to YES (the default) Doxygen will
# generate HTML output.

GENERATE_HTML          = YES

# The HTML_OUTPUT tag is used to specify where the HTML docs will be put.
# If a relative path is entered the value of OUTPUT_DIRECTORY will be
# put in front of it. If left blank `html' will be used as the default path.

HTML_OUTPUT            = html

# The HTML_FILE_EXTENSION tag can be used to specify the file extension for
# each generated HTML page (for example: .htm,.php,.asp). If it is left blank
# doxygen will generate files with .html extension.

HTML_FILE_EXTENSION    = .html

# The HTML_HEADER tag can be used to specify a personal HTML header for
# each generated HTML page. If it is left blank doxygen will generate a
# standard header.

HTML_HEADER            =

# The HTML_FOOTER tag can be used to specify a personal HTML footer for
# each generated HTML page. If it is left blank doxygen will generate a
# standard footer.

HTML_FOOTER            =

# The HTML_STYLESHEET tag can be used to specify a user-defined cascading
# style sheet that is used by each HTML page. It can be used to
# fine-tune the look of the HTML output. If the tag is left blank doxygen
# will generate a default style sheet. Note that doxygen will try to copy
# the style sheet file to the HTML output directory, so don't put your own
# stylesheet in the HTML output directory as well, or it will be erased!

HTML_STYLESHEET        =

# If the HTML_TIMESTAMP tag is set to YES then the footer of each generated HTML
# page will contain the date and time when the page was generated. Setting
# this to NO can help when comparing the output of multiple runs.

HTML_TIMESTAMP         = YES

# If the HTML_ALIGN_MEMBERS tag is set to YES, the members of classes,
# files or namespaces will be aligned in HTML using tables. If set to
# NO a bullet list will be used.

HTML_ALIGN_MEMBERS     = YES

# If the HTML_DYNAMIC_SECTIONS tag is set to YES then the generated HTML
# documentation will contain sections that can be hidden and shown after the
# page has loaded. For this to work a browser that supports
# JavaScript and DHTML is required (for instance Mozilla 1.0+, Firefox
# Netscape 6.0+, Internet explorer 5.0+, Konqueror, or Safari).

HTML_DYNAMIC_SECTIONS  = NO

# If the GENERATE_DOCSET tag is set to YES, additional index files
# will be generated that can be used as input for Apple's Xcode 3
# integrated development environment, introduced with OSX 10.5 (Leopard).
# To create a documentation set, doxygen will generate a Makefile in the
# HTML output directory. Running make will produce the docset in that
# directory and running "make install" will install the docset in
# ~/Library/Developer/Shared/Documentation/DocSets so that Xcode will find
# it at startup.
# See http://developer.apple.com/tools/creatingdocsetswithdoxygen.html for more information.

GENERATE_DOCSET        = NO

# When GENERATE_DOCSET tag is set to YES, this tag determines the name of the
# feed. A documentation feed provides an umbrella under which multiple
# documentation sets from a single provider (such as a company or product suite)
# can be grouped.

DOCSET_FEEDNAME        = "Doxygen generated docs"

# When GENERATE_DOCSET tag is set to YES, this tag specifies a string that
# should uniquely identify the documentation set bundle. This should be a
# reverse domain-name style string, e.g. com.mycompany.MyDocSet. Doxygen
# will append .docset to the name.

DOCSET_BUNDLE_ID       = org.doxygen.Project

# If the GENERATE_HTMLHELP tag is set to YES, additional index files
# will be generated that can be used as input for tools like the
# Microsoft HTML help workshop to generate a compiled HTML help file (.chm)
# of the generated HTML documentation.

GENERATE_HTMLHELP      = NO

# If the GENERATE_HTMLHELP tag is set to YES, the CHM_FILE tag can
# be used to specify the file name of the resulting .chm file. You
# can add a path in front of the file if the result should not be
# written to the html output directory.

CHM_FILE               =

# If the GENERATE_HTMLHELP tag is set to YES, the HHC_LOCATION tag can
# be used to specify the location (absolute path including file name) of
# the HTML help compiler (hhc.exe). If non-empty doxygen will try to run
# the HTML help compiler on the generated index.hhp.

HHC_LOCATION           =

# If the GENERATE_HTMLHELP tag is set to YES, the GENERATE_CHI flag
# controls if a separate .chi index file is generated (YES) or that
# it should be included in the master .chm file (NO).

GENERATE_CHI           = NO

# If the GENERATE_HTMLHELP tag is set to YES, the CHM_INDEX_ENCODING
# is used to encode HtmlHelp index (hhk), content (hhc) and project file
# content.

CHM_INDEX_ENCODING     =

# If the GENERATE_HTMLHELP tag is set to YES, the BINARY_TOC flag
# controls whether a binary table of contents is generated (YES) or a
# normal table of contents (NO) in the .chm file.

BINARY_TOC             = NO

# The TOC_EXPAND flag can be set to YES to add extra items for group members
# to the contents of the HTML help documentation and to the tree view.

TOC_EXPAND             = NO

# If the GENERATE_QHP tag is set to YES and both QHP_NAMESPACE and QHP_VIRTUAL_FOLDER
# are set, an additional index file will be generated that can be used as input for
# Qt's qhelpgenerator to generate a Qt Compressed Help (.qch) of the generated
# HTML documentation.

GENERATE_QHP           = NO

# If the QHG_LOCATION tag is specified, the QCH_FILE tag can
# be used to specify the file name of the resulting .qch file.
# The path specified is relative to the HTML output folder.

QCH_FILE               =

# The QHP_NAMESPACE tag specifies the namespace to use when generating
# Qt Help Project output. For more information please see
# http://doc.trolltech.com/qthelpproject.html#namespace

QHP_NAMESPACE          = org.doxygen.Project

# The QHP_VIRTUAL_FOLDER tag specifies the namespace to use when generating
# Qt Help Project output. For more information please see
# http://doc.trolltech.com/qthelpproject.html#virtual-folders

QHP_VIRTUAL_FOLDER     = doc

# If QHP_CUST_FILTER_NAME is set, it specifies the name of a custom filter to add.
# For more information please see
# http://doc.trolltech.com/qthelpproject.html#custom-filters

QHP_CUST_FILTER_NAME   =

# The QHP_CUST_FILT_ATTRS tag specifies the list of the attributes of the custom filter to add.For more information please see
# <a href="http://doc.trolltech.com/qthelpproject.html#custom-filters">Qt Help Project / Custom Filters</a>.

QHP_CUST_FILTER_ATTRS  =

# The QHP_SECT_FILTER_ATTRS tag specifies the list of the attributes this project's
# filter section matches.
# <a href="http://doc.trolltech.com/qthelpproject.html#filter-attributes">Qt Help Project / Filter Attributes</a>.

QHP_SECT_FILTER_ATTRS  =

# If the GENERATE_QHP tag is set to YES, the QHG_LOCATION tag can
# be used to specify the location of Qt's qhelpgenerator.
# If non-empty doxygen will try to run qhelpgenerator on the generated
# .qhp file.

QHG_LOCATION           =

# If the GENERATE_ECLIPSEHELP tag is set to YES, additional index files
#  will be generated, which together with the HTML files, form an Eclipse help
#  plugin. To install this plugin and make it available under the help contents
# menu in Eclipse, the contents of the directory containing the HTML and XML
# files needs to be copied into the plugins directory of eclipse. The name of
# the directory within the plugins directory should be the same as
# the ECLIPSE_DOC_ID value. After copying Eclipse needs to be restarted before the help appears.

GENERATE_ECLIPSEHELP   = NO

# A unique identifier for the eclipse help plugin. When installing the plugin
# the directory name containing the HTML and XML files should also have
# this name.

ECLIPSE_DOC_ID         = org.doxygen.Project

# The DISABLE_INDEX tag can be used to turn on/off the condensed index at
# top of each HTML page. The value NO (the default) enables the index and
# the value YES disables it.

DISABLE_INDEX          = NO

# This tag can be used to set the number of enum values (range [1..20])
# that doxygen will group on one line in the generated HTML documentation.

ENUM_VALUES_PER_LINE   = 4

# The GENERATE_TREEVIEW tag is used to specify whether a tree-like index
# structure should be generated to display hierarchical information.
# If the tag value is set to YES, a side panel will be generated
# containing a tree-like index structure (just like the one that
# is generated for HTML Help). For this to work a browser that supports
# JavaScript, DHTML, CSS and frames is required (i.e. any modern browser).
# Windows users are probably better off using the HTML help feature.

GENERATE_TREEVIEW      = NO

# By enabling USE_INLINE_TREES, doxygen will generate the Groups, Directories,
# and Class Hierarchy pages using a tree view instead of an ordered list.

USE_INLINE_TREES       = NO

# If the treeview is enabled (see GENERATE_TREEVIEW) then this tag can be
# used to set the initial width (in pixels) of the frame in which the tree
# is shown.

TREEVIEW_WIDTH         = 250

# Use this tag to change the font size of Latex formulas included
# as images in the HTML documentation. The default is 10. Note that
# when you change the font size after a successful doxygen run you need
# to manually remove any form_*.png images from the HTML output directory
# to force them to be regenerated.

FORMULA_FONTSIZE       = 10

# When the SEARCHENGINE tag is enabled doxygen will generate a search box for the HTML output. The underlying search engine uses javascript
# and DHTML and should work on any modern browser. Note that when using HTML help (GENERATE_HTMLHELP), Qt help (GENERATE_QHP), or docsets (GENERATE_DOCSET) there is already a search function so this one should
# typically be disabled. For large projects the javascript based search engine
# can be slow, then enabling SERVER_BASED_SEARCH may provide a better solution.

SEARCHENGINE           = NO

# When the SERVER_BASED_SEARCH tag is enabled the search engine will be implemented using a PHP enabled web server instead of at the web client using Javascript. Doxygen will generate the search PHP script and index
# file to put on the web server. The advantage of the server based approach is that it scales better to large projects and allows full text search. The disadvances is that it is more difficult to setup
# and does not have live searching capabilities.

SERVER_BASED_SEARCH    = NO

#---------------------------------------------------------------------------
# configuration options related to the LaTeX output
#---------------------------------------------------------------------------

# If the GENERATE_LATEX tag is set to YES (the default) Doxygen will
# generate Latex output.

GENERATE_LATEX         = YES

# The LATEX_OUTPUT tag is used to specify where the LaTeX docs will be put.
# If a relative path is entered the value of OUTPUT_DIRECTORY will be
# put in front of it. If left blank `latex' will be used as the default path.

LATEX_OUTPUT           = latex

# The LATEX_CMD_NAME tag can be used to specify the LaTeX command name to be
# invoked. If left blank `latex' will be used as the default command name.
# Note that when enabling USE_PDFLATEX this option is only used for
# generating bitmaps for formulas in the HTML output, but not in the
# Makefile that is written to the output directory.

LATEX_CMD_NAME         = latex

# The MAKEINDEX_CMD_NAME tag can be used to specify the command name to
# generate index for LaTeX. If left blank `makeindex' will be used as the
# default command name.

MAKEINDEX_CMD_NAME     = makeindex

# If the COMPACT_LATEX tag is set to YES Doxygen generates more compact
# LaTeX documents. This may be useful for small projects and may help to
# save some trees in general.

COMPACT_LATEX          = NO

# The PAPER_TYPE tag can be used to set the paper type that is used
# by the printer. Possible values are: a4, a4wide, letter, legal and
# executive. If left blank a4wide will be used.

PAPER_TYPE             = a4wide

# The EXTRA_PACKAGES tag can be to specify one or more names of LaTeX
# packages that should be included in the LaTeX output.

EXTRA_PACKAGES         =

# The LATEX_HEADER tag can be used to specify a personal LaTeX header for
# the generated latex document. The header should contain everything until
# the first chapter. If it is left blank doxygen will generate a
# standard header. Notice: only use this tag if you know what you are doing!

LATEX_HEADER           =

# If the PDF_HYPERLINKS tag is set to YES, the LaTeX that is generated
# is prepared for conversion to pdf (using ps2pdf). The pdf file will
# contain links (just like the HTML output) instead of page references
# This makes the output suitable for online browsing using a pdf viewer.

PDF_HYPERLINKS         = NO

# If the USE_PDFLATEX tag is set to YES, pdflatex will be used instead of
# plain latex in the generated Makefile. Set this option to YES to get a
# higher quality PDF documentation.

USE_PDFLATEX           = NO

# If the LATEX_BATCHMODE tag is set to YES, doxygen will add the \\batchmode.
# command to the generated LaTeX files. This will instruct LaTeX to keep
# running if errors occur, instead of asking the user for help.
# This option is also used when generating formulas in HTML.

LATEX_BATCHMODE        = NO

# If LATEX_HIDE_INDICES is set to YES then doxygen will not
# include the index chapters (such as File Index, Compound Index, etc.)
# in the output.

LATEX_HIDE_INDICES     = NO

# If LATEX_SOURCE_CODE is set to YES then doxygen will include source code with syntax highlighting in the LaTeX output. Note that which sources are shown also depends on other settings such as SOURCE_BROWSER.

LATEX_SOURCE_CODE      = NO

#---------------------------------------------------------------------------
# configuration options related to the RTF output
#---------------------------------------------------------------------------

# If the GENERATE_RTF tag is set to YES Doxygen will generate RTF output
# The RTF output is optimized for Word 97 and may not look very pretty with
# other RTF readers or editors.

GENERATE_RTF           = NO

# The RTF_OUTPUT tag is used to specify where the RTF docs will be put.
# If a relative path is entered the value of OUTPUT_DIRECTORY will be
# put in front of it. If left blank `rtf' will be used as the default path.

RTF_OUTPUT             = rtf

# If the COMPACT_RTF tag is set to YES Doxygen generates more compact
# RTF documents. This may be useful for small projects and may help to
# save some trees in general.

COMPACT_RTF            = NO

# If the RTF_HYPERLINKS tag is set to YES, the RTF that is generated
# will contain hyperlink fields. The RTF file will
# contain links (just like the HTML output) instead of page references.
# This makes the output suitable for online browsing using WORD or other
# programs which support those fields.
# Note: wordpad (write) and others do not support links.

RTF_HYPERLINKS         = NO

# Load stylesheet definitions from file. Syntax is similar to doxygen's
# config file, i.e. a series of assignments. You only have to provide
# replacements, missing definitions are set to their default value.

RTF_STYLESHEET_FILE    =

# Set optional variables used in the generation of an rtf document.
# Syntax is similar to doxygen's config file.

RTF_EXTENSIONS_FILE    =

#---------------------------------------------------------------------------
# configuration options related to the man page output
#---------------------------------------------------------------------------

# If the GENERATE_MAN tag is set to YES (the default) Doxygen will
# generate man pages

GENERATE_MAN           = YES

# The MAN_OUTPUT tag is used to specify where the man pages will be put.
# If a relative path is entered the value of OUTPUT_DIRECTORY will be
# put in front of it. If left blank `man' will be used as the default path.

MAN_OUTPUT             = man

# The MAN_EXTENSION tag determines the extension that is added to
# the generated man pages (default is the subroutine's section .3)

MAN_EXTENSION          = .3

# If the MAN_LINKS tag is set to YES and Doxygen generates man output,
# then it will generate one additional man file for each entity
# documented in the real man page(s). These additional files
# only source the real man page, but without them the man command
# would be unable to find the correct page. The default is NO.

MAN_LINKS              = NO

#---------------------------------------------------------------------------
# configuration options related to the XML output
#---------------------------------------------------------------------------

# If the GENERATE_XML tag is set to YES Doxygen will
# generate an XML file that captures the structure of
# the code including all documentation.

GENERATE_XML           = NO

# The XML_OUTPUT tag is used to specify where the XML pages will be put.
# If a relative path is entered the value of OUTPUT_DIRECTORY will be
# put in front of it. If left blank `xml' will be used as the default path.

XML_OUTPUT             = xml

# The XML_SCHEMA tag can be used to specify an XML schema,
# which can be used by a validating XML parser to check the
# syntax of the XML files.

XML_SCHEMA             =

# The XML_DTD tag can be used to specify an XML DTD,
# which can be used by a validating XML parser to check the
# syntax of the XML files.

XML_DTD                =

# If the XML_PROGRAMLISTING tag is set to YES Doxygen will
# dump the program listings (including syntax highlighting
# and cross-referencing information) to the XML output. Note that
# enabling this will significantly increase the size of the XML output.

XML_PROGRAMLISTING     = YES

#---------------------------------------------------------------------------
# configuration options for the AutoGen Definitions output
#---------------------------------------------------------------------------

# If the GENERATE_AUTOGEN_DEF tag is set to YES Doxygen will
# generate an AutoGen Definitions (see autogen.sf.net) file
# that captures the structure of the code including all
# documentation. Note that this feature is still experimental
# and incomplete at the moment.

GENERATE_AUTOGEN_DEF   = NO

#---------------------------------------------------------------------------
# configuration options related to the Perl module output
#---------------------------------------------------------------------------

# If the GENERATE_PERLMOD tag is set to YES Doxygen will
# generate a Perl module file that captures the structure of
# the code including all documentation. Note that this
# feature is still experimental and incomplete at the
# moment.

GENERATE_PERLMOD       = NO

# If the PERLMOD_LATEX tag is set to YES Doxygen will generate
# the necessary Makefile rules, Perl scripts and LaTeX code to be able
# to generate PDF and DVI output from the Perl module output.

PERLMOD_LATEX          = NO

# If the PERLMOD_PRETTY tag is set to YES the Perl module output will be
# nicely formatted so it can be parsed by a human reader.
# This is useful
# if you want to understand what is going on.
# On the other hand, if this
# tag is set to NO the size of the Perl module output will be much smaller
# and Perl will parse it just the same.

PERLMOD_PRETTY         = YES

# The names of the make variables in the generated doxyrules.make file
# are prefixed with the string contained in PERLMOD_MAKEVAR_PREFIX.
# This is useful so different doxyrules.make files included by the same
# Makefile don't overwrite each other's variables.

PERLMOD_MAKEVAR_PREFIX =

#---------------------------------------------------------------------------
# Configuration options related to the preprocessor
#---------------------------------------------------------------------------

# If the ENABLE_PREPROCESSING tag is set to YES (the default) Doxygen will
# evaluate all C-preprocessor directives found in the sources and include
# files.

ENABLE_PREPROCESSING   = YES

# If the MACRO_EXPANSION tag is set to YES Doxygen will expand all macro
# names in the source code. If set to NO (the default) only conditional
# compilation will be performed. Macro expansion can be done in a controlled
# way by setting EXPAND_ONLY_PREDEF to YES.

MACRO_EXPANSION        = NO

# If the EXPAND_ONLY_PREDEF and MACRO_EXPANSION tags are both set to YES
# then the macro expansion is limited to the macros specified with the
# PREDEFINED and EXPAND_AS_DEFINED tags.

EXPAND_ONLY_PREDEF     = NO

# If the SEARCH_INCLUDES tag is set to YES (the default) the includes files
# in the INCLUDE_PATH (see below) will be search if a #include is found.

SEARCH_INCLUDES        = YES

# The INCLUDE_PATH tag can be used to specify one or more directories that
# contain include files that are not input files but should be processed by
# the preprocessor.

INCLUDE_PATH           =

# You can use the INCLUDE_FILE_PATTERNS tag to specify one or more wildcard
# patterns (like *.h and *.hpp) to filter out the header-files in the
# directories. If left blank, the patterns specified with FILE_PATTERNS will
# be used.

INCLUDE_FILE_PATTERNS  =

# The PREDEFINED tag can be used to specify one or more macro names that
# are defined before the preprocessor is started (similar to the -D option of
# gcc). The argument of the tag is a list of macros of the form: name
# or name=definition (no spaces). If the definition and the = are
# omitted =1 is assumed. To prevent a macro definition from being
# undefined via #undef or recursively expanded use the := operator
# instead of the = operator.

PREDEFINED             =

# If the MACRO_EXPANSION and EXPAND_ONLY_PREDEF tags are set to YES then
# this tag can be used to specify a list of macro names that should be expanded.
# The macro definition that is found in the sources will be used.
# Use the PREDEFINED tag if you want to use a different macro definition.

EXPAND_AS_DEFINED      =

# If the SKIP_FUNCTION_MACROS tag is set to YES (the default) then
# doxygen's preprocessor will remove all function-like macros that are alone
# on a line, have an all uppercase name, and do not end with a semicolon. Such
# function macros are typically used for boiler-plate code, and will confuse
# the parser if not removed.

SKIP_FUNCTION_MACROS   = YES

#---------------------------------------------------------------------------
# Configuration::additions related to external references
#---------------------------------------------------------------------------

# The TAGFILES option can be used to specify one or more tagfiles.
# Optionally an initial location of the external documentation
# can be added for each tagfile. The format of a tag file without
# this location is as follows:
#
# TAGFILES = file1 file2 ...
# Adding location for the tag files is done as follows:
#
# TAGFILES = file1=loc1 "file2 = loc2" ...
# where "loc1" and "loc2" can be relative or absolute paths or
# URLs. If a location is present for each tag, the installdox tool
# does not have to be run to correct the links.
# Note that each tag file must have a unique name
# (where the name does NOT include the path)
# If a tag file is not located in the directory in which doxygen
# is run, you must also specify the path to the tagfile here.

TAGFILES               =

# When a file name is specified after GENERATE_TAGFILE, doxygen will create
# a tag file that is based on the input files it reads.

GENERATE_TAGFILE       =

# If the ALLEXTERNALS tag is set to YES all external classes will be listed
# in the class index. If set to NO only the inherited external classes
# will be listed.

ALLEXTERNALS           = NO

# If the EXTERNAL_GROUPS tag is set to YES all external groups will be listed
# in the modules index. If set to NO, only the current project's groups will
# be listed.

EXTERNAL_GROUPS        = YES

# The PERL_PATH should be the absolute path and name of the perl script
# interpreter (i.e. the result of `which perl').

PERL_PATH              = /usr/bin/perl

#---------------------------------------------------------------------------
# Configuration options related to the dot tool
#---------------------------------------------------------------------------

# If the CLASS_DIAGRAMS tag is set to YES (the default) Doxygen will
# generate a inheritance diagram (in HTML, RTF and LaTeX) for classes with base
# or super classes. Setting the tag to NO turns the diagrams off. Note that
# this option is superseded by the HAVE_DOT option below. This is only a
# fallback. It is recommended to install and use dot, since it yields more
# powerful graphs.

CLASS_DIAGRAMS         = YES

# You can define message sequence charts within doxygen comments using the \msc
# command. Doxygen will then run the mscgen tool (see
# http://www.mcternan.me.uk/mscgen/) to produce the chart and insert it in the
# documentation. The MSCGEN_PATH tag allows you to specify the directory where
# the mscgen tool resides. If left empty the tool is assumed to be found in the
# default search path.

MSCGEN_PATH            =

# If set to YES, the inheritance and collaboration graphs will hide
# inheritance and usage relations if the target is undocumented
# or is not a class.

HIDE_UNDOC_RELATIONS   = YES

# If you set the HAVE_DOT tag to YES then doxygen will assume the dot tool is
# available from the path. This tool is part of Graphviz, a graph visualization
# toolkit from AT&T and Lucent Bell Labs. The other options in this section
# have no effect if this option is set to NO (the default)

HAVE_DOT               = NO

# By default doxygen will write a font called FreeSans.ttf to the output
# directory and reference it in all dot files that doxygen generates. This
# font does not include all possible unicode characters however, so when you need
# these (or just want a differently looking font) you can specify the font name
# using DOT_FONTNAME. You need need to make sure dot is able to find the font,
# which can be done by putting it in a standard location or by setting the
# DOTFONTPATH environment variable or by setting DOT_FONTPATH to the directory
# containing the font.

DOT_FONTNAME           = FreeSans

# The DOT_FONTSIZE tag can be used to set the size of the font of dot graphs.
# The default size is 10pt.

DOT_FONTSIZE           = 10

# By default doxygen will tell dot to use the output directory to look for the
# FreeSans.ttf font (which doxygen will put there itself). If you specify a
# different font using DOT_FONTNAME you can set the path where dot
# can find it using this tag.

DOT_FONTPATH           =

# If the CLASS_GRAPH and HAVE_DOT tags are set to YES then doxygen
# will generate a graph for each documented class showing the direct and
# indirect inheritance relations. Setting this tag to YES will force the
# the CLASS_DIAGRAMS tag to NO.

CLASS_GRAPH            = YES

# If the COLLABORATION_GRAPH and HAVE_DOT tags are set to YES then doxygen
# will generate a graph for each documented class showing the direct and
# indirect implementation dependencies (inheritance, containment, and
# class references variables) of the class with other documented classes.

COLLABORATION_GRAPH    = YES

# If the GROUP_GRAPHS and HAVE_DOT tags are set to YES then doxygen
# will generate a graph for groups, showing the direct groups dependencies

GROUP_GRAPHS           = YES

# If the UML_LOOK tag is set to YES doxygen will generate inheritance and
# collaboration diagrams in a style similar to the OMG's Unified Modeling
# Language.

UML_LOOK               = NO

# If set to YES, the inheritance and collaboration graphs will show the
# relations between templates and their instances.

TEMPLATE_RELATIONS     = YES

# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDE_GRAPH, and HAVE_DOT
# tags are set to YES then doxygen will generate a graph for each documented
# file showing the direct and indirect include dependencies of the file with
# other documented files.

INCLUDE_GRAPH          = YES

# If the ENABLE_PREPROCESSING, SEARCH_INCLUDES, INCLUDED_BY_GRAPH, and
# HAVE_DOT tags are set to YES then doxygen will generate a graph for each
# documented header file showing the documented files that directly or
# indirectly include this file.

INCLUDED_BY_GRAPH      = YES

# If the CALL_GRAPH and HAVE_DOT options are set to YES then
# doxygen will generate a call dependency graph for every global function
# or class method. Note that enabling this option will significantly increase
# the time of a run. So in most cases it will be better to enable call graphs
# for selected functions only using the \callgraph command.

CALL_GRAPH             = NO

# If the CALLER_GRAPH and HAVE_DOT tags are set to YES then
# doxygen will generate a caller dependency graph for every global function
# or class method. Note that enabling this option will significantly increase
# the time of a run. So in most cases it will be better to enable caller
# graphs for selected functions only using the \callergraph command.

CALLER_GRAPH           = NO

# If the GRAPHICAL_HIERARCHY and HAVE_DOT tags are set to YES then doxygen
# will graphical hierarchy of all classes instead of a textual one.

GRAPHICAL_HIERARCHY    = YES

# If the DIRECTORY_GRAPH, SHOW_DIRECTORIES and HAVE_DOT tags are set to YES
# then doxygen will show the dependencies a directory has on other directories
# in a graphical way. The dependency relations are determined by the #include
# relations between the files in the directories.

DIRECTORY_GRAPH        = YES

# The DOT_IMAGE_FORMAT tag can be used to set the image format of the images
# generated by dot. Possible values are png, jpg, or gif
# If left blank png will be used.

DOT_IMAGE_FORMAT       = png

# The tag DOT_PATH can be used to specify the path where the dot tool can be
# found. If left blank, it is assumed the dot tool can be found in the path.

DOT_PATH               =

# The DOTFILE_DIRS tag can be used to specify one or more directories that
# contain dot files that are included in the documentation (see the
# \dotfile command).

DOTFILE_DIRS           =

# The DOT_GRAPH_MAX_NODES tag can be used to set the maximum number of
# nodes that will be shown in the graph. If the number of nodes in a graph
# becomes larger than this value, doxygen will truncate the graph, which is
# visualized by representing a node as a red box. Note that doxygen if the
# number of direct children of the root node in a graph is already larger than
# DOT_GRAPH_MAX_NODES then the graph will not be shown at all. Also note
# that the size of a graph can be further restricted by MAX_DOT_GRAPH_DEPTH.

DOT_GRAPH_MAX_NODES    = 50

# The MAX_DOT_GRAPH_DEPTH tag can be used to set the maximum depth of the
# graphs generated by dot. A depth value of 3 means that only nodes reachable
# from the root by following a path via at most 3 edges will be shown. Nodes
# that lay further from the root node will be omitted. Note that setting this
# option to 1 or 2 may greatly reduce the computation time needed for large
# code bases. Also note that the size of a graph can be further restricted by
# DOT_GRAPH_MAX_NODES. Using a depth of 0 means no depth restriction.

MAX_DOT_GRAPH_DEPTH    = 0

# Set the DOT_TRANSPARENT tag to YES to generate images with a transparent
# background. This is disabled by default, because dot on Windows does not
# seem to support this out of the box. Warning: Depending on the platform used,
# enabling this option may lead to badly anti-aliased labels on the edges of
# a graph (i.e. they become hard to read).

DOT_TRANSPARENT        = NO

# Set the DOT_MULTI_TARGETS tag to YES allow dot to generate multiple output
# files in one run (i.e. multiple -o and -T options on the command line). This
# makes dot run faster, but since only newer versions of dot (>1.8.10)
# support this, this feature is disabled by default.

DOT_MULTI_TARGETS      = YES

# If the GENERATE_LEGEND tag is set to YES (the default) Doxygen will
# generate a legend page explaining the meaning of the various boxes and
# arrows in the dot generated graphs.

GENERATE_LEGEND        = YES

# If the DOT_CLEANUP tag is set to YES (the default) Doxygen will
# remove the intermediate dot files that are used to generate
# the various graphs.

DOT_CLEANUP            = YES
0707010000000E000081A40000000200000002000000015D8693EF000009B2000000000000000000000000000000000000002800000000wfmath-1569100783.d0f8a54/doc/index.txtThis is the Worldforge math library. It's licensed under the GPL
(see file COPYING), and basic compilation instructions are in
the file INSTALL. The current maintainer is Ron Steinke
<rsteinke@w-link.net>.

The currently implemented classes can be divided into two sorts. The
first kind are basic mathematical objects, whose members are all fundamental
types. The second kind are shapes, which implement the shape class
interface described in doc/shape.h. There are four classes of the first kind:

Vector<>	A basic mathematical vector
RotMatrix<>	An orthogonal matrix of determinant 1, useful for
		describing rotations.
Point<>		A point in space. This basic class also implements
		the shape interface in doc/shape.h.
Quaternion	A quaternion

The shape classes are:

AxisBox<>	A box oriented parallel to the coordinate axes
Ball<>		Ball<2> is a circle, Ball<3> is a sphere, etc.
Segment<>	A line segment, defined by its endpoints
RotBox<>	Like AxisBox<>, but it can be rotated to arbitrary
		angles
Polygon<>	A 2 dimensional polygon contained in a (possibly)
		larger dimensional space

Anyone interested in contributing to this project should do three things:

1) Send me an email. This is mostly to let me know someone else is working
   with the CVS repository, so I can be careful about merging commits.

2) Look at the file doc/CLASS_LAYOUT, which specifies which member functions
   all classes should have, and what order they should appear in.
   This only applies to significant classes, not things like
   ColinearVectors in error.h, which is only there to be thrown as
   as exception.

3) Update the ChangeLog _every_ time you commit to CVS. This makes
   it possible for other people to have some idea what you're working on.

The documentation is at this point confined to the doc/CLASS_LAYOUT file
and comments in the code. There's also a sample shape class definition
in the file shape.h in the doc directory. This has comments about
what member functions all shape classes are supposed to have, and what they
do.
0707010000000F000081A40000000200000002000000015D8693EF00001BCE000000000000000000000000000000000000002600000000wfmath-1569100783.d0f8a54/doc/shape.h// shape.h (A general base class for shapes)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

// This class borrows heavily from the base shape class in libCoal,
// plus certain intersection ideas from stage/shepherd/sylvanus

#ifndef WFMATH_SHAPE_H
#define WFMATH_SHAPE_H

#include <wfmath/vector.h>
#include <wfmath/point.h>
#include <wfmath/const.h>
#include <wfmath/rotmatrix.h>
#include <wfmath/axisbox.h>
#include <wfmath/ball.h>
#include <wfmath/intersect_decls.h>

namespace WFMath {

/// A fake class which documents the generic parts of the WFMath interface
/**
 * This fake class documents two parts of the WFMath generic
 * class interface. With a few exceptions (e.g. classes derived
 * from std::exception), every class in WFMath implements
 * the part of the interface labeled as 'generic'. The 'shape'
 * interface is implemented by several classes, which identify
 * themselves in their own documentation. Every class which
 * implements the 'shape' interface also implements the 'generic'
 * interface. Classes will not generally document their
 * generic and shape interface functions.
 **/
template<const int dim>
class Shape
{
 public:
  // The first things in the Shape class are the functions required
  // by CLASS_LAYOUT for all classes

///
  Shape() {}
  ///
  Shape(const Shape<dim>& s) {}
  ///
  ~Shape() {}

/// generic: Print an instance to a stream
  friend std::ostream& operator<< <dim>(std::ostream& os, const Shape& s);
  /// generic: Parse an instance from a stream
  friend std::istream& operator>> <dim>(std::istream& is, Shape& s);

///
  Shape& operator=(const Shape& a);

/// generic: check if two classes are equal, up to a given tolerance
  bool isEqualTo(const Shape& s, CoordType tolerance = numeric_constants<CoordType>::epsilon()) const;
  /// generic: check if two classes are equal, up to tolerance WFMATH_EPSILON
  bool operator==(const Shape& s) const	{return isEqualTo(s);}
  /// generic: check if two classes are not equal, up to tolerance WFMATH_EPSILON
  bool operator!=(const Shape& s) const	{return !isEqualTo(s);}

/// generic: returns true if the class instance has been initialized
  bool isValid() const {return m_valid;}

// Now we begin with the functions in the shape interface

// Descriptive characteristics

/// shape: return the number of corners in the shape.
  /**
   * For many shape classes, this is a fixed constant
   **/
  size_t numCorners() const; // The number of corners, returns zero for Ball<>
  /// shape: return the position of the i'th corner, where 0 <= i < numCorners()
  Point<dim> getCorner(size_t i) const; // Must have i >= 0 && i < numCorners()
  /// shape: return the position of the center of the shape
  Point<dim> getCenter() const; // Returns the barycenter of the object

// Movement functions

/// shape: move the shape by an amount given by the Vector v
  Shape& shift(const Vector<dim>& v); // Move the shape a certain distance
  /// shape: move the shape, moving the given corner to the Point p
  /**
   * The corner in question is getCorner(corner).
   **/
  Shape& moveCornerTo(const Point<dim>& p, size_t corner)
	{return shift(p - getCorner(corner));}
  /// shape: move the shape, moving the center to the Point p
  /**
   * The center is defined by getCenter()
   **/
  Shape& moveCenterTo(const Point<dim>& p)
	{return shift(p - getCenter());}

/// shape: rotate the shape while holding the given corner fixed
  /**
   * The corner in question is getCorner(corner).
   **/
  Shape& rotateCorner(const RotMatrix<dim>& m, size_t corner)
	{return rotatePoint(m, getCorner(corner));}
  /// shape: rotate the shape while holding the center fixed
  /**
   * The center is defined by getCenter()
   **/
  Shape& rotateCenter(const RotMatrix<dim>& m)
	{return rotatePoint(m, getCenter());}
  /// shape: rotate the shape while holding the Point p fixed.
  /**
   * Note that p can be any Point, it does not have to lie within
   * the shape.
   **/
  Shape& rotatePoint(const RotMatrix<dim>& m, const Point<dim>& p);

// Intersection functions

/// shape: return the minimal axis-aligned bounding box
  AxisBox<dim> boundingBox() const;
  /// shape: return the minimal bounding sphere
  Ball<dim> boundingSphere() const;
  /// shape: return an approximate bounding sphere, guaranteed
  /// to contain the minimal bounding sphere
  /**
   * boundingSphereSloppy() uses
   * SloppyDistance() instead of Distance() to calculate it's
   * radius, except in cases like Point<> and Ball<> where it
   * would be silly. Thus, the result of boundingSphereSloppy()
   * is guaranteed to contain the result of boundingSphere().
   **/
  Ball<dim> boundingSphereSloppy() const;

/// shape: Returns true if the two shapes intersect.
  /**
   * If the 'proper' argument is true, shapes which only touch on their
   * boundary do not count as intersecting. If it is false, they do.
   * This function is symmetric in its first two arguments
   * (Intersect(a, b, proper) == Intersect(b, a, proper)).
   * The two shapes do
   * not have to be the same class, but must have the same dimension.
   **/
  friend bool Intersect<dim>(Shape<dim>& s1, Shape<dim>& s2, bool proper);
  /// shape: Returns true if the first shape contains the second.
  /**
   * If the 'proper' argument is true, the inner shape is not contained
   * if it touches the boundary of the outer shape. Otherwise, it
   * does. Therefore, any shape contains itself
   * (Contains(foo, foo, false) == true), but no shape contains itself
   * properly (Contains(foo, foo, true) == false). Because of this,
   * an empty shape (e.g. a Polygon with zero corners)
   * is properly contained by any other shape. A Point, or any single
   * point shape (e.g. a Segment where the endpoints are equal)
   * properly contains an empty shape, and contains (but not properly)
   * any other single point shape which occupies the same point.
   * The two shapes do
   * not have to be the same class, but must have the same dimension.
   **/
  friend bool Contains<dim>(Shape<dim>& s1, Shape<dim>& s2, bool proper);

private:
  bool m_valid;
};

//#include<wfmath/shape_funcs.h>

} // namespace WFMath

#endif  // WFMATH_SHAPE_H
07070100000010000081A40000000200000002000000015D8693EF0000052E000000000000000000000000000000000000003100000000wfmath-1569100783.d0f8a54/mingw32-wfmath.spec.in%define __strip %{_mingw32_strip}
%define __objdump %{_mingw32_objdump}
%define _use_internal_dependency_generator 0
%define __find_requires %{_mingw32_findrequires}
%define __find_provides %{_mingw32_findprovides}

%define name mingw32-wfmath
%define version @VERSION@
%define release 1
%define libsuffix @WFMATH_LIB_SUFFIX@

Summary: A math library.
Name: %{name}
Version: %{version}
Release: %{release}
License: GPL
Group: System Environment/Libraries
URL: http://www.worldforge.org/dev/eng/libraries/wfmath
Packager: Al Riddoch <alriddoch@googlemail.com>
Vendor: WorldForge
Distribution: Mason
Source: wfmath-%{version}.tar.bz2
BuildRoot: %{_tmppath}/%{name}-%{version}-%{release}-root
BuildArch: noarch
BuildRequires:  mingw32-filesystem >= 49
BuildRequires:  mingw32-gcc
BuildRequires:  mingw32-binutils

%description
This is the WorldForge math library. The primary focus of wfmath is
geometric objects.

%prep
%setup -q -n wfmath-%{version}

%build
%{_mingw32_configure} --enable-static --disable-shared
make

%install
rm -rf $RPM_BUILD_ROOT
make DESTDIR=$RPM_BUILD_ROOT install
rm $RPM_BUILD_ROOT%{_mingw32_libdir}/lib*.la

%clean
rm -rf $RPM_BUILD_ROOT

%files
%defattr(-,root,root)
%{_mingw32_libdir}/lib*.a
%{_mingw32_libdir}/pkgconfig/*
%{_mingw32_includedir}/wfmath%{libsuffix}
%doc AUTHORS COPYING NEWS README
07070100000011000041ED0000000200000002000000025D8693EF00000000000000000000000000000000000000000000002200000000wfmath-1569100783.d0f8a54/support07070100000012000081A40000000200000002000000015D8693EF0000B7B0000000000000000000000000000000000000003000000000wfmath-1569100783.d0f8a54/support/ChangeLog-CVS2012-01-18  Al Riddoch  <alriddoch@googlemail.com>

* Release 0.3.12, interface version 6

2012-01-18  Al Riddoch  <alriddoch@googlemail.com>

* Fix a number of portability bugs. Make a bunch of performance
	  improvements, mostly be avoiding converting between double and float.
	  Switch to using standard C++ library for math functions, as the way
	  templates work makes getting the right float type way more efficient.
	  Fix some bad namespacing which broke on some compilers.

2011-02-12  Al Riddoch  <alriddoch@googlemail.com>

* Release 0.3.11, interface version 5

2011-02-12  Al Riddoch  <alriddoch@googlemail.com>

* Inline all Atlas related methods in atlasconv.h to avoid linking
	  issues. Explicitly instantiate all templates and avoid including
	  headers full of big functions in client apps. Make all public
	  templates default to 3 dimensions. Clean out assertions
	  which might cause runtime crashes, or lead to instability in
	  non-debug builds. Fix a number of bugs with intersection and
	  barycenter functions.

2009-12-29  Al Riddoch  <alriddoch@googlemail.com>

* Release 0.3.10

2009-12-29  Al Riddoch  <alriddoch@googlemail.com>

* wfmath/int_to_string.cpp: Reduce the scope of some const variables.

* wfmath/vector.cpp: Add some template specialisations.

2009-08-04  Al Riddoch  <alriddoch@googlemail.com>

* wfmath/axisbox.h: Add writable accessors to the axisbox
	  corner points.

2009-06-18  Al Riddoch  <alriddoch@googlemail.com>

* wfmath/point.h, wfmath/point_funcs.h,
	  wfmath/vector.h, wfmath/vector_funcs.h: Fix copy constructors
	  to take a reference, and don't inline the heavy loop.

2009-01-26  Al Riddoch  <alriddoch@googlemail.com>

* Release 0.3.9

* NEWS: Update date on release news item.

2009-01-12  Al Riddoch  <alriddoch@googlemail.com>

* wfmath/axisbox.cpp, wfmath/axisbox.h: Fix a missing include.

2009-01-12  Al Riddoch  <alriddoch@googlemail.com>

* wfmath/atlasconv.h: Move the inlined constructor from Atlas
	  data here to keep it out of the library compiled code.

* wfmath/axisbox.cpp, wfmath/axisbox.h: Don't include all the code
	  as inlined by default, and instead force instantiation of the
	  templates in the library.

* wfmath/const.h: Fill out the set for forward declarations.

* wfmath/intersect_decls.h, wfmath/axisbox.h:
	  Remove the now redundant forward declarations.

* wfmath/point.cpp: Include axisbox_funcs.h as it contains
	  Point functions which require AxisBox.

2009-01-11  Al Riddoch  <alriddoch@googlemail.com>

* wfmath/zero.h: Add a new line to the end of zero.h.

* configure.ac: Check for fabsf.

* wfmath/atlasconv.h: Move inlined constructors into this file
	  to ensure code that requires Atlas-C++ isn't linked by the main
	  library.

* wfmath/const.cpp: Add a special float implementation of Equal
	  to use more efficient underlying mechanism.

* wfmath/const.h: Add forward declarations for major classes.

* wfmath/point.cpp, wfmath/vector.cpp: Add specialisations of
	  some previously inlined code to reduce dependency mess.
	  Force instantation of templates so code is included in the
	  library for things that should not be inlined.

* wfmath/point.h, wfmath/vector.h: Remove forward declarations
	  and unnecessary includes. Strip out asserts as including cassert
	  interferes with application code. Remove some messy inlined
	  code and clean up the declaraions of 3D only methods. Don't
	  force inclusaion of the _funcs.h headers which contains most
	  of the implementation.

* wfmath/point_funcs.h, wfmath/vector_funcs.h: Clean up formatting
	  and scoping. Remove inline from a number of methods.

* wfmath/quaternion.cpp: Use CoordType, not float.

* wfmath/rotbox.h: Include quaternion.h as required.

* wfmath/rotmatrix.h: Remove asserts as they interfere with
	  application code.

* wfmath/rotmatrix_funcs.h: Add cassert include back here as
	  required.

2009-01-05 Erik Hjortsberg <erik@worldforge.org>

* wfmath/atlasconv.h: Provide proper templated parsing methods for all 
	current terrain mods and shapes.

* wfmath/zero.h: Add a helper class for holding zero values of points
	and vectors.

* wfmath/ball.h, wfmath/polygon.h, wfmath/rotbox.h: Add toAtlas and 
	fromAtlas methods, implemented in atlasconv.h. Also add contstructor
	which takes Atlas data.

* wfmath/atlas_0_6_test.cpp: Added tests for parsing shapes from Atlas.

2008-11-15  Al Riddoch  <alriddoch@googlemail.com>

* Release 0.3.8

* NEWS: Update date on release news item.

* configure.ac: Increment version number.

2008-11-10  Al Riddoch  <alriddoch@googlemail.com>

* wfmath/intstring_test.cpp, wfmath/probability_test.cpp:
	  Force debug mode before including <cassert>.

2008-11-10  Al Riddoch  <alriddoch@googlemail.com>

* wfmath/quaternion_test.cpp, wfmath/rotmatrix_test.cpp,
	  wfmath/shape_test.cpp, wfmath/vector_test.cpp: Force debug mode
	  before include <cassert>.

2008-11-09  Al Riddoch  <alriddoch@googlemail.com>

* wfmath/polygon_intersect.h: Convery the warning about unfinished
	  functionality to a big FIXME section.

2008-11-09  Al Riddoch  <alriddoch@googlemail.com>

* wfmath/intersect.h: Add another set of parentheses to make things
	  clearer.

2008-11-07  Al Riddoch  <alriddoch@googlemail.com>

* wfmath/intersect.h: Move parentheses to a more appropriate place.

2008-11-04  Anders Petersson  <demitar@worldforge.org>

* configure.ac: Added AC_PROG_CXX to prevent a circular dependency in
	  AC_CHECK_HEADERS(sstream strstream, ...)

2007-11-25  Al Riddoch  <alriddoch@googlemail.com>

* wfmath.spec.in: Create new sub package for generated documentation.

2007-11-25  Al Riddoch  <alriddoch@googlemail.com>

* configure.ac: Add support for cross compiling, and fix up the
	  comments.

2007-11-25  Al Riddoch  <alriddoch@googlemail.com>

* Release 0.3.7

2007-11-25  Al Riddoch  <alriddoch@googlemail.com>

* NEWS: Update date on release news item.

* acinclude.m4: Include the latest version of the pkgconfig macro.

* configure.ac: Increment version number, and use latest pkgconfig
	  check syntax.

* AUTHORS, wfmath.spec.in: Update contact email addresses,

* atlas/Makefile.am: Remove Atlas-C++ 0.4 test programs.

2007-11-24  Al Riddoch  <alriddoch@zepler.org>

* wfmath.spec.in: Split static libraries out into their own
	  package.

2007-11-20  Al Riddoch  <alriddoch@zepler.org>

* wfmath/atlasconv.h: Initialise age when setting up Quaternion from
	  Atlas data.

2007-07-20  Al Riddoch  <alriddoch@zepler.org>

* NEWS: Update date on release news item.

* Release 0.3.6

2007-07-18  Al Riddoch  <alriddoch@zepler.org>

* configure.ac: Increment version number to 0.3.6

2007-07-18  Al Riddoch  <alriddoch@zepler.org>

* wfmath/axisbox.h, wfmath/axisbox_funcs.h, wfmath/ball.h,
	  wfmath/ball_funcs.h, wfmath/point.h, wfmath/point_funcs.h:
	  Tighten up template specicialisations to deal with stricter
	  rules in gcc 4.2.

2007-02-13  Al Riddoch  <alriddoch@zepler.org>

* wfmath/polygon_intersect.cpp, wfmath/polygon_intersect.h,
	  wfmath/rotmatrix_funcs.h: When an assert is used to detect
	  a bad condition in a function, ensure that in a production build
	  where asserts are disabled, the function still returns a sane
	  value, to avoid compiler warnings.

2006-08-18  Al Riddoch  <alriddoch@zepler.org>

* NEWS: Update date on release news item.

* Release 0.3.5

2006-08-18  Al Riddoch  <alriddoch@zepler.org>

* autogen.sh: Get rid of non-functional --enable-compile-warnings
	  flag, and enable debug by default when invoking configure from
	  autogen.

2006-08-17  Al Riddoch  <alriddoch@zepler.org>

* wfmath/Makefile.am: Remove useless AM_CXXFLAGS.

* configure.ac: Straighten out interface version numbers, remove
	  unused substitutions, and add debug compiler flag support. Increment
	  version for release.

* NEWS: Add provisional news item for release.

2006-08-17  Al Riddoch  <alriddoch@zepler.org>

* wfmath/point.h, wfmath/point_funcs.h, wfmath/quaternion.cpp,
	  wfmath/quaternion.h, wfmath/vector.h, wfmath/vector_funcs.h:
	  Re-order and reimplement some of the operators, so they
	  are more efficient and in some cases cleaner.

* wfmath/quaternion_test.cpp: Output values for the results of
	  test calculations to make them easier to debug when they fail.

2006-08-16  Al Riddoch  <alriddoch@zepler.org>

* wfmath/intstring_test.cpp: Switch to using atol instead of
	  atoi to ensure longs work on platforms where long is bigger
	  than int.

2006-08-04  Al Riddoch  <alriddoch@zepler.org>

* wfmath/quaternion.cpp: If a quaternion is initialised with values
	  which would make it normalise with division by zero, or be
	  initialised with NaN, mark as invalid and return.

* autogen.sh: Remove references to long removed mainainer mode.

2005-12-02  James Turner  <james@worldforge.org>

* Add X-Code 2.0 project file (ProjectBuilder project will be deleted
	  shortly).

2005-09-22  Al Riddoch  <alriddoch@zepler.org>

* wfmath/atlasconv.h: If a quaternion is initialised with values
	  which would make it normalise with division by zero, mark
	  as invalid and return.

2005-06-11  Al Riddoch  <alriddoch@zepler.org>

* wfmath.spec.in: Minor changes to spec.

* NEWS: Update NEWS.

* Release 0.3.4

2005-04-30  Al Riddoch  <alriddoch@zepler.org>

* wfmath/Makefile.am: Don't force compilation with -O2. There are
	  good reasons not to.

* configure.ac: Update autoconf usage.

* acinclude.m4: Remove unused AM_PATH_ATLAS, and add required
	  pkg-config macro.

2005-04-12  Al Riddoch  <alriddoch@zepler.org>

* configure.ac: Fix a bug in initialising the version to a non-literal.

* doc/Doxyfile.in: Use VERSION instead of WFMATH_VERSION as intended by
	  autoconf.

2005-04-11  Al Riddoch  <alriddoch@zepler.org>

* configure.ac: Increment version to 0.3.4 for release, and clean
	  up a bit.

2004-12-31  Al Riddoch  <alriddoch@zepler.org>

* wfmath.spec.in: Update spec with License URL Package Vendor
	  and Distribution tags.

Sunday, October 10th, 2004   Ron Steinke <rsteinke@w-link.net>

* Changed CXXFLAGS to AM_CXXFLAGS in the atlas
	  Makefile.am to fix a configure warning.
	* Change a comma operator in an assert() to && to
	  fix a compile warning.

Saturday, October 9th, 2004   Ron Steinke <rsteinke@w-link.net>

* Added missing 'inline' keywords in int_to_string.h.

2004-07-19  Al Riddoch  <alriddoch@zepler.org>

* Minor update to the rpm spec. No need to re-spin the release.

Wednesday, July 19th, 2004   Ron Steinke <rsteinke@w-link.net>

* 0.3.3 release.

Wednesday, June 30th, 2004   Ron Steinke <rsteinke@w-link.net>

* Erik Hjortsberg's gcc 3.4 compile fixes, part 2.

Wednesday, June 30th, 2004   Ron Steinke <rsteinke@w-link.net>

* Erik Hjortsberg's gcc 3.4 compile fixes.

2004-06-06  Al Riddoch  <alriddoch@zepler.org>

* Fix devel dependencies in rpm spec.

2004-06-03  James Turner  <james@worldforge.org>

* XCode project updates

Saturday, March 6th, 2004 Al Riddoch <alriddoch@zepler.org>

* wfmath/atlasconv.h: Add typedefs so the tests still work
	  with the 0.4 series.

Wednesday, March 3rd, 2004 James Turner <james@worldforge.org>

* Made atlasconv.h use the new Atlas::Message public typdefs, instead
	  of the current Element typedefs, which are becoming private.
	* ProjectBuilder updates for X-Code 
	
Wednesday, February 18th, 2004   Ron Steinke <rsteinke@w-link.net>

* Fixed 'no newline at end of file' warning for timestamp_test.cpp.

Sunday, February 15th, 2004   Ron Steinke <rsteinke@w-link.net>

* Changed the Atlas forward declaration workaround to return
	  a reference to Atlas::Message::Element instead of a copy.

Thursday, February 5th, 2004   Ron Steinke <rsteinke@w-link.net>

* Got the fooCorner() fix right.
	* 0.3.2 release! for the last time!

Wednesday, February 4th, 2004   Ron Steinke <rsteinke@w-link.net>

* Added wfmath.spec to EXTRA_DIST to ease rpm building.
	* 0.3.2 release! (no, really! this time I mean it!)

Wednesday, February 4th, 2004   Ron Steinke <rsteinke@w-link.net>

* Added a missing word to some descriptive text in wfmath.spec.
	* 0.3.2 release!

Friday, January 30th, 2004   Ron Steinke <rsteinke@w-link.net>

* Changed the fooCorner() functions in Ball from {assert(false);}
	  to {assert(false); abort();}, per Al's comments, so they
	  fail properly if used when NDEBUG is defined.

Thursday, January 29th, 2004   Ron Steinke <rsteinke@w-link.net>

* Updated the AUTHORS file.

Thursday, January 29th, 2004   Ron Steinke <rsteinke@w-link.net>

* Bumped version to 0.3.2, in preparation for a release
	  tommorow.

Thursday, January 29th, James Turner <james@worldforge.org>

* Add a test for the timestamp/timediff code (not exhaustive
          by any means)

Thursday, January 29th, 2004   Ron Steinke <rsteinke@w-link.net>

* Fixed the TimeDiff constructor from milliseconds to
	  set the is_valid flag (thanks James!).

Tuesday, January 27th, 2004   Ron Steinke <rsteinke@w-link.net>

* Changed the Shuffle() function to use the new random
	  number API instead of the old one, and use
	  std::vector<>::size_type instead of unsigned for
	  greater portability. Added a basic test to make sure
	  it builds and runs.

Sunday, January 18th, 2004   Ron Steinke <rsteinke@w-link.net>

* Made the Quaternion costructor from a Vector<3> (for
	  a rotation around that axis) 'explicit'.

Sunday, January 18th, 2004   Ron Steinke <rsteinke@w-link.net>

* Added round-off age checks to the functions where
	  Quaternion and RotMatrix<3> rotate each other.
	* Added rotate() convienience wrappers to RotMatrix,
	  Quaternion and Vector for cases where rotation
	  is just multiplication.

Sunday, January 18th, 2004   Ron Steinke <rsteinke@w-link.net>

* wfmath/point.h, wfmath/axisbox.h, wfmath/axisbox_funcs.h,
	  wfmath/segment.h, wfmath/segment_funcs.h, wfmath/ball.h,
	  wfmath/rotbox.h, wfmath/rotbox_funcs.h, wfmath/polygon.h,
	  wfmath/polygon_funcs.h, wfmath/polygon.cpp: Added
	  Quaternion-based rotation functions and toParentCoords(),
	  toLocalCoords() to all shapes, in parallel to those
	  functions previously added to Point.
	* wfmath/rotmatrix*, wfmath/quaternion*: Added functions
	  to let RotMatrix<3> and Quaternion rotate each other.
	  RotMatrix<3>::rotate(Quaternion) was needed for
	  Quaternion-based rotation of RotBox<3>.

Sunday, January 18th, 2004   Ron Steinke <rsteinke@w-link.net>

* wfmath/MersenneTwister.h, wfmath/const.h, wfmath/miniball_funcs.h:
	  Replace ANSI C headers #include <foo.h> with #include <cfoo>.
	* wfmath/stream.h: Removed commented-out sstream #include.
	* wfmath/timestamp.*: Moved winsock.h #include into the .cpp file,
	  moved timeval class declaration for win32 inside the TimeStamp
	  class.

Sunday, January 11th, 2004   Ron Steinke <rsteinke@w-link.net>

* wfmath/timestamp.h: Pull winsock #include outside of
	  WFMath namespace.

Sunday, December 21st, 2003   Ron Steinke <rsteinke@w-link.net>

* wfmath/timestamp.h: Pull in winsock2.h instead of winsock.h
	  under win32.

Friday, December 19th, 2003   Al Riddoch <alriddoch@zepler.org>

* Remove Serial from rpm spec as it is not required, and messes up
	  deps.

Saturday, December 6th, 2003   Ron Steinke <rsteinke@w-link.net>

* wfmath/polygon_intersect.cpp: Got rid of the only
	  new/delete calls in the whole library, as the
	  object in question could just as well be declared
	  on the stack.

Saturday, December 6th, 2003   Ron Steinke <rsteinke@w-link.net>

* wfmath/timestamp.cpp: Added James' patch to make
	  valgrind happy.

Thursday, November 27th, 2003   Ron Steinke <rsteinke@w-link.net>

* Only one of the Point/Quaterion and Point/Matrix coordinate
	  transformation functions can or needs to have a default
	  rotation argument.

Thursday, November 27th, 2003   Ron Steinke <rsteinke@w-link.net>

* The inverse of a Quaternion is q.inverse(), not -q.

Thursday, November 27th, 2003   Ron Steinke <rsteinke@w-link.net>

* Added local/parent coordinate transformation functions
	  and quaternion based 3D rotations to Point, still need to
	  add these to the rest of the shape classes.

Sunday, October 26th, 2003   Ron Steinke <rsteinke@w-link.net>

* wfmath/quaternion.cpp, wfmath/atlasconv.h: Set validity
	  of vector component of Quaternion in three other places
	  we'd missed.
	* wfmath/rotmatrix*, wfmath/quaternion*: Added roundoff aging
	  code. As we do many floating point calculations, RotMatrix
	  and Quaternion will tend to drift from their respective
	  normalizations due to roundoff error. The new code adds
	  an m_age, which keeps track of how many computations ago
	  they were normalized, and automatically renomalizes them
	  after a given number of computations. Because we know that
	  they're still close to being normalized, the renormalization
	  code is linearized, so it's not too horrible as a speed hit.

Sunday, October 26th, 2003   Al Riddoch <alriddoch@zepler.org>

* wfmath/quaternion.cpp: Ensure vector component is valid when
	  constructing a valid quaternion.

Sunday, September 21st, 2003   Ron Steinke <rsteinke@w-link.net>

* Some cleanups to int_to_string.cpp
	* Added some macros to const.h for future
	  normalization-aging checks in RotMatrix
	  and Quaterion.
	* 0.3.1 release

Monday, August 25nd, 2003   Ron Steinke <rsteinke@w-link.net>

* Moved hash() function out of MersenneTwister.h to
	  randgen.cpp, to get time_t and clock_t out of the
	  header.

Friday, August 22nd, 2003   Ron Steinke <rsteinke@w-link.net>

* Forgot to make deprecated IRand(), Drand() (which
	  now wrap Mersenne Twister) inline. Now fixed.

Tuesday, August 19th, 2003   Al Riddoch <alriddoch@zepler.org>

* Remove obsolete file wfmath.m4.

Tuesday, August 19th, 2003   Al Riddoch <alriddoch@zepler.org>

* Updated spec.

Sunday, August 17th, 2003   Ron Steinke <rsteinke@w-link.net>

* Moved config.h include after timestamp.h include
	  in timestamp.cpp, since it's only the unistd.h include
	  that's causing the FreeBSD problem.

Sunday, August 17th, 2003   Al Riddoch <alriddoch@zepler.org>

* wfmath/timestamp.cpp: Moved include of timestamp.h
	  to workaround problem on FreeBSD.

* Makefile.am: Remove obsolete .pbxproj from DIST list.

Saturday, August 16th, 2003   James Turner <james@worldforge.org>

* Update ProjectBuilder files. Move along, nothing to see
	  here, unless you're on OS-X. If you are, please let me
	  know if these are useful.

Thursday, August 14th, 2003   Ron Steinke <rsteinke@w-link.net>

* Fixed typos in a #error message in atlasconv.h.
	* Changed atlas/Makefile.am to build the tests with 0.3.
	* 0.3.0 release!

Friday, August 8th, 2003   Ron Steinke <rsteinke@w-link.net>

* Changed to using Mersenne Twister for random number
	  generation. Anyone who wants the old interface
	  should #define WFMATH_USE_OLD_RAND.
	* Dropped old, deprecated intersect interface version.
	  This version of the API was used briefly in stage
	  at one point, and that was at least a year ago.

Friday, August 8th, 2003   Ron Steinke <rsteinke@w-link.net>

* Forgot to change to 0.3 in wfmath/Makefile.am, fixed that.
	* Got rid of support for old 'list of lists' encoding
	  for AxisBox in atlasconv.h. Also got rid of a bunch
	  of push_back() calls by predeclaring the size of
	  Atlas::Message::Foo::ListType instances.

Friday, August 8th, 2003   Ron Steinke <rsteinke@w-link.net>

* Updated version number to 0.3 in preparation for doing
	  a release next week.
	* Got rid of wfmath-config, we won't support it in 0.3.
	* Added instring_test, which tests both IntToString() and IRand().
	* Got rid of operator<() in all classes except for those
	  in timestamp.*. It was only there 'so we could use wfmath
	  classes as keys in std::map'. However, since equality
	  isn't transitive (a == b && b == c does not imply a == c),
	  this has some problems. If you really want a map of spatial
	  objects, you probably want something like stage's OctTree
	  instead.
	* Fixed IRand() to deal with the fact that UINT_MAX is often
	  larger than RAND_MAX.
	* Added a few inline IntToString() cases to make sure short
	  and int get cast to the appropriate (signed or unsigned)
	  version of long.
	* Added int_to_string.h to wfmath.h.

Monday, August 4th, 2003   Ron Steinke <rsteinke@w-link.net>

* Added IntToString() utility function, because I'm tired of
	  writing the same code in a dozen different applications.

Tuesday, July 22nd, 2003   Ron Steinke <rsteinke@w-link.net>

* More poly-atlas tweaks. Forgot to inline some wrapper
	  functions, had to add a template AtlasInType constructor
	  to take advantange of the fact that the Atlas::Message::Foo
	  constructor is overloaded (needed that to build Eris).

Tuesday, July 22nd, 2003   Ron Steinke <rsteinke@w-link.net>

* Changes to support both Atlas-C++ 0.4 and 0.6 with atlasconv.h
	* Changed needless 'const CoordType' for pass-by-value
	  in some Quaternion function calls to 'CoordType'

Tuesday, July 22nd, 2003   Ron Steinke <rsteinke@w-link.net>

* Fixed a couple more m_valid bugs.

Monday, July 21st, 2003   Al Riddoch <alriddoch@zepler.org>

* wfmath/atlasconv.h: Use AsNum() rather than AsFloat() so that
	  integers don't cause exceptions.

* wfmath/quaternion.h: Fix operator=() so it copies m_valid to
	  the assignee.

Thursday, July 3rd, 2003   Al Riddoch <alriddoch@zepler.org>

* Update rpm spec to be cleaner, and make the technical sections
	  more generic.

Friday, June 27th, 2003   Ron Steinke <rsteinke@w-link.net>

* Did a Quaternion-specific implementation of rotation(from, to)
	  instead of just calling the RotMatrix version and
	  converting. Also changed RotMatrix<2>::rotation(from, to)
	  not to throw ColinearVectors in the case where the
	  inputs are antiparallel, since in 2d there's only
	  one possible plane of rotation and we can give
	  a canonical answer.

Tuesday, June 24th, 2003   Ron Steinke <rsteinke@w-link.net>

* Fixed a bug in RotMatrix::rotation(from, to),
	  added a Quaternion wrapper for the same function

Tuesday, June 3rd, 2003   Ron Steinke <rsteinke@w-link.net>

* Instantiated Intersect(), Contains() functions
	  and stream operators for dim=2,3 in .cpp files
	* Made most template functions inline, bumped
	  the interface number in case this broke
	  compatibility

Tuesday, May 27th, 2003   Ron Steinke <rsteinke@w-link.net>

* Added elements() const accessors to the underlying
	  arrays in Vector and Point.

Sunday, May 4th, 2003   Ron Steinke <rsteinke@w-link.net>

* Toned down chuck's more explicit message for the
	  failure of the configure check for Atlas. Anyone
	  who doesn't know what Atlas is isn't going to care
	  about the Atlas::Message::Object encoding code
	  stubs, and it's best not to make them think they
	  need to download another library if they don't have to.

Thursday, May 1st, 2003   Ron Steinke <rsteinke@w-link.net>

* Changed configure.in to configure.ac, since
	  it now contains code which is incompatible
	  with autoconf 2.13

Thursday, April 24th, 2003   Al Riddoch <alriddoch@zepler.org>

* Add news item, and fix rpm spec.

* Release 0.2.11, API 0.2, interface version 1.

Wednesday, April 23rd, 2003   Al Riddoch <alriddoch@zepler.org>

* Update spec file, and set the interface version ready for
	  release.

Wednesday, April 23rd, 2003   James Turner <james@worldforge.org>

* Updated configure.in to use pkg-config to detect Atlas-C++,
	  removing the need for AM_PATH_ATLAS in one more place.
	* Wrapped the sstream / strstream include tests in an
	  AC_LANG(C++) section, which they need in order to detect
	  correctly, at least on OS-X.

Tuesday, April 22nd, 2003   James Turner <james@worldforge.org>

* Added the ProjectBuilder files to EXTRA_DIST in
	  anticipation of a new stable release.

Tuesday, April 22nd, 2003 	Ron Steinke <rsteinke@w-link.net>

* Added trivial RotMatrix<>::parity() function.

Thursday, April 17th, 2003	James Turner <james@worldforge.org>

* Add support for the Atlas tests to the ProjectBuilder files
	  (you'll need to update the reference to Atlas.framework to
	  whereever you built it). Again, all the tests pass.

Wednesday, April 16th, 2003 	James Turner <james@worldforge.org>

* Updated the ProjectBuilder files, including targets for some of
	  the test cases, which all pass with flying colours.

Friday, January 31, 2003	Al Riddoch <alriddoch@zepler.org>

* Convert to using pkg-config

Saturday, January 11, 2003	James Turner <james@worldforge.org>

* Changed 'libtool' to 'libtoolize' in autogen.sh so
	  an autoXXXX build works under Mac OS-X.
	* Added project builder files to produce a WFMath framework
	  If you use this or have any comments, please let me know.

Monday, November 4, 2002	Ron Steinke <rsteinke@w-link.net>

* Added isValid() member functions to TimeStamp, TimeDiff
	  (the flags were already there)
	* Improved TimeStamp, TimeDiff documentation

Saturday, November 2, 2002	Ron Steinke <rsteinke@w-link.net>

* Added documentation. With the exception of those associated
	  with Polygon, all API functions should now be documented.

Saturday, November 2, 2002	Al Riddoch <alriddoch@zepler.org>

* Add rpm spec.

Friday, November 1, 2002	Ron Steinke <rsteinke@w-link.net>

* Added Doxyfile.in to CVS, did some work towards docs

Wednesday, October 30, 2002     Michael Koch <konqueror@gmx.de>

* Added manpage for wfmath-config.

Wednesday, October 23, 2002	Ron Steinke <rsteinke@w-link.net>

* Portability fix. Apparently debian on sparc uses
	  int instead of long for the usec field of struct timeval.

Monday, October 10, 2002	Ron Steinke <rsteinke@w-link.net>

* Changed operator==() for quaternions to regard two
	  quaternions as equal iff they produce the same
	  3x3 rotation matrix. This means q == -q is true.
        * Added a Shuffle() function which randomizes the order
          of elements contained in a std::vector.
	* Doc updates
	* Bumped version number to 0.2.10

Monday, September 2, 2002	Ron Steinke <rsteinke@w-link.net>

* Bumped version number to 0.2.9

Friday, August 2, 2002		Ron Steinke <rsteinke@w-link.net>

* Fixed a bug involving the machine dependence of the
	  behavior of % for negative numbers

Monday, July 22, 2002		Ron Steinke <rsteinke@w-link.net>

* Wraped a declaration of a variable which is only used in
	  an assert() in #ifndef NDEBUG

Saturday, June 23, 2002		Ron Steinke <rsteinke@w-link.net>

* Added timestamp class from Eris
	* Added random number generators (really wrappers for rand())
	* Added Quaternion::inverse()

Saturday, May 11, 2002		Ron Steinke <rsteinke@w-link.net>

* Bumped version number to 0.2.8, due to the sign convention changes

Friday, May 10, 2002		Ron Steinke <rsteinke@w-link.net>

* Added an isValid() flag to all classes. Point and Vector
	  also have a setValid() function, since you can assign
	  values directly to the array elements.
	* Switched _Poly2Orient to use the Point and Vector isValid()
	  flags, rather than having its own flags.

Friday, May 10, 2002		Ron Steinke <rsteinke@w-link.net>

* Switched sign convention for quaternions to match
	  the more sensible convention used by cyphesis.
	  This fixes a bug with wfmath and cyphesis miscommunicating
	  about orientations over the network, but introduces
	  a similar problem with older versions of wfmath.
	  Everyone is urged to upgrade wfmath.

Friday, April 26, 2002		Ron Steinke <rsteinke@w-link.net>

* Added WFMATH_DEPRECATE_OLD_INTERSECT flag to build
	  without the old intersect API. Fixed wfmath to build
	  with the old API removed.

Friday, April 26, 2002		Ron Steinke <rsteinke@w-link.net>

* Bumped version number for 0.2.7 release

Sunday, April 21, 2002		Ron Steinke <rsteinke@w-link.net>

* Changed format sent by AxisBox<>::toAtlas() for better
	  network optimization

Wednesday, April 9, 2002		Ron Steinke <rsteinke@w-link.net>

* The eris-support-on-msvc changes now work

Wednesday, April 9, 2002		Ron Steinke <rsteinke@w-link.net>

* Hopefully have enough of wfmath working on msvc now to support eris

Tuesday, April 9, 2002		Ron Steinke <rsteinke@w-link.net>

* (Continued work on MSVC++ workarounds).7

Tuesday, April 9, 2002		Ron Steinke <rsteinke@w-link.net>

* (Continued work on MSVC++ workarounds).6

Tuesday, April 9, 2002		Ron Steinke <rsteinke@w-link.net>

* (Continued work on MSVC++ workarounds).5

Tuesday, April 9, 2002		Ron Steinke <rsteinke@w-link.net>

* (Continued work on MSVC++ workarounds).4

Tuesday, April 9, 2002		Ron Steinke <rsteinke@w-link.net>

* (Continued work on MSVC++ workarounds).3

Tuesday, April 9, 2002		Ron Steinke <rsteinke@w-link.net>

* (Continued work on MSVC++ workarounds).2

Tuesday, April 9, 2002		Ron Steinke <rsteinke@w-link.net>

* Continued work on MSVC++ workarounds

Tuesday, April 9, 2002		Ron Steinke <rsteinke@w-link.net>

* Started adding workarounds to compile with MSVC++
	* Started adding doxygen docs

Friday, March 24, 2002		Ron Steinke <rsteinke@w-link.net>

* Tweaked the syntax of the new Parallel() function slightly

Thursday, March 23, 2002	Ron Steinke <rsteinke@w-link.net>

* Finished Intersect(Polygon, Polygon). Now I've just got to
	  test all those intersection functions
	* Added Parallel() and Perpendicular() functions to compare the
	  orientation of two vectors
	* Incremented version number to 0.2.6

Tuesday, March 23, 2002		Ron Steinke <rsteinke@w-link.net>

* Fixed bug with declaring the default value of the "proper"
	  argument of the intersection functions twice
	* Moved the function definitions for intersection-oriented
	  members of _Poly2Orient from polygon_funcs.h into
	  polygon_intersect.h
	* Wrote definitions for Contains(Polygon, AxisBox),
	  Contains(Polygon, RotBox), and Contains(Polygon, Polygon).
	  Got most of Intersect(Polygon, Polygon) done, except
	  for the case where the two planes containing the polygons
	  intersect in a line (the standard case in 3d)

Thursday, March 21, 2002	Ron Steinke <rsteinke@w-link.net>

* Fixed Polygon<> intersection functions with AxisBox<> and
	  RotBox<> in polygon_intersect.h
	* Replaced separate Intersect() and IntersectProper() functions
	  with a "bool proper" argument to Intersect(), did the same
	  for Contains(). For backwards compatibility, make the "proper"
	  argument default to false, and wrote generic IntersectProper()
	  and ContainsProper() templates to call Intersect() and Contains()
	  with proper = true (keep them? deprecate them? which API is better?).

Tuesday, March 12, 2002		Ron Steinke <rsteinke@w-link.net>

* Added a default value of 1.0 for the norm in Vector::normalize()
	* Added a virtual destructor to the exception defined in atlasconv.h
	* Fixed a terminate-the-loop-proberly bug in probability.cpp
	  (replaced DBL_MIN by DBL_EPSILON)
	* Got test functions to compile with gcc-3.0

Saturday, March 9, 2002		Dan Tomalesky <grim@xynesis.com>

* Added acinclude.m4 for atlas so people without atlas can still
      autogen.sh and configure will give warning instead of getting
      bizarre macro missing error for atlas when atlas is not installed

Thursday, March 7, 2002		Ron Steinke <rsteinke@w-link.net>

* Fixed error in configure check for sstream vs. strstream

Wednesday, March 6, 2002	Ron Steinke <rsteinke@w-link.net>

* Merged in Grimicus' patch to add wfmath-config

Wednesday, March 6, 2002	Ron Steinke <rsteinke@w-link.net>

* Redid sstream vs. strstream compatibility code

Wednesday, March 6, 2002	Ron Steinke <rsteinke@w-link.net>

* Got rid of stupid "set fail bit" on parse errors for
	  operator>>(), it now throws instead
	* Added configure check for sstream vs. strstream,
	  compatibility code

Monday, March 04, 2002	Al Riddoch <alriddoch@zepler.org>

* wfmath/error.h: Added destructor with throw(); to exception class.

* wfmath/polygon.h: Removed trailing comma from enumeration.

* wfmath/polygon.h, wfmath/stream.h: Fixed std:: namespace issues,
	  and made typenames explicit.

Wednesday, February 27, 2002	Ron Steinke <rsteinke@w-link.net>

* Commented out horribly broken intersection functions
	  with AxisBox and RotBox in polygon_intersect.h

Wednesday, February 27, 2002	Ron Steinke <rsteinke@w-link.net>

* Autogen.sh cleanups

Tuesday, February 26, 2002	Ron Steinke <rsteinke@w-link.net>

* Bump version number to 0.2.5, so we can have an official
	  version needed by the stage patches.

Monday, February 25, 2002	Ron Steinke <rsteinke@w-link.net>

* Added rotation() functions to RotMatrix<3> and Quaternion
	  which take a single Vector<3> as argument (as opposed to
	  a vector for the rotation axis and an angle), and determine
	  the rotation angle from the length of the vector. This
	  is nice for things like the rotation generated by
	  (angular velocity) * dT, since it handles the zero-length
	  axis case cleanly, and avoids an extra call to sqrt().
	* Fixed an error in atlasconv.h, where specializations
	  of AxisBox<>::fromAtlas() to particular dimensions
	  weren't marked as inline

Friday, February 22, 2002	Ron Steinke <rsteinke@w-link.net>

* Broke the Polygon<> intersection functions out of
	  polygon_funcs.h and polygon.cpp into the separate
	  files polygon_intersect.h and polygon_intersect.cpp 
	* Moved the implementations of the boundingBox() and
	  boundingSphere() functions in Point out of point_funcs.h
	  into axisbox_funcs.h and ball_funcs.h. This lets me
	  remove the include dependence of Point on AxisBox and Ball.
	* Fixed up list of files included in wfmath.h. It now
	  includes everything but atlasconv.h, which is intentionally
	  excluded.

Wednesday, February 20, 2002	Ron Steinke <rsteinke@w-link.net>

* Fixed RotBox to match the new sense of RotMatrix<>
	  rotation, still need to look at its interaction
	  with Polygon<> to get that right
	* Wrote Intersect(RotBox, AxisBox) for 2d, 3d
	* Removed a needless <iostream> dependency from atlasconv.h
	* Bump version number to 0.2.4

Sunday, February 17, 2002	Ron Steinke <rsteinke@w-link.net>

* Some doc fixes
	* Added a #warning about using the Polygon<> Intersect()
	  and Contains() functions

Thursday, February 14, 2002	Ron Steinke <rsteinke@w-link.net>

* Missed a change in rotation sense in Vector<3>::rotate(const Quaterion&),
	  fixed now

Thursday, February 14, 2002	Ron Steinke <rsteinke@w-link.net>

* Added comments to many assert()'s
	* Switched the sense of rotation in RotMatrix<> and Quaternion
	  to be compatible with OpenGL and the rest of Worldforge. Also
	  used this as an excuse to scrap all the Euler angle stuff,
	  since: 1) with different axis conventions floating around, it's
	  very confusing, and 2) I have yet to see someone try to use
	  it in the case where it is the correct solution

Tuesday, February 12, 2002	Ron Steinke <rsteinke@w-link.net>

* Changed Point<>:origin() to Point<>::setToOrigin()
	* Added assert() checks on array indices passed to
	  many functions

Tuesday, February 12, 2002	Ron Steinke <rsteinke@w-link.net>

* Added Equal() template to call foo->isEqualTo().
	* Replaced "const CoordType&" with CoordType everywhere it
	  was used.
	* Got rid of scaleEpsilon member function in Point<> in favor
	  of calling _ScaleEpsilon directly, minimized use of
	  _scaleEpsilon member function in Vector<>
	* Improved efficiency of some member functions in Segment<>
	* Got rid of <iostream> in wrapped_array.h, got rid of
	  MINIBALL_NO_STD_NAMESPACE test on whether to include
	  <list> or <list.h> and <cassert> or <assert.h> (since
	  we're including them as <list> and <assert.h> elsewhere),
	  got rid of miniball_config.h

Friday, February 1, 2002	Ron Steinke <rsteinke@w-link.net>

* Changed IsFloatEqual() to Equal(), removed FloatAdd()
	  and FloatSubtract(), vastly improved precision checks
	  for round-off error. The intersection functions still
	  need to be audited to make sure they're handling it
	  right.
	* API change, increment version to 0.2.3

Monday, January 28, 2002	Ron Steinke <rsteinke@w-link.net>

* Cleanups to const.h, const.cpp suggested by Jesse Jones
	  in the code review, and associated repurcussions to the
	  rest of the codebase.

Friday, January 25, 2002	Ron Steinke <rsteinke@w-link.net>

* Some efficiency improvements and generalizations to the
	  backend of the probability functions
	* Wrote Polygon<3> intersections with AxisBox<3> and RotBox<3>

Thursday, January 24, 2002	Ron Steinke <rsteinke@w-link.net>

* Karsten's Makefile.am fixes for srcdir != builddir
	* New probability distribution functions, Gaussian
	  and Poisson distributions
	* Increment version to 0.2.2

Tuesday, January 22, 2002	Ron Steinke <rsteinke@w-link.net>

* Changed namespace from WF::Math to WFMath
	* Changed fromAtlas() to throw an exception instead of
	  returning bool, added constructors from Atlas::Message::Object
	  to appropriate types
	* Incremented version number to 0.2.1, since there were API changes
	  and other people are starting to care about dependencies on this
	  library; there'll probably be a lot of 0.2 versions

Tuesday, January 22, 2002	Ron Steinke <rsteinke@w-link.net>

* Changed the atlas functions for Quaternion and AxisBox<>
	  to conform to atlas specs, got rid of atlas functions which
	  still used string conversion
	* Fixed Contains(Polygon<2>, Segment<2>) and
	  Contains(Polygon<2>, Polygon<2>) for endpoint intersection;
	  commented out Intersect(RotBox<>, AxisBox<>) and
	  IntersectProper(RotBox<>, AxisBox<>) because I'm
	  pretty sure the algorithm's wrong
	* Added another rotation() function to RotMatrix<>, this
	  one constructs the rotation necessary to rotate one vector
	  into another
	* Got versioning on library build working correctly
	* Changed version to 0.2.0, implementation of remaining
	  Polygon<> intersection routines delayed until a later version

Sunday, January 20, 2002	Ron Steinke <rsteinke@w-link.net>

* Wrote all the Polygon<2> intersection functions, and
	  about half of the general Polygon<> intersection functions;
	  a few of the 2d functions still need more work
	* Changed intersect_test back to shape_test; decided one
	  test program was sufficient for all of AxisBox<>, Ball<>,
	  Segment<>, and RotBox<>
	* Wrote test code for Polygon<> to call the generic tests;
	  added the generic tests to shape_test; wrote fairly complete
	  test code for Quaternion
	* Changed from FromAtlas() and ToAtlas() functions to fromAtlas()
	  and toAtlas() member functions; changed Vector<> and Point<>
	  from sending string objects to atlas to sending lists, so
	  we're more compatible with the getPos() and getVelocity()
	  methods of Atlas::Objects::Entity::RootEntityData
	* Upped version number to 0.1.9. The library now implements
	  the functionality in stage/math, plus the mathematical
	  parts of coal and eris. Will go to 0.2 when the polygon
	  intersect functions are done, and the unit tests are
	  more complete

Tuesday, January 15, 2002	Ron Steinke <rsteinke@w-link.net>

* Cleaned up Euler angle stuff in RotMatrix<> and Quaternion,
	  changed everything to z-y-z convention
	* Moved template specialization declarations from vector.h
	  to vector_funcs.h
	* Made Vector<> and Point<> mathematical operators all friends
	  instead of members, to allow friendship for mathematical
	  operators which take mixed types

Friday, January 11, 2002	Ron Steinke <rsteinke@w-link.net>

* Added Quaternion class, based on code from eris
	* Renamed matrix.h, matrix_funcs.h, matrix.cpp, matrix_test.cpp
	  to rotmatrix.h, rotmatrix_funcs.h, rotmatrix.cpp, rotmatrix_test.cpp;
	  this matches the name of the class, and it's best to have the
	  matrix.h slot available in case we need it later. Need to do
	  this now before everyone starts using the library

Wednesday, January 9, 2002	Ron Steinke <rsteinke@w-link.net>

* Added BoundingBox(), BoundingSphere() functions for a
	  container of points. The BoundingSphere() function
	  uses the (GPL'd) miniball code of Bernd Gaertner
	  <http://www.inf.ethz.ch/personal/gaertner>
	* Moved the implementations of operator<<() and operator>>()
	  for Polygon<2> out of stream.h and into stream.cpp, fixing
	  a linker error for any file which included stream.h (oops).

Wednesday, January 9, 2002	Ron Steinke <rsteinke@w-link.net>

* Started on Polygon<> class
	* Wrote some test functions for the generic
	  part of the class interface (operator=(), isEqualTo(), etc.)
	  and the generic shape interface (getCorner(), boundingBox(), etc.)
	* Added Midpoint() function in point.h
	* Cleaned up operator<() to check !IsFloatEqual()
	  when comparing variables of type CoordType
	* Added autogen.sh

Friday, January 4, 2002		Ron Steinke <rsteinke@w-link.net>

* Got atlas_test working

Thursday, January 3, 2002	Ron Steinke <rsteinke@w-link.net>

* Changed Barycenter() to take a container of Point<>
	  instead of an array, added BoundingBox() for a
	  container of AxisBox<>
	* Optimized special cases in AxisBox::getCorner() and
	  RotBox::getCorner(), got rid of AxisBox::lowCorner()
	  and AxisBox::highCorner()
	* Extended RotMatrix<> to allow for mirror image flips
	  in addition to rotations, added mirror() functions to
	  both RotMatrix<> and Vector<>
	* Removed foolish const from return value of
	  RotMatrix<>::rotation()
	* Wrote better member accessors for most shapes (there's
	  no reason not to have direct access to the members in
	  anything but AxisBox<>)
	* Inlined some of the simpler class member functions
	* Moved atlasconv.h from atlas/ into wfmath/, since we don't
	  need Atlas to install it, just to build the test code

Monday, December 31, 2001	Ron Steinke <rsteinke@w-link.net>

* Added boundingSphere(), boundingSphereSloppy() to all
	  the shapes
	* Wrote FloatMin(), FloatMax(), and FloatClamp(). This
	  let me remove std::min() and std::max(), and with
	  them the dependency on <algorithm>
	* Cleaned up the inclusion of outside headers
	* Replaced double with CoordType everywhere, with the
	  exception of the precision/tolerance/epsilon arguments
	  of float comparison functions and the intenals of
	  IsFloatEqual()
	* Switched CoordType from double to float. This puts
	  the library precision at about 3e-6 (on my machine),
	  close to the precision of the strings being passed by
	  ToAtlas() and FromAtlas()
	* Replaced fromStream() with operator>>(), using fail()
	  flag to indicate a bad parse
	* Upped the version number from 0.0.1 to 0.1.0, as
	  the shape API appears to be settling down, and
	  it sure doesn't feel like 0.0 anymore

Monday, December 31, 2001	Ron Steinke <rsteinke@w-link.net>

* Cleaned up string and stream stuff, classes only need
	  to include <iosfwd>, everything else is in stream.h/stream.cpp,
	  removed stringconv.h/stringconv.cpp

Sunday, December 30, 2001	Ron Steinke <rsteinke@w-link.net>

* Finished the RotBox<> intersection functions
	* Cleaned up use of namespaces in *.cpp files
	* Added to the test code
	* Miscelaneous bug fixes

Saturday, December 29, 2001	Ron Steinke <rsteinke@w-link.net>

* Fixed an error in the README

Saturday, December 29, 2001	Ron Steinke <rsteinke@w-link.net>

* Wrote some documentation, cleaned up the little that was
	  already there.

Saturday, December 29, 2001	Ron Steinke <rsteinke@w-link.net>

* Removed some unnecessary template specifications, changed
	  Vector<len> to Vector<dim> and RotMatrix<size> to RotMatrix<dim>
	  for cross class consistency in the name of the template parameter
	* Removed the base Shape<> class, leaving a bunch of simple classes
	  for basic shapes which possess a common interface
	* Changed test code to use toString() method directly rather than
	  through operator<<()
	* Changed ToAtlas() and FromAtlas() to use toString() and fromString(),
	  eliminating the need for a separately compiled atlas conversion
	  library
	* Added the shape interface functions to Point<>
	* Replaced the symlinks to COPYING and INSTALL files added by automake
	  with the files themselves. This should hopefully let me get them
	  into CVS.
	* More work on intersection functions

Tuesday, December 18, 2001	Ron Steinke <rsteinke@w-link.net>

* Some cleanup on RotMatrix<>::setVals() backend, Atlas conversion
	  functions
	* Added Ball<>, Segment<>, RotBox<> classes (not all RotBox<>
	  intersection functions written yet)

Monday, December 17, 2001	Ron Steinke <rsteinke@w-link.net>

* Wrote Shape<> base class
	* Wrote AxisBox<> class
	* Cleaned up header file naming convention, so foo_funcs.h is
	  always the function templates for the class in foo.h

Friday, December 14, 2001	Ron Steinke <rsteinke@w-link.net>

* .cvsignore fixes
	* Rearranged the ordering of function declarations in the
	  classes in an attempt at a cross-class standard, added
	  some bits I'd missed
	* Added polar, spherical coordinate conversions to Point<> and Vector<>

Thursday, December 13, 2001	Ron Steinke <rsteinke@w-link.net>

* Added setVals() method to Matrix<>
	* Added operator>> for Vector<>, Matrix<>, Point<> to give
	  string read capability, added stream_funcs.cpp
	* Added toString() and fromString() for Vector<>, Matrix<>, Point<>,
	  changed operator<< to use toString(), removed operator>>

Wednesday, December 12, 2001	Ron Steinke <rsteinke@w-link.net>

* Created atlas_funcs.cpp, wrote GetAtlasDoubleList() and
	  SetAtlasDoubleList() to handle most of the Atlas
	  interface work
	* Got a test for Atlas into configure.in
	* First CVS upload
`	* Copied the CoalCoord class in as Point<>, moved CoordType
	  and IsFloatEqual() into const.h, const.cpp
	* Added FloatAdd() and FloatSubtract() to handle numbers
	  whose sum/difference is (nearly) zero
	* Modified Vector<> and Matrix<> to use CoordType

Tuesday, December 11, 2001	Ron Steinke <rsteinke@w-link.net>

* Got test functions working with RotMatrix<>
	* Created atlas_funcs.h to hold Atlas interface code,
	  wrote ToAtlas() and FromAtlas() for Vector<> and
	  Matrix<>

Monday, December 10, 2001	Ron Steinke <rsteinke@w-link.net>

* After coversation with Rakshasa about how matrices are actually
	  being used in stage, replaced Matrix<> with RotMatrix<>

Friday, December 7, 2001	Ron Steinke <rsteinke@w-link.net>

* Created some tests in matrix_test
	* Added GPL information to all the source files

Thursday, December 6, 2001	Ron Steinke <rsteinke@w-link.net>

* Added more tests to vector_test
	* Implemented sloppyMag and associated functions
	  for Vector<2>, Vector<3>
	* Added a script, bc_sloppy_mag_3, to calculate some constants
	  for the Vector<3> implementation of sloppyMag
	* Got rid of RowVector<> and ColumnVector<> classes,
	  added rowSet() and columnSet() to Matrix<>

Wednesday, December 5, 2001	Ron Steinke <rsteinke@w-link.net>

* First ChangeLog entry
	* Autoconf is working, and the Vector<> and Matrix<> class compile
	* Got the README, AUTHORS, and TODO files written
	* Changed #include "foo.h" to #include <wfmath/foo.h> in
	  the header files
	* Added const.h
	* Created vector_test.cpp, matrix_test.cpp, started work on
	  vector_test
07070100000013000081ED0000000200000002000000015D8693EF00000698000000000000000000000000000000000000003800000000wfmath-1569100783.d0f8a54/support/generate-ChangeLog.sh#! /bin/sh
#A script for combining the legacy ChangeLog found in ChangeLog-CVS with one output from git. The script will only run if the current ChangeLog contains exactly one line.
#This makes it possible to do a new "make dist" from an existing source distribution (as the ChangeLog would then be complete.).
top_srcdir=$1
distdir=$2
commitid=$3
if [ x${distdir} = "x" ] || [ x${top_srcdir} = "x" ] || [ x${commitid} = "x" ]; then
	echo "This script will generate an aggregated ChangeLog by combining the legacy ChangeLog-CVS file with the output from git log. It therefore needs to be run in a git source directory."
	echo "Params: <source directory path> <distribution directory path> <SHA1 of first git commit>"	
	exit 1
fi
#Only do the aggregation if the ChangeLog file is exactly one line. If not the aggregation has already been done.
if [ `cat ${distdir}/ChangeLog | wc -l` = "0" ]; then
	echo "Generating ChangeLog by appending the old CVS ChangeLog to the one generated from git. This requires that you create the dist in the git repository."

chmod u+w ${distdir}/ChangeLog && git log ${commitid}..HEAD --stat --name-only --date=short --abbrev-commit > ${distdir}/ChangeLog && echo "" >> ${distdir}/ChangeLog && cat ${top_srcdir}/support/ChangeLog-CVS >> ${distdir}/ChangeLog
	#Put a notice in the legacy ChangeLog-CVS file, thus bringing the size of the dist down a bit.
	chmod u+w ${distdir}/support/ChangeLog-CVS && echo "This file was needed for generating the proper ChangeLog as an aggregate of the code held in git and older code in CVS. It's now empty, but needs to be included in the source distribution to not upset automake." > ${distdir}/support/ChangeLog-CVS
fi
07070100000014000081ED0000000200000002000000015D8693EF00000914000000000000000000000000000000000000003900000000wfmath-1569100783.d0f8a54/support/generate_abi_report.sh#!/bin/bash

if [ $# -ne 1 ]
then
  echo "Performs an ABI check against an older version, using the ABI_compliance_checker tool."
  echo "You must have the ABI_compliance_checker installed to use this script. Get it from http://ispras.linuxbase.org/index.php/ABI_compliance_checker"
  echo "This script must be run from the Git source directory."
  echo "Usage: `basename $0` <older_version>"
  echo "<older_version> is the name of an older tag (or commit) which this script will check out from Git"
  exit -1
fi

command -v git >/dev/null 2>&1 || { echo "Git command not available." > $1; exit 0; }
command -v abi-compliance-checker >/dev/null 2>&1 || { echo "abi-compliance-checker command not available; get it from http://ispras.linuxbase.org/index.php/ABI_compliance_checker." > $1; exit 0; }

SOURCE_DIR=$PWD

#Figure out the name of the lib by looking in "configure"
LIBRARY_NAME=`grep PACKAGE_NAME= $SOURCE_DIR/configure | sed -e s/PACKAGE_NAME=\'//g | sed -e s/\'//g`

ABI_REPORT_DIR=$PWD/abi_report

#Disable warnings to counteract -Werror (older code might cause warnings with newer compilers, and fail through -Werror).
export CXXFLAGS="$CXXFLAGS -w"

OLD_VERSION=$1
OLD_SOURCE_DIR=$ABI_REPORT_DIR/${OLD_VERSION}_source
OLD_BUILD_DIR=$ABI_REPORT_DIR/${OLD_VERSION}_build
OLD_INSTALL_DIR=$ABI_REPORT_DIR/${OLD_VERSION}_install
MASTER_BUILD_DIR=$ABI_REPORT_DIR/master_build
MASTER_INSTALL_DIR=$ABI_REPORT_DIR/master_install

mkdir -p $ABI_REPORT_DIR
mkdir -p $OLD_SOURCE_DIR
mkdir -p $OLD_BUILD_DIR
mkdir -p $MASTER_BUILD_DIR

#Check out the older version into a separate tree
git archive $OLD_VERSION | tar -x -C $OLD_SOURCE_DIR

if [ $? != 0 ]
then
  echo "Could not check out '$OLD_VERSION'. Make sure that this is something that's available in Git."
  exit -1
fi

echo "Building master version"
cd $MASTER_BUILD_DIR && $SOURCE_DIR/configure --prefix $MASTER_INSTALL_DIR && make install

echo "Building older version"
cd $OLD_SOURCE_DIR && NOCONFIGURE=1 ./autogen.sh && cd $OLD_BUILD_DIR && $OLD_SOURCE_DIR/configure --prefix $OLD_INSTALL_DIR && make install

if [ $? != 0 ]
then
  echo "Error when building old version."
  exit -1
fi

cd $ABI_REPORT_DIR
echo "Performing ABI compliance check"
abi-compliance-checker -l $LIBRARY_NAME -v1 $OLD_VERSION -v2 master -old $OLD_INSTALL_DIR -new $MASTER_INSTALL_DIR

07070100000015000041ED0000000200000002000000035D8693EF00000000000000000000000000000000000000000000002100000000wfmath-1569100783.d0f8a54/wfmath07070100000016000041ED0000000200000002000000025D8693EF00000000000000000000000000000000000000000000002800000000wfmath-1569100783.d0f8a54/wfmath.pbproj07070100000017000081A40000000200000002000000015D8693EF0000A0A7000000000000000000000000000000000000003800000000wfmath-1569100783.d0f8a54/wfmath.pbproj/project.pbxproj// !$*UTF8*$!
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0707010000001C000081A40000000200000002000000015D8693EF00000D0A000000000000000000000000000000000000003300000000wfmath-1569100783.d0f8a54/wfmath/MersenneTwister.h// MersenneTwister.h
//
//  The WorldForge Project
//  Copyright (C) 2013  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License along
//  with this program; if not, write to the Free Software Foundation, Inc.,
//  51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//
#ifndef WFMATH_MERSENNE_TWISTER_H_
#define WFMATH_MERSENNE_TWISTER_H_

#include <iosfwd>
#include <climits>
#include <cmath>
#include <stdint.h>

namespace WFMath {

class MTRand {
public:
  typedef uint32_t uint32;

static const uint32 state_size = 624;

public:
  MTRand();
  MTRand(uint32 oneSeed);
  MTRand(uint32* const bigSeed, uint32 const seedLength = state_size);

// real-valued random numbers on [0, 1] or [0, n]
  template<typename FloatT>
    FloatT rand();
  double rand();
  double rand(const double& n);

// integer-valued random numbers on [0, 2^32-1] or [0, n]
  uint32 randInt();
  uint32 randInt(uint32 n);

void seed();
  void seed(uint32 oneSeed);
  void seed(uint32* const init_vector, uint32 init_vector_length = state_size);

std::ostream& save(std::ostream&) const;
  std::istream& load(std::istream&);

static MTRand instance;

private:
  uint32 state[state_size];
  uint32 index;
};

inline MTRand::MTRand(uint32 s)
: index(0)
{ seed(s); }

inline MTRand::MTRand(uint32* const bigSeed, const uint32 seedLength)
: index(0)
{ seed(bigSeed, seedLength); }

inline MTRand::MTRand()
: index(0)
{ seed(); }

template<>
inline float MTRand::rand<float>()
{ return float(randInt()) * (1.0f/4294967295.0f); }

template<>
inline double MTRand::rand<double>()
{ return double(randInt()) * (1.0/4294967295.0); }

inline double MTRand::rand()
{ return double(randInt()) * (1.0/4294967295.0); }

inline double MTRand::rand( const double& n )
{ return rand() * n; }

inline MTRand::uint32 MTRand::randInt(uint32 n)
{
  uint32 used = n;
  used |= used >> 1;
  used |= used >> 2;
  used |= used >> 4;
  used |= used >> 8;
  used |= used >> 16;

uint32 i;
  do
    i = randInt() & used;
  while( i > n );
  return i;
}

#if 0
inline void MTRand::save(uint32* saveArray) const
{
  register uint32 *sa = saveArray;
  register const uint32 *s = state;
  register int i = state_size;
  for( ; i--; *sa++ = *s++ ) {}
  *sa = left;
}

inline void MTRand::load(uint32 *const loadArray)
{
  register uint32 *s = state;
  register uint32 *la = loadArray;
  register int i = state_size;
  for( ; i--; *s++ = *la++ ) {}
  left = *la;
  pNext = &state[state_size-left];
}
#endif

std::ostream& operator<<(std::ostream& os, MTRand const& mtrand);
std::istream& operator>>(std::istream& is, MTRand& mtrand);

} // namespace

#endif // WFMATH_MERSENNE_TWISTER_H_
0707010000001D000081A40000000200000002000000015D8693EF00003069000000000000000000000000000000000000002D00000000wfmath-1569100783.d0f8a54/wfmath/atlasconv.h// atlasconv.h (Functions to convert WFMath library object to/from an Atlas Message)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-11

// Since we don't want WFMath and Atlas to depend on each other,
// we're putting all the atlas interface functions into this header.

// WARNING! WARNING! Do not include this file in any other file in wfmath.

#ifndef WFMATH_ATLAS_CONV_H
#define WFMATH_ATLAS_CONV_H

#include <wfmath/point.h>
#include <wfmath/vector.h>
#include <wfmath/quaternion.h>
#include <wfmath/axisbox.h>
#include <wfmath/polygon.h>
#include <wfmath/ball.h>
#include <wfmath/rotbox.h>
#include <wfmath/line.h>

#include <cmath>

namespace WFMath {

#ifndef ATLAS_MESSAGE_ELEMENT_H
#error "You must include Atlas/Message/Element.h before wfmath/atlasconv.h"
#endif

typedef Atlas::Message::WrongTypeException _AtlasBadParse;

class AtlasInType
{
 public:
  AtlasInType(const Atlas::Message::Element& val) : m_val(val) {}
  // allow nice conversions when necessary
  template<class C> AtlasInType(C c) : m_obj(c), m_val(m_obj) {}
  operator const Atlas::Message::Element&() const {return m_val;}
  bool IsList() const {return m_val.isList();}
  const Atlas::Message::ListType& AsList() const {return m_val.asList();}
 private:
  Atlas::Message::Element m_obj;
  const Atlas::Message::Element& m_val;
};

class AtlasOutType
{
 public:
  AtlasOutType(const Atlas::Message::ListType& l) : m_val(l) {}
  AtlasOutType(const Atlas::Message::MapType& l) : m_val(l) {}
  operator Atlas::Message::Element&() {return m_val;}
  operator const Atlas::Message::Element&() const {return m_val;}
 private:
  Atlas::Message::Element m_val;
};

inline AtlasOutType _ArrayToAtlas(const CoordType* array, unsigned len)
{
  Atlas::Message::ListType a(len);

for(unsigned i = 0; i < len; ++i)
    a[i] = array[i];

return a;
}

inline void _ArrayFromAtlas(CoordType* array, unsigned len, const AtlasInType& a)
{
  if(!a.IsList())
    throw _AtlasBadParse();

const Atlas::Message::ListType& list(a.AsList());

if(list.size() != (unsigned int) len)
    throw _AtlasBadParse();

for(unsigned i = 0; i < len; ++i)
    array[i] = list[i].asNum();
}

template<int dim>
inline Vector<dim>::Vector(const AtlasInType& a)
{
  fromAtlas(a);
}

template<int dim>
inline void Vector<dim>::fromAtlas(const AtlasInType& a)
{
  _ArrayFromAtlas(m_elem, dim, a);
  for (int i = 0; i < dim; ++i) {
    if (!std::isfinite(m_elem[i])) {
      m_valid = false;
      return;
    }
  }
  m_valid = true;
}

template<int dim>
inline AtlasOutType Vector<dim>::toAtlas() const
{
  return _ArrayToAtlas(m_elem, dim);
}

inline void Quaternion::fromAtlas(const AtlasInType& a)
{
  if(!a.IsList())
    throw _AtlasBadParse();

const Atlas::Message::ListType& list(a.AsList());

if(list.size() != 4)
    throw _AtlasBadParse();

for(int i = 0; i < 3; ++i)
    m_vec[i] = list[i].asNum();

for (int i = 0; i < 3; ++i) {
    if (!std::isfinite(m_vec[i])) {
      m_valid = false;
      m_vec.setValid(false);
      return;
    }
  }

m_w = list[3].asNum();
  if (!std::isfinite(m_w)) {
    m_valid = false;
    return;
  }

CoordType norm = std::sqrt(m_w * m_w + m_vec.sqrMag());

if (norm <= numeric_constants<CoordType>::epsilon()) {
    m_valid = false;
    m_vec.setValid(false);
    return;
  }

m_vec /= norm;
  m_w /= norm;

m_valid = true;
  m_age = 1;
  m_vec.setValid();
}

inline AtlasOutType Quaternion::toAtlas() const
{
  Atlas::Message::ListType a(4);

for(int i = 0; i < 3; ++i)
    a[i] = m_vec[i];
  a[3] = m_w;

return a;
}

template<int dim>
inline Point<dim>::Point(const AtlasInType& a)
{
  fromAtlas(a);
}

template<int dim>
inline void Point<dim>::fromAtlas(const AtlasInType& a)
{
  _ArrayFromAtlas(m_elem, dim, a);
  for (int i = 0; i < dim; ++i) {
    if (!std::isfinite(m_elem[i])) {
      m_valid = false;
      return;
    }
  }
  m_valid = true;
}

template<int dim>
inline AtlasOutType Point<dim>::toAtlas() const
{
  return _ArrayToAtlas(m_elem, dim);
}

template<int dim>
inline AxisBox<dim>::AxisBox(const AtlasInType& a)
{
  fromAtlas(a);
}

template<int dim>
inline void AxisBox<dim>::fromAtlas(const AtlasInType& a)
{
  if(!a.IsList())
    throw _AtlasBadParse();

const Atlas::Message::ListType& list(a.AsList());

switch(list.size()) {
    case dim:
      m_low.setToOrigin();
      m_high.fromAtlas(a);
      break;
    case (2 * dim):
      for(int i = 0; i < dim; ++i) {
        m_low[i] = list[i].asNum();
        if (!std::isfinite((m_low[i]))) {
          m_low.setValid(false);
          return;
        }
        m_high[i] = list[i+dim].asNum();
        if (!std::isfinite((m_high[i]))) {
          m_high.setValid(false);
          return;
        }
      }
      m_low.setValid();
      m_high.setValid();
      break;
    default:
      throw _AtlasBadParse();
  }

for(int i = 0; i < dim; ++i) {
    if(m_low[i] > m_high[i]) { // spec may allow this?
      CoordType tmp = m_low[i];
      m_low[i] = m_high[i];
      m_high[i] = tmp;
    }
  }
}

template<int dim>
inline AtlasOutType AxisBox<dim>::toAtlas() const
{
  int i;

for(i = 0; i < dim; ++i)
    if(m_low[i] != 0)
      break;

if(i == dim)
    return m_high.toAtlas(); // matches case 'dim' above

// Do case '2 * dim' above

Atlas::Message::ListType a(2*dim);
  for(i = 0; i < dim; ++i) {
    a[i] = m_low[i];
    a[dim+i] = m_high[i];
  }

return a;
}

template<int dim>
inline void Ball<dim>::fromAtlas(const AtlasInType& a)
{
  const Atlas::Message::Element& message(a);
  if (message.isMap()) {
    const Atlas::Message::MapType& shapeElement(message.asMap());
    // Get sphere's radius
    auto shape_I = shapeElement.find("radius");
    if (shape_I != shapeElement.end()) {
      const Atlas::Message::Element& shapeRadiusElem(shape_I->second);
      if (shapeRadiusElem.isNum()) {
        m_radius = shapeRadiusElem.asNum();
        //Perhaps we should add a check to Ball::isValid for non-nan radius? Until that we'll just invalidate the center instead.
        if (!std::isfinite(m_radius)) {
          m_center.setValid(false);
          return;
        }
      }
    }
    auto pos_I = shapeElement.find("position");
    if (pos_I != shapeElement.end()) {
      const Atlas::Message::Element& posElem(pos_I->second);
      if (posElem.isList()) {
        m_center.fromAtlas(posElem);
      }
    }
  }
}

template<int dim>
inline AtlasOutType Ball<dim>::toAtlas() const
{
  Atlas::Message::MapType map;
  map.insert(Atlas::Message::MapType::value_type("radius", m_radius));
  map.insert(Atlas::Message::MapType::value_type("position", m_center.toAtlas()));
  return map;
}

template<int dim>
inline Ball<dim>::Ball(const AtlasInType& a) : m_center(Point<dim>::ZERO()),
                                               m_radius(0)
{
  fromAtlas(a);
}

inline bool _ListNumCheck(const Atlas::Message::ListType & list, int dim)
{
  for(int i = 0; i < dim; ++i) {
    if (!list[i].isNum()) {
      return false;
    }
  }
  return true;
}

template<template <int> class ShapeT>
inline void _AddCorner(ShapeT<3> & shape,
                       const Atlas::Message::ListType & point)
{
  Point<3> wpt(point[0].asNum(), point[1].asNum(), point[2].asNum());
  if (!std::isfinite(wpt.x()) || !std::isfinite(wpt.y()) || !std::isfinite(wpt.z())) {
    return;
  }
  shape.addCorner(shape.numCorners(), wpt);
}

template<template <int> class ShapeT>
inline void _AddCorner(ShapeT<2> & shape,
                       const Atlas::Message::ListType & point)
{
  Point<2> wpt(point[0].asNum(), point[1].asNum());
  if (!std::isfinite(wpt.x()) || !std::isfinite(wpt.y())) {
    return;
  }
  shape.addCorner(shape.numCorners(), wpt);
}

template<template <int> class ShapeT, int dim>
inline void _CornersFromAtlas(ShapeT<dim> & shape,
                              const Atlas::Message::Element& message)
{
  if (message.isList()) {
    const Atlas::Message::ListType& pointsData(message.asList());
    
    for (const auto & p : pointsData) {
      if (!p.isList()) {
        continue;
      }
      
      const Atlas::Message::ListType& point(p.asList());
      if ((point.size() < dim) || !_ListNumCheck(point, dim)) {
        continue;
      }
      
      _AddCorner(shape, point);
    }
  }
}

inline void Polygon<2>::fromAtlas(const AtlasInType& a)
{
  const Atlas::Message::Element& message(a);
  if (message.isMap()) {
    const Atlas::Message::MapType& shapeElement(message.asMap());
    auto it = shapeElement.find("points");
    if ((it != shapeElement.end()) && it->second.isList()) {
      _CornersFromAtlas(*this, it->second);
      if (numCorners() > 2) {
        return;
      }
    }
  } else if (message.isList()) {
    _CornersFromAtlas(*this, message);
    if (numCorners() > 2) {
      return;
    }
  }
  throw _AtlasBadParse();
}

inline AtlasOutType Polygon<2>::toAtlas() const
{
  Atlas::Message::ListType points;
  for (const auto & point : m_points)
  {
    points.push_back(point.toAtlas());
  }
  Atlas::Message::MapType map;
  map.insert(Atlas::Message::MapType::value_type("points", points));
  return map;
}

template<int dim>
inline void Line<dim>::fromAtlas(const AtlasInType& a)
{
  const Atlas::Message::Element& message(a);
  if (message.isMap()) {
    const Atlas::Message::MapType& shapeElement(message.asMap());
    auto it = shapeElement.find("points");
    if ((it != shapeElement.end()) && it->second.isList()) {
      _CornersFromAtlas(*this, it->second);
      if (numCorners() > 0) {
        return;
      }
    }
  } else if (message.isList()) {
    _CornersFromAtlas(*this, message);
    if (numCorners() > 0) {
      return;
    }
  }
  throw _AtlasBadParse();
}

template<int dim>
inline AtlasOutType Line<dim>::toAtlas() const
{
  Atlas::Message::ListType points;
  for (const_iterator I = m_points.begin(); I != m_points.end(); ++I) 
  {
    points.push_back(I->toAtlas());
  }
  Atlas::Message::MapType map;
  map.insert(Atlas::Message::MapType::value_type("points", points));
  return map;
}

template<int dim>
inline Line<dim>::Line(const AtlasInType& a) {
  fromAtlas(a);
}

template<int dim>
inline void RotBox<dim>::fromAtlas(const AtlasInType& a)
{
  const Atlas::Message::Element& message(a);
  if (message.isMap()) {
    const Atlas::Message::MapType& shapeElement(message.asMap());
    // Get rotbox's position
    auto shape_I = shapeElement.find("point");
    if (shape_I != shapeElement.end()) {
      const Atlas::Message::Element& shapePointElem(shape_I->second);
      Point<dim> shapePoint;
      shapePoint.fromAtlas(shapePointElem);
      // Get rotbox's vector
      shape_I = shapeElement.find("size");
      if (shape_I != shapeElement.end()) {
        const Atlas::Message::Element& shapeVectorElem(shape_I->second);
        Vector<dim> shapeVector;
        shapeVector.fromAtlas(shapeVectorElem);
        m_corner0 = shapePoint;
        m_size = shapeVector;
        m_orient = RotMatrix<dim>().identity(); //TODO: parse rotation matrix (is it needed?)
        return;
      }
    }
  }
  throw _AtlasBadParse();
}

template<int dim>
inline AtlasOutType RotBox<dim>::toAtlas() const
{
  Atlas::Message::MapType map;
  map.insert(Atlas::Message::MapType::value_type("point", m_corner0.toAtlas()));
  map.insert(Atlas::Message::MapType::value_type("size", m_size.toAtlas()));
  //TODO: also add the rotmatrix
  return map;
}

template<int dim>
inline RotBox<dim>::RotBox(const AtlasInType& a) {
  fromAtlas(a);
}

} // namespace WFMath

#endif // WFMATH_ATLAS_CONV_H
0707010000001E000081A40000000200000002000000015D8693EF000007A9000000000000000000000000000000000000002D00000000wfmath-1569100783.d0f8a54/wfmath/axisbox.cpp// vector.cpp (Vector<> implementation)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Alistair Riddoch
// Created: 2009-01-12

#include "axisbox_funcs.h"

#include "rotmatrix.h"
#include "vector.h"

#include <vector>

#include <cmath>

namespace WFMath {

template class AxisBox<3>;
template class AxisBox<2>;

template bool Intersection<3>(const AxisBox<3>&, const AxisBox<3>&, AxisBox<3>&);
template bool Intersection<2>(const AxisBox<2>&, const AxisBox<2>&, AxisBox<2>&);

template AxisBox<3> Union<3>(const AxisBox<3> &, const AxisBox<3> &);
template AxisBox<2> Union<2>(const AxisBox<2>&, const AxisBox<2>&);

template AxisBox<3> BoundingBox<3, std::vector>(const std::vector<AxisBox<3>, std::allocator<AxisBox<3> > > &);
template AxisBox<2> BoundingBox<2, std::vector>(const std::vector<AxisBox<2>, std::allocator<AxisBox<2> > > &);

template AxisBox<3> BoundingBox<3, std::vector>(const std::vector<Point<3>, std::allocator<Point<3> > >&);
template AxisBox<2> BoundingBox<2, std::vector>(const std::vector<Point<2>, std::allocator<Point<2> > >&);

}
0707010000001F000081A40000000200000002000000015D8693EF00001DB2000000000000000000000000000000000000002B00000000wfmath-1569100783.d0f8a54/wfmath/axisbox.h// axisbox.h (An axis-aligned box)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

// The implementation of this class is based on the geometric
// parts of the Tree and Placement classes from stage/shepherd/sylvanus

#ifndef WFMATH_AXIS_BOX_H
#define WFMATH_AXIS_BOX_H

#include <wfmath/intersect_decls.h>
#include <wfmath/point.h>

#include <iosfwd>

namespace WFMath {

template<int dim>
bool Intersection(const AxisBox<dim>& a1, const AxisBox<dim>& a2, AxisBox<dim>& out);
template<int dim>
AxisBox<dim> Union(const AxisBox<dim>& a1, const AxisBox<dim>& a2);

template<int dim>
std::ostream& operator<<(std::ostream& os, const AxisBox<dim>& m);
template<int dim>
std::istream& operator>>(std::istream& is, AxisBox<dim>& m);

/// Get the axis-aligned bounding box for a set of boxes
template<int dim, template<class, class> class container>
AxisBox<dim> BoundingBox(const container<AxisBox<dim>, std::allocator<AxisBox<dim> > >& c);

/// Get the axis-aligned bounding box for a set of points
template<int dim, template<class, class> class container>
AxisBox<dim> BoundingBox(const container<Point<dim>, std::allocator<Point<dim> > >& c);

/// A dim dimensional axis-aligned box
/**
 * This class implements the full shape interface, as described in
 * the fake class Shape, with the exception of the rotation functions.
 **/
template<int dim = 3>
class AxisBox
{
 public:
  /// Construct an uninitialized box
  AxisBox() : m_low(), m_high() {}
  /// Construct a box with opposite corners p1 and p2
  AxisBox(const Point<dim>& p1, const Point<dim>& p2, bool ordered = false) :
    m_low(), m_high()
    {setCorners(p1, p2, ordered);}
  /// Construct a copy of a box
  AxisBox(const AxisBox& a) : m_low(a.m_low), m_high(a.m_high) {}
  /// Construct a box from an object passed by Atlas
  explicit AxisBox(const AtlasInType& a);

friend std::ostream& operator<< <dim>(std::ostream& os, const AxisBox& a);
  friend std::istream& operator>> <dim>(std::istream& is, AxisBox& a);

/// Create an Atlas object from the box
  AtlasOutType toAtlas() const;
  /// Set the box's value to that given by an Atlas object
  void fromAtlas(const AtlasInType& a);

AxisBox& operator=(const AxisBox& a)
  {m_low = a.m_low; m_high = a.m_high; return *this;}

bool isEqualTo(const AxisBox& b, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const;
  bool operator==(const AxisBox& a) const	{return isEqualTo(a);}
  bool operator!=(const AxisBox& a) const	{return !isEqualTo(a);}

bool isValid() const {return m_low.isValid() && m_high.isValid();}

// Descriptive characteristics

size_t numCorners() const {return 1 << dim;}
  Point<dim> getCorner(size_t i) const;
  Point<dim> getCenter() const {return Midpoint(m_low, m_high);}

/// Get a reference to corner 0
  const Point<dim>& lowCorner() const {return m_low;}
  Point<dim>& lowCorner() {return m_low;}
  /// Get a reference to corner (2^dim)-1
  const Point<dim>& highCorner() const {return m_high;}
  Point<dim>& highCorner() {return m_high;}

/// Get the lower bound of the box on the i'th axis
  CoordType lowerBound(const int axis) const	{return m_low[axis];}
  /// Get the upper bound of the box on the i'th axis
  CoordType upperBound(const int axis) const	{return m_high[axis];}

/// Set the box to have opposite corners p1 and p2
  /**
   * The 'ordered' variable may be set to true if p1[i] <= p2[i] for all
   * i. It is always safe to leave 'ordered' as false, it is a speed
   * optimization primarily intended for use inside the library.
   **/
  AxisBox& setCorners(const Point<dim>& p1, const Point<dim>& p2,
  bool ordered = false);

// Movement functions

AxisBox& shift(const Vector<dim>& v)
  {m_low += v; m_high += v; return *this;}
  AxisBox& moveCornerTo(const Point<dim>& p, size_t corner)
  {return shift(p - getCorner(corner));}
  AxisBox& moveCenterTo(const Point<dim>& p)
  {return shift(p - getCenter());}

// No rotation functions, this shape can't rotate

// Intersection functions

AxisBox boundingBox() const {return *this;}
  Ball<dim> boundingSphere() const;
  Ball<dim> boundingSphereSloppy() const;

AxisBox toParentCoords(const Point<dim>& origin) const
        {return AxisBox(m_low.toParentCoords(origin), m_high.toParentCoords(origin), true);}
  AxisBox toParentCoords(const AxisBox<dim>& coords) const
        {return AxisBox(m_low.toParentCoords(coords), m_high.toParentCoords(coords), true);}

// toLocal is just like toParent, expect we reverse the order of
  // translation and rotation and use the opposite sense of the rotation
  // matrix

AxisBox toLocalCoords(const Point<dim>& origin) const
        {return AxisBox(m_low.toLocalCoords(origin), m_high.toLocalCoords(origin), true);}
  AxisBox toLocalCoords(const AxisBox<dim>& coords) const
        {return AxisBox(m_low.toLocalCoords(coords), m_high.toLocalCoords(coords), true);}

/// Return true if the boxes intersect, and set 'out' to their intersection
  friend bool Intersection<dim>(const AxisBox& a1, const AxisBox& a2, AxisBox& out);
  /// Get the minimal box that contains a1 and a2
  friend AxisBox Union<dim>(const AxisBox& a1, const AxisBox& a2);

friend bool Intersect<dim>(const AxisBox& b, const Point<dim>& p, bool proper);
  friend bool Contains<dim>(const Point<dim>& p, const AxisBox& b, bool proper);

friend bool Intersect<dim>(const AxisBox& b1, const AxisBox& b2, bool proper);
  friend bool Contains<dim>(const AxisBox& outer, const AxisBox& inner, bool proper);

friend bool Intersect<dim>(const Ball<dim>& b, const AxisBox& a, bool proper);
  friend bool Contains<dim>(const Ball<dim>& b, const AxisBox& a, bool proper);
  friend bool Contains<dim>(const AxisBox& a, const Ball<dim>& b, bool proper);

friend bool Intersect<dim>(const Segment<dim>& s, const AxisBox& b, bool proper);
  friend bool Contains<dim>(const Segment<dim>& s, const AxisBox& b, bool proper);

friend bool Intersect<dim>(const RotBox<dim>& r, const AxisBox& b, bool proper);
  friend bool Contains<dim>(const RotBox<dim>& r, const AxisBox& b, bool proper);
  friend bool Contains<dim>(const AxisBox& b, const RotBox<dim>& r, bool proper);

friend bool Intersect<dim>(const Polygon<dim>& p, const AxisBox& b, bool proper);
  friend bool Contains<dim>(const Polygon<dim>& p, const AxisBox& b, bool proper);
  friend bool Contains<dim>(const AxisBox& b, const Polygon<dim>& p, bool proper);

private:

Point<dim> m_low, m_high;
};

template<int dim>
inline bool AxisBox<dim>::isEqualTo(const AxisBox<dim>& b, CoordType epsilon) const
{
  return Equal(m_low, b.m_low, epsilon)
       && Equal(m_high, b.m_high, epsilon);
}

} // namespace WFMath

#endif  // WFMATH_AXIS_BOX_H
07070100000020000081A40000000200000002000000015D8693EF000014EA000000000000000000000000000000000000003100000000wfmath-1569100783.d0f8a54/wfmath/axisbox_funcs.h// axisbox_funcs.h (Axis-aligned box implementation)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

// The implementation of this class is based on the geometric
// parts of the Tree and Placement classes from stage/shepherd/sylvanus

#ifndef WFMATH_AXIS_BOX_FUNCS_H
#define WFMATH_AXIS_BOX_FUNCS_H

#include <wfmath/axisbox.h>

#include <wfmath/point.h>
#include <wfmath/ball.h>

namespace WFMath {

template<int dim>
bool Intersection(const AxisBox<dim>& a1, const AxisBox<dim>& a2, AxisBox<dim>& out)
{
  for(int i = 0; i < dim; ++i) {
    out.m_low[i] = FloatMax(a1.m_low[i], a2.m_low[i]);
    out.m_high[i] = FloatMin(a1.m_high[i], a2.m_high[i]);
    if(out.m_low[i] > out.m_high[i])
      return false;
  }

out.m_low.setValid(a1.m_low.isValid() && a2.m_low.isValid());
  out.m_high.setValid(a1.m_high.isValid() && a2.m_high.isValid());

return true;
}

template<int dim>
AxisBox<dim> Union(const AxisBox<dim>& a1, const AxisBox<dim>& a2)
{
  AxisBox<dim> out;

for(int i = 0; i < dim; ++i) {
    out.m_low[i] = FloatMin(a1.m_low[i], a2.m_low[i]);
    out.m_high[i] = FloatMax(a1.m_high[i], a2.m_high[i]);
  }

out.m_low.setValid(a1.m_low.isValid() && a2.m_low.isValid());
  out.m_high.setValid(a1.m_high.isValid() && a2.m_high.isValid());

return out;
}

template<int dim>
AxisBox<dim>& AxisBox<dim>::setCorners(const Point<dim>& p1, const Point<dim>& p2,
				       bool ordered)
{
  if(ordered) {
    m_low = p1;
    m_high = p2;
    return *this;
  }

for(int i = 0; i < dim; ++i) {
    if(p1[i] > p2[i]) {
      m_low[i] = p2[i];
      m_high[i] = p1[i];
    }
    else {
      m_low[i] = p1[i];
      m_high[i] = p2[i];
    }
  }

m_low.setValid();
  m_high.setValid();

return *this;
}

template<int dim>
Point<dim> AxisBox<dim>::getCorner(size_t i) const
{
  if(i < 1)
    return m_low;
  if(i >= (1 << dim) - 1)
    return m_high;

Point<dim> out;

for(int j = 0; j < dim; ++j)
    out[j] = (i & (1 << j)) ? m_high[j] : m_low[j];

out.setValid(m_low.isValid() && m_high.isValid());

return out;
}

template<int dim>
inline Ball<dim> AxisBox<dim>::boundingSphere() const
{
  return Ball<dim>(getCenter(), Distance(m_low, m_high) / 2);
}

template<int dim>
inline Ball<dim> AxisBox<dim>::boundingSphereSloppy() const
{
  return Ball<dim>(getCenter(), SloppyDistance(m_low, m_high) / 2);
}

template<int dim, template<class, class> class container>
AxisBox<dim> BoundingBox(const container<AxisBox<dim>, std::allocator<AxisBox<dim> > >& c)
{
  typename container<AxisBox<dim>, std::allocator<AxisBox<dim> > >::const_iterator i = c.begin(), end = c.end();

if(i == end) {
    return AxisBox<dim>();
  }

Point<dim> low = i->lowCorner(), high = i->highCorner();
  bool low_valid = low.isValid(), high_valid = high.isValid();

while(++i != end) {
    const Point<dim> &new_low = i->lowCorner(), &new_high = i->highCorner();
    low_valid = low_valid && new_low.isValid();
    high_valid = high_valid && new_high.isValid();
    for(int j = 0; j < dim; ++j) {
      low[j] = FloatMin(low[j], new_low[j]);
      high[j] = FloatMax(high[j], new_high[j]);
    }
  }

low.setValid(low_valid);
  high.setValid(high_valid);

return AxisBox<dim>(low, high, true);
}

template<int dim, template<class, class> class container>
AxisBox<dim> BoundingBox(const container<Point<dim>, std::allocator<Point<dim> > >& c)
{
  typename container<Point<dim>, std::allocator<Point<dim> > >::const_iterator i = c.begin(), end = c.end();

if(i == end) {
    return AxisBox<dim>();
  }

Point<dim> low = *i, high = *i;
  bool valid = i->isValid();

while(++i != end) {
    valid = valid && i->isValid();
    for(int j = 0; j < dim; ++j) {
      low[j] = FloatMin(low[j], (*i)[j]);
      high[j] = FloatMax(high[j], (*i)[j]);
    }
  }

low.setValid(valid);
  high.setValid(valid);

return AxisBox<dim>(low, high, true);
}

// This is here, instead of defined in the class, to
// avoid include order problems

template<int dim>
inline AxisBox<dim> Point<dim>::boundingBox() const
{
  return AxisBox<dim>(*this, *this, true);
}

template<int dim>
Point<dim> Point<dim>::toParentCoords(const AxisBox<dim>& coords) const
{
  return coords.lowCorner() + (*this - Point().setToOrigin());
}

template<int dim>
Point<dim> Point<dim>::toLocalCoords(const AxisBox<dim>& coords) const
{
  return Point().setToOrigin() + (*this - coords.lowCorner());
}

} // namespace WFMath

#endif  // WFMATH_AXIS_BOX_FUNCS_H
07070100000021000081A40000000200000002000000015D8693EF00000BA7000000000000000000000000000000000000002A00000000wfmath-1569100783.d0f8a54/wfmath/ball.cpp// vector.cpp (Vector<> implementation)
//
//  The WorldForge Project
//  Copyright (C) 2011  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Alistair Riddoch
// Created: 2011-1-27

// Extensive amounts of this material come from the Vector2D
// and Vector3D classes from stage/math, written by Bryce W.
// Harrington, Kosh, and Jari Sundell (Rakshasa).

#include "ball_funcs.h"
#include "miniball_funcs.h"
#include "vector.h"

#include <vector>
#include <cmath>

namespace WFMath {

template<> Ball<3>& Ball<3>::rotateCorner(const Quaternion&, size_t)
{
  return *this;
}

template<> Ball<3>& Ball<3>::rotateCenter(const Quaternion&)
{
  return *this;
}

template<> Ball<3>& Ball<3>::rotatePoint(const Quaternion& q, const Point<3>& p)
{
  m_center.rotate(q, p); return *this;
}

template<> Ball<3> Ball<3>::toParentCoords(const Point<3>& origin,
                                           const Quaternion& rotation) const
{
  return Ball<3>(m_center.toParentCoords(origin, rotation), m_radius);
}

template<> Ball<3> Ball<3>::toLocalCoords(const Point<3>& origin,
                                          const Quaternion& rotation) const
{
  return Ball<3>(m_center.toLocalCoords(origin, rotation), m_radius);
}

template Ball<2> BoundingSphere<2, std::vector>(std::vector<Point<2>,
                                                std::allocator<Point<2> > > const&);

template Ball<2> BoundingSphereSloppy<2, std::vector>(std::vector<Point<2>,
                                                      std::allocator<Point<2> > > const&);

template Ball<3> BoundingSphere<3, std::vector>(std::vector<Point<3>,
                                                std::allocator<Point<3> > > const&);

template Ball<3> BoundingSphereSloppy<3, std::vector>(std::vector<Point<3>,
                                                      std::allocator<Point<3> > > const&);

template Ball<2> Point<2>::boundingSphere() const;
template Ball<2> Point<2>::boundingSphereSloppy() const;

template Ball<3> Point<3>::boundingSphere() const;
template Ball<3> Point<3>::boundingSphereSloppy() const;

template class Ball<2>;
template class Ball<3>;

}
07070100000022000081A40000000200000002000000015D8693EF00001E0B000000000000000000000000000000000000002800000000wfmath-1569100783.d0f8a54/wfmath/ball.h// ball.h (A n-dimensional ball)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_BALL_H
#define WFMATH_BALL_H

#include <wfmath/point.h>
#include <wfmath/intersect_decls.h>

namespace WFMath {

template<int dim> class Ball;

/// get the minimal bounding sphere for a set of points
template<int dim, template<class, class> class container>
Ball<dim> BoundingSphere(const container<Point<dim>, std::allocator<Point<dim> > >& c);
/// get a bounding sphere for a set of points
template<int dim, template<class, class> class container>
Ball<dim> BoundingSphereSloppy(const container<Point<dim>, std::allocator<Point<dim> > >& c);

template<int dim>
std::ostream& operator<<(std::ostream& os, const Ball<dim>& m);
template<int dim>
std::istream& operator>>(std::istream& is, Ball<dim>& m);

/// A dim dimensional ball
/**
 * This class implements the full shape interface, as described in
 * the fake class Shape.
 *
 * This class is called Ball<> instead of Sphere to be more in tune
 * with the usual mathematical naming conventions, where a ball is
 * a filled object, while a sphere is just the outer shell. It also
 * helps that a Ball<n> corresponds to an n-ball, while a Sphere<n>
 * would correspond to an (n-1)-sphere.
 **/
template<int dim = 3>
class Ball
{
 public:
  /// construct an uninitialized ball
  Ball() : m_center(), m_radius(0.f) {}
  /// construct a ball with the given center and radius
  Ball(const Point<dim>& center, CoordType radius)
  : m_center(center), m_radius(radius) { if (radius < 0) m_center.setValid(false); }
  /// construct a copy of a ball
  Ball(const Ball& b) : m_center(b.m_center), m_radius(b.m_radius) {}
  /// Construct a ball from an object passed by Atlas
  explicit Ball(const AtlasInType& a);

~Ball() = default;

friend std::ostream& operator<< <dim>(std::ostream& os, const Ball& b);
  friend std::istream& operator>> <dim>(std::istream& is, Ball& b);

/// Create an Atlas object from the box
  AtlasOutType toAtlas() const;
  /// Set the box's value to that given by an Atlas object
  void fromAtlas(const AtlasInType& a);

Ball& operator=(const Ball& b)
  {m_radius = b.m_radius; m_center = b.m_center; return *this;}

bool isEqualTo(const Ball& b, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const;

bool operator==(const Ball& b) const	{return isEqualTo(b);}
  bool operator!=(const Ball& b) const	{return !isEqualTo(b);}

bool isValid() const {return m_center.isValid();}

// Descriptive characteristics

size_t numCorners() const {return 0;}
  // This next function exists so that Ball can be used by code
  // that finds the number of corners with numCorners(), and does something
  // with each corner with getCorner(). No idea how useful that is, but
  // it's not a particularly complicated function to write.
  Point<dim> getCorner(size_t) const {return m_center;}
  Point<dim> getCenter() const {return m_center;}

/// get the center of the ball
  const Point<dim>& center() const {return m_center;}
  /// get the center of the ball
  Point<dim>& center() {return m_center;}
  /// get the radius of the ball
  CoordType radius() const {return m_radius;}
  /// get the radius of the ball
  CoordType& radius() {return m_radius;}

// Movement functions

Ball& shift(const Vector<dim>& v) {m_center += v; return *this;}
  Ball& moveCornerTo(const Point<dim>&, size_t) {return *this;}
  Ball& moveCenterTo(const Point<dim>& p) {m_center = p; return *this;}

Ball& rotateCorner(const RotMatrix<dim>&, size_t) {return *this;}
  Ball& rotateCenter(const RotMatrix<dim>&) {return *this;}
  Ball& rotatePoint(const RotMatrix<dim>& m, const Point<dim>& p)
  {m_center.rotate(m, p); return *this;}

// 3D rotation function
  Ball& rotateCorner(const Quaternion&, size_t corner);
  Ball& rotateCenter(const Quaternion&);
  Ball& rotatePoint(const Quaternion& q, const Point<dim>& p);

// Intersection functions

AxisBox<dim> boundingBox() const;
  Ball boundingSphere() const		{return *this;}
  Ball boundingSphereSloppy() const	{return *this;}

Ball toParentCoords(const Point<dim>& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
        {return Ball(m_center.toParentCoords(origin, rotation), m_radius);}
  Ball toParentCoords(const AxisBox<dim>& coords) const
        {return Ball(m_center.toParentCoords(coords), m_radius);}
  Ball toParentCoords(const RotBox<dim>& coords) const
        {return Ball(m_center.toParentCoords(coords), m_radius);}

// toLocal is just like toParent, expect we reverse the order of
  // translation and rotation and use the opposite sense of the rotation
  // matrix

Ball toLocalCoords(const Point<dim>& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
        {return Ball(m_center.toLocalCoords(origin, rotation), m_radius);}
  Ball toLocalCoords(const AxisBox<dim>& coords) const
        {return Ball(m_center.toLocalCoords(coords), m_radius);}
  Ball toLocalCoords(const RotBox<dim>& coords) const
        {return Ball(m_center.toLocalCoords(coords), m_radius);}

// 3D only
  Ball toParentCoords(const Point<dim>& origin, const Quaternion& rotation) const;
  Ball toLocalCoords(const Point<dim>& origin, const Quaternion& rotation) const;

friend bool Intersect<dim>(const Ball& b, const Point<dim>& p, bool proper);
  friend bool Contains<dim>(const Point<dim>& p, const Ball& b, bool proper);

friend bool Intersect<dim>(const Ball& b, const AxisBox<dim>& a, bool proper);
  friend bool Contains<dim>(const Ball& b, const AxisBox<dim>& a, bool proper);
  friend bool Contains<dim>(const AxisBox<dim>& a, const Ball& b, bool proper);

friend bool Intersect<dim>(const Ball& b1, const Ball& b2, bool proper);
  friend bool Contains<dim>(const Ball& outer, const Ball& inner, bool proper);

friend bool Intersect<dim>(const Segment<dim>& s, const Ball& b, bool proper);
  friend bool Contains<dim>(const Segment<dim>& s, const Ball& b, bool proper);

friend bool Intersect<dim>(const RotBox<dim>& r, const Ball& b, bool proper);
  friend bool Contains<dim>(const RotBox<dim>& r, const Ball& b, bool proper);
  friend bool Contains<dim>(const Ball& b, const RotBox<dim>& r, bool proper);

friend bool Intersect<dim>(const Polygon<dim>& p, const Ball& b, bool proper);
  friend bool Contains<dim>(const Polygon<dim>& p, const Ball& b, bool proper);
  friend bool Contains<dim>(const Ball& b, const Polygon<dim>& p, bool proper);

private:

Point<dim> m_center;
  CoordType m_radius;
};

template<int dim>
inline bool Ball<dim>::isEqualTo(const Ball<dim>& b, CoordType epsilon) const
{
  return Equal(m_center, b.m_center, epsilon)
      && Equal(m_radius, b.m_radius, epsilon);
}

} // namespace WFMath

#endif  // WFMATH_BALL_H
07070100000023000081A40000000200000002000000015D8693EF00001304000000000000000000000000000000000000002E00000000wfmath-1569100783.d0f8a54/wfmath/ball_funcs.h// ball_funcs.h (n-dimensional ball implementation)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_BALL_FUNCS_H
#define WFMATH_BALL_FUNCS_H

#include <wfmath/ball.h>

#include <wfmath/axisbox.h>
#include <wfmath/miniball.h>

#include <cassert>

namespace WFMath {

template<int dim>
AxisBox<dim> Ball<dim>::boundingBox() const
{
  Point<dim> p_low, p_high;

for(int i = 0; i < dim; ++i) {
    p_low[i] = m_center[i] - m_radius;
    p_high[i] = m_center[i] + m_radius;
  }

bool valid = m_center.isValid();

p_low.setValid(valid);
  p_high.setValid(valid);

return AxisBox<dim>(p_low, p_high, true);
}

template<int dim, template<class, class> class container>
Ball<dim> BoundingSphere(const container<Point<dim>, std::allocator<Point<dim> > >& c)
{
  _miniball::Miniball<dim> m;
  _miniball::Wrapped_array<dim> w;

typename container<Point<dim>, std::allocator<Point<dim> > >::const_iterator i, end = c.end();
  bool valid = true;

for(i = c.begin(); i != end; ++i) {
    valid = valid && i->isValid();
    for(int j = 0; j < dim; ++j)
      w[j] = (*i)[j];
    m.check_in(w);
  }

m.build();

#ifndef NDEBUG
  double dummy;
#endif
  assert("Check that bounding sphere is good to library accuracy" &&
         m.accuracy(dummy) < numeric_constants<CoordType>::epsilon());

w = m.center();
  Point<dim> center;

for(int j = 0; j < dim; ++j)
    center[j] = w[j];

center.setValid(valid);

return Ball<dim>(center, std::sqrt(m.squared_radius()));
}

template<int dim, template<class, class> class container>
Ball<dim> BoundingSphereSloppy(const container<Point<dim>, std::allocator<Point<dim> > >& c)
{
  // This is based on the algorithm given by Jack Ritter
  // in Volume 2, Number 4 of Ray Tracing News
  // <http://www.acm.org/tog/resources/RTNews/html/rtnews7b.html>

typename container<Point<dim>, std::allocator<Point<dim> > >::const_iterator i = c.begin(),
						end = c.end();
  if (i == end) {
    return Ball<dim>();
  }

CoordType min[dim], max[dim];
  typename container<Point<dim>, std::allocator<Point<dim> > >::const_iterator min_p[dim], max_p[dim];
  bool valid = i->isValid();

for(int j = 0; j < dim; ++j) {
    min[j] = max[j] = (*i)[j];
    min_p[j] = max_p[j] = i;
  }

while(++i != end) {
    valid = valid && i->isValid();
    for(int j = 0; j < dim; ++j) {
      if(min[j] > (*i)[j]) {
        min[j] = (*i)[j];
        min_p[j] = i;
      }
      if(max[j] < (*i)[j]) {
        max[j] = (*i)[j];
        max_p[j] = i;
      }
    }
  }

CoordType span = -1;
  int direction = -1;

for(int j = 0; j < dim; ++j) {
    CoordType new_span = max[j] - min[j];
    if(new_span > span) {
      span = new_span;
      direction = j;
    }
  }

assert("Have a direction of maximum size" && direction != -1);

Point<dim> center = Midpoint(*(min_p[direction]), *(max_p[direction]));
  CoordType dist = SloppyDistance(*(min_p[direction]), center);

for(i = c.begin(); i != end; ++i) {
    if(i == min_p[direction] || i == max_p[direction])
      continue; // We already have these

CoordType new_dist = SloppyDistance(*i, center);

if(new_dist > dist) {
      CoordType delta_dist = (new_dist - dist) / 2;
      // Even though new_dist may be too large, delta_dist / new_dist
      // always gives enough of a shift to include the new point.
      center += (*i - center) * delta_dist / new_dist;
      dist += delta_dist;
      assert("Shifted ball contains new point" &&
             SquaredDistance(*i, center) <= dist * dist);
    }
  }

center.setValid(valid);

return Ball<dim>(center, dist);
}

// These two are here, instead of defined in the class, to
// avoid include order problems

template<int dim>
inline Ball<dim> Point<dim>::boundingSphere() const
{
  return Ball<dim>(*this, 0);
}

template<int dim>
inline Ball<dim> Point<dim>::boundingSphereSloppy() const
{
  return Ball<dim>(*this, 0);
}

} // namespace WFMath

#endif  // WFMATH_BALL_FUNCS_H
07070100000024000081A40000000200000002000000015D8693EF00000524000000000000000000000000000000000000002F00000000wfmath-1569100783.d0f8a54/wfmath/ball_test.cpp// vector_test.cpp (Vector<> test functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Alistair Riddoch
// Created: 2011-01-26

#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include "ball.h"

#include <cassert>

using namespace WFMath;

int main()
{
  Ball<2> b1(Point<2>(0,0), 1);

assert(b1.isValid());

Ball<2> b2(Point<2>(0,0), -1);

assert(!b2.isValid());

return 0;
}
07070100000025000081A40000000200000002000000015D8693EF00000970000000000000000000000000000000000000002900000000wfmath-1569100783.d0f8a54/wfmath/basis.h// basis.h (Cartesian/polar/spherical conversion for the WFMath library)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-15

#ifndef WFMATH_BASIS_H
#define WFMATH_BASIS_H

#include <wfmath/const.h>

#include <cmath>

namespace WFMath {

// These are used internally in point.cpp and vector.cpp. This header
// file is not included in any other, nor are these functions exported,
// so we don't install this in $(includedir)/wfmath.

// Expects (r, theta) for polar, (x, y) for cart
inline void _CartToPolar(const CoordType *in, CoordType *out)
{
  out[0] = std::sqrt(in[0] * in[0] + in[1] * in[1]);
  out[1] = std::atan2(in[0], in[1]);
}

// Expects (r, theta) for polar, (x, y) for cart
inline void _PolarToCart(const CoordType *in, CoordType *out)
{
  out[0] = in[0] * std::cos(in[1]);
  out[1] = in[0] * std::sin(in[1]);
}

// Expects (r, theta, phi) for spherical, (x, y, z) for cart
inline void _CartToSpherical(const CoordType *in, CoordType *out)
{
  out[0] = std::sqrt(in[0] * in[0] + in[1] * in[1] + in[2] * in[2]);
  out[1] = std::atan2(in[2], std::sqrt(in[0] * in[0] + in[1] * in[1]));
  out[2] = std::atan2(in[0], in[1]);
}

// Expects (r, theta, phi) for spherical, (x, y, z) for cart
inline void _SphericalToCart(const CoordType *in, CoordType *out)
{
  CoordType stheta = std::sin(in[1]);

out[0] = in[0] * stheta * std::cos(in[2]);
  out[1] = in[0] * stheta * std::sin(in[2]);
  out[2] = in[0] * std::cos(in[1]);
}

} // namespace WFMath

#endif // WFMATH_BASIS_H
07070100000026000081A40000000200000002000000015D8693EF00000305000000000000000000000000000000000000003100000000wfmath-1569100783.d0f8a54/wfmath/bc_sloppy_mag_3print "This is a bc script which computes sloppyMagMax for Vector<3>.\n"
print "You have to run it with the -l option to take advantage of the\n"
print "math library.\n"

scale = 50

p = sqrt(2) - 1
q = sqrt(3) + 1 - (2 * sqrt(2))

print "p = ", p, "\n"
print "q = ", q, "\n"

r = p / (-2 * q)
f = (q - 1) / (3 * q)

print "r = ", r, "\n"
print "f = ", f, "\n"

s = sqrt((f^3) + (r^2))

print "s = ", s, "\n"

/* Cube roots */

z1 = e(l(r + s) / 3)
z2 = -e(l(s - r) / 3)

print "z1 = ", z1, "\n"
print "z2 = ", z2, "\n"

test = e((l(e(3)) / 3) - 1)

print "Test? ", test, "\n"

point = z1 + z2

print "point = ", point, "\n"

val = 1 / sqrt((1 + (2 * (point^2)))/((1 + (2 * p * point) + (q * (point^2)))^2))

print "val = ", val, "\n"
print "sqrt(val) = ", sqrt(val), "\n"
07070100000027000081A40000000200000002000000015D8693EF00000E58000000000000000000000000000000000000002B00000000wfmath-1569100783.d0f8a54/wfmath/const.cpp// const.cpp (basic comparison functions)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001, 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include <wfmath/const.h>

#include <cmath>

#include <cassert>

// Implementation of IsFloatEqual() is borrowed from Jesse Jones (thanks!).
// The comments also belong to him.  The names have been changed
// to protect the innocent....
//
// Comparing floating point numbers for equality is tricky because
// the limited precision of the hardware introduces small errors
// so that two numbers that should compare equal don't. So what
// we do is consider the numbers equal if their difference is less
// than some epsilon value. But choosing this epsilon is also tricky
// because if the numbers are large epsilon should also be large,
// and if the numbers are very small the epsilon must be even smaller.
// To get around this we'll use a technique from Knuth's "Seminumerical
// Algorithms" section 4.2.2 and scale epsilon by the exponent of
// one of the specified numbers.
//
//---------------------------------------------------------------

namespace WFMath {

bool Equal(double x1, double x2, double epsilon)
{
    // If the difference between the numbers is smaller than the
    // scaled epsilon we'll consider the numbers to be equal.

return std::fabs(x1 - x2) <= _ScaleEpsilon(x1, x2, epsilon);
}

bool Equal(float x1, float x2, float epsilon)
{
    // If the difference between the numbers is smaller than the
    // scaled epsilon we'll consider the numbers to be equal.

return std::fabs(x1 - x2) <= _ScaleEpsilon(x1, x2, epsilon);
}

double _ScaleEpsilon(double x1, double x2, double epsilon)
{
    // Get the exponent of the smaller of the two numbers (using the
    // smaller of the two gives us a tighter epsilon value).
    int exponent;
    (void) std::frexp(std::fabs(x1) < std::fabs(x2) ? x1 : x2, &exponent);

// Scale epsilon by the exponent.
    return std::ldexp(epsilon, exponent);
}

float _ScaleEpsilon(float x1, float x2, float epsilon)
{
    // Get the exponent of the smaller of the two numbers (using the
    // smaller of the two gives us a tighter epsilon value).
    int exponent;
    (void) std::frexp(std::fabs(x1) < std::fabs(x2) ? x1 : x2, &exponent);

// Scale epsilon by the exponent.
    return std::ldexp(epsilon, exponent);
}

CoordType _ScaleEpsilon(const CoordType* x1, const CoordType* x2,
                        int length, CoordType epsilon)
{
  assert(length > 0);

float max1 = 0, max2 = 0;

for(int i = 0; i < length; ++i) {
    float val1 = std::fabs(x1[i]), val2 = std::fabs(x2[i]);
    if(val1 > max1)
      max1 = val1;
    if(val2 > max2)
      max2 = val2;
  }

return _ScaleEpsilon(max1, max2, epsilon);
}

}
07070100000028000081A40000000200000002000000015D8693EF00001733000000000000000000000000000000000000002900000000wfmath-1569100783.d0f8a54/wfmath/const.h// const.h (Defined constants for the WFMath library)
//
//  The WorldForge Project
//  Copyright (C) 2001, 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#ifndef WFMATH_CONST_H
#define WFMATH_CONST_H

#include <limits>

#ifdef _MSC_VER
  #if _MSC_VER < 1500
    #error "You are using an older version of MSVC++ with extremely poor"
    #error "template support. Please use at least version 2008,"
    #error "or try a different compiler."
  #endif
#endif

/// Generic library namespace
namespace WFMath {

// WFMath::Foo::toAtlas() has to return a definite type,
// we deal with supporting both 0.4 and 0.6 by forward declaring
// types which we define in the AtlasConv header
class AtlasInType;
class AtlasOutType;

template<int dim> class AxisBox;
template<int dim> class Ball;
template<int dim> class Point;
template<int dim> class Polygon;
template<int dim> class RotBox;
template<int dim> class RotMatrix;
template<int dim> class Segment;
template<int dim> class Vector;
class Quaternion;

// Constants

/// Determines how close to machine precision the library tries to come.
#define WFMATH_PRECISION_FUDGE_FACTOR 30

template<typename FloatType>
struct numeric_constants
{
  /// The constant pi
  static FloatType pi();
  /// The square root of pi
  static FloatType sqrt_pi();
  /// The natural logarithm of pi
  static FloatType log_pi();
  /// The square root of 2
  static FloatType sqrt2();
  /// The square root of 3
  static FloatType sqrt3();
  /// The natural logarithm of 2
  static FloatType log2();
  /// This is the attempted precision of the library.
  static FloatType epsilon();
};

template<>
struct numeric_constants<float>
{
  static float pi() {
    return 3.14159265358979323846264338327950288419716939937508F;
  }
  static float sqrt_pi() {
    return 1.77245385090551602729816748334114518279754945612237F;
  }
  static float log_pi() {
    return 1.14472988584940017414342735135305871164729481291530F;
  }
  static float sqrt2() {
    return 1.41421356237309504880168872420969807856967187537693F;
  }
  static float sqrt3() {
    return 1.73205080756887729352744634150587236694280525381037F;
  }
  static float log2() {
    return 0.69314718055994530941723212145817656807550013436025F;
  }
  static float epsilon() {
    return (WFMATH_PRECISION_FUDGE_FACTOR *
            std::numeric_limits<float>::epsilon());
  }
};

template<>
struct numeric_constants<double>
{
  static double pi() {
    return 3.14159265358979323846264338327950288419716939937508;
  }
  static double sqrt_pi() {
    return 1.77245385090551602729816748334114518279754945612237;
  }
  static double log_pi() {
    return 1.14472988584940017414342735135305871164729481291530;
  }
  static double sqrt2() {
    return 1.41421356237309504880168872420969807856967187537693;
  }
  static double sqrt3() {
    return 1.73205080756887729352744634150587236694280525381037;
  }
  static double log2() {
    return 0.69314718055994530941723212145817656807550013436025;
  }
  static double epsilon() {
    return (WFMATH_PRECISION_FUDGE_FACTOR *
            std::numeric_limits<double>::epsilon());
  }
};

/// How long we can let RotMatrix and Quaternion go before fixing normalization
#define WFMATH_MAX_NORM_AGE ((WFMATH_PRECISION_FUDGE_FACTOR * 2) / 3)

/// Basic floating point type
typedef float CoordType;

// Basic comparisons

double _ScaleEpsilon(double x1, double x2, double epsilon);
float _ScaleEpsilon(float x1, float x2, float epsilon);
CoordType _ScaleEpsilon(const CoordType* x1, const CoordType* x2,
		        int length, CoordType epsilon = numeric_constants<CoordType>::epsilon());

/// Test for equality up to precision epsilon
/**
 * Returns true if the difference between the numbers is less
 * than epsilon. Note that epsilon is multiplied by 2 raised
 * to the power of the exponent of the smaller number. So,
 * for example, Equal(0.00010000, 0.00010002, 1.0e-4) will not
 * compare equal, but Equal(0.00010000, 0.00010002, 1.0e-3) will.
 **/
template<class C>
inline bool Equal(const C& c1, const C& c2, CoordType epsilon = numeric_constants<CoordType>::epsilon())
	{return c1.isEqualTo(c2, epsilon);}

bool Equal(double x1, double x2, double epsilon = numeric_constants<double>::epsilon());
// Avoid template and expensive casts from float to doubles.
bool Equal(float x1, float x2, float epsilon = numeric_constants<float>::epsilon());

// These let us avoid including <algorithm> for the sake of
// std::max() and std::min().

inline CoordType FloatMax(CoordType a, CoordType b)
	{return (a > b) ? a : b;}
inline CoordType FloatMin(CoordType a, CoordType b)
	{return (a < b) ? a : b;}
inline CoordType FloatClamp(CoordType val, CoordType min, CoordType max)
	{return (min >= val) ? min : (max <= val ? max : val);}

inline double DoubleMax(double a, double b)
	{return (a > b) ? a : b;}
inline double DoubleMin(double a, double b)
	{return (a < b) ? a : b;}
inline double DoubleClamp(double val, double min, double max)
	{return (min >= val) ? min : (max <= val ? max : val);}

} // namespace WFMath

#endif // WFMATH_CONST_H
07070100000029000081A40000000200000002000000015D8693EF00000658000000000000000000000000000000000000003000000000wfmath-1569100783.d0f8a54/wfmath/const_test.cpp// const_test.cpp (Equal() test functions)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-1-28

#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include "const.h"

#include <cassert>

using namespace WFMath;

// TestEqual() directly stolen from Numbers.cpp in Willow (thanks, Jesse!)

static void TestEqual()
{
        assert( Equal(1.0001, 1.0, 1.0e-3));
        assert(!Equal(1.0001, 1.0, 1.0e-5));

assert( Equal(0.00010000, 0.00010002, 1.0e-3));
        assert(!Equal(0.00010000, 0.00010002, 1.0e-6));

assert( Equal(1000100.0, 1000000.0, 1.0e-3));
        assert(!Equal(1000100.0, 1000000.0, 1.0e-6));
}

int main()
{
  TestEqual();

return 0;
}
0707010000002A000081A40000000200000002000000015D8693EF000007E1000000000000000000000000000000000000002900000000wfmath-1569100783.d0f8a54/wfmath/error.h// -*-C++-*-
// error.h (Class structures for errors thrown by the WFMath library)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#ifndef WFMATH_ERROR_H
#define WFMATH_ERROR_H

#include <stdexcept>
#include <wfmath/vector.h>

namespace WFMath {

/// An error thrown by certain functions when passed parallel vectors.
template<int dim>
struct ColinearVectors : virtual public std::exception {
	ColinearVectors(const Vector <dim>& v1_in, const Vector <dim>& v2_in)
			: v1(v1_in), v2(v2_in) {}

ColinearVectors(const ColinearVectors& rhs) noexcept
			: v1(rhs.v1), v2(rhs.v2) {}

~ColinearVectors() noexcept override = default;

Vector <dim> v1, v2;

const char* what() const noexcept override {
		return "WFMath::ColinearVectors exception. Supplied vectors are parallel.";
	}
};

/// An error thrown by operator>>() when it fails to parse wfmath types
struct ParseError : virtual public std::runtime_error {
	ParseError() : std::runtime_error("WFMath::ParseError exception.") {}

~ParseError() noexcept override = default;
};

} // namespace WFMath

#endif // WFMATH_ERROR_H
0707010000002B000081A40000000200000002000000015D8693EF00000741000000000000000000000000000000000000003000000000wfmath-1569100783.d0f8a54/wfmath/general_test.h// general_test.h (generic class interface test functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-1-6

#ifndef WFMATH_GENERAL_TEST_H
#define WFMATH_GENERAL_TEST_H

#include "const.h"
#include "stream.h"
#include <string>
#include <iostream>

#include <cstdlib>

namespace WFMath {

template<class C>
void test_general(const C& c)
{
  C c1, c2(c); // Generic and copy constructors

c1 = c; // operator=()

assert(Equal(c1, c2));
  assert(c1 == c2);
  assert(!(c1 != c2));

std::string s = ToString(c); // Uses operator<<() implicitly
  C c3;
  try {
    FromString(c3, s); // Uses operator>>() implicitly
  }
  catch(const ParseError&) {
    std::cerr << "Couldn't parse generated string: " << s << std::endl;
    abort();
  }

// We lose precision in string conversion
  assert(Equal(c3, c, FloatMax(numeric_constants<CoordType>::epsilon(), 1e-5F)));
}

} // namespace WFMath

#endif // WFMATH_GENERAL_TEST_H
0707010000002C000081A40000000200000002000000015D8693EF000008A7000000000000000000000000000000000000003300000000wfmath-1569100783.d0f8a54/wfmath/int_to_string.cpp#include "const.h"
#include "int_to_string.h"

#include <climits>

namespace WFMath {

// This takes a pointer pointing to the character after the end of
// a buffer, prints the number into the tail of the buffer,
// and returns a pointer to the first character in the number.
// Make sure your buffer's big enough, this doesn't check.
static char* DoIntToString(unsigned long val, char* bufhead)
{
  // deal with any possible encoding problems
  const char digits[10] = {'0', '1', '2', '3', '4', '5', '6', '7', '8', '9'};

*(--bufhead) = '\0';

if(val == 0)
    *(--bufhead) = '0';
  else do {
    *(--bufhead) = digits[val % 10];
    val /= 10;
  } while(val);

return bufhead;
}

#ifndef _MSC_VER
// note that all floating point math is done at compile time
static const double log_10_of_2 = 0.30102995664;
static const unsigned ul_max_digits = (unsigned)
	(8 * sizeof(unsigned long) // number of bits
	* log_10_of_2 // base 10 vs. base 2 digits
	+ 1 // log(1) == 0, have to add one for leading digit
	+ numeric_constants<CoordType>::epsilon()); // err on the safe side of roundoff
#else // _MSC_VER
static const unsigned ul_max_digits = 10;
#endif // _MSC_VER

std::string IntToString(unsigned long val)
{
  static const unsigned bufsize = ul_max_digits + 1; // add one for \0
  char buffer[bufsize];

return DoIntToString(val, buffer + bufsize);
}

// Deals with the fact that while, e.g. 0x80000000 (in 32 bit),
// is a valid (negative) signed value, the negative
// of it can only be expressed as an unsigned quantity.
static unsigned long SafeAbs(long val)
{
#if LONG_MAX + LONG_MIN >= 0
  // a signed variable can hold -LONG_MIN, we're completely safe
  return (val >= 0) ? val : -val;
#else
  if(val >= 0)
    return val;
  else if(val >= -LONG_MAX) // -LONG_MAX is a valid signed long
    return -val;
  else // LONG_MAX + val < 0
    return LONG_MAX + (unsigned long) (-(LONG_MAX + val));
#endif
}

std::string IntToString(long val)
{
  static const unsigned bufsize = ul_max_digits + 2; // one for \0, one for minus sign
  char buffer[bufsize];

char* bufhead = DoIntToString(SafeAbs(val), buffer + bufsize);

if(val < 0)
    *(--bufhead) = '-';

return bufhead;
}

} // namespace WFMath
0707010000002D000081A40000000200000002000000015D8693EF00000652000000000000000000000000000000000000003100000000wfmath-1569100783.d0f8a54/wfmath/int_to_string.h// int_to_string.h (Simple integer to std::string conversion)
//
//  The WorldForge Project
//  Copyright (C) 2001, 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2003-8-4

#ifndef WFMATH_INT_TO_STRING_H
#define WFMATH_INT_TO_STRING_H

#include <string>

namespace WFMath {

std::string IntToString(unsigned long);
std::string IntToString(long);
inline std::string IntToString(unsigned int val) {return IntToString((unsigned long) val);}
inline std::string IntToString(int val) {return IntToString((long) val);}
inline std::string IntToString(unsigned short val) {return IntToString((unsigned long) val);}
inline std::string IntToString(short val) {return IntToString((long) val);}

} // namespace WFMath

#endif // WFMATH_INT_TO_STRING_H
0707010000002E000081A40000000200000002000000015D8693EF0000398D000000000000000000000000000000000000002F00000000wfmath-1569100783.d0f8a54/wfmath/intersect.cpp// intersect.cpp (Backends to intersection functions)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#include "intersect.h"

#include <cmath>

#include <cassert>

namespace WFMath {

// The 2d implementation was inspired as a simplification of the 3d.
// It used the fact that two not-similarly-oriented rectangles a and b
// intersect each other if and only if a's bounding box in b's coordinate
// system intersects b, and vice versa.
//
// To see this, it is only necessary to consider the bounding box intersection
// => intersection side of the assertion, since if the rectangles intersect,
// clearly their bounding boxes will as well. Let B(a) be the bounding box of
// a in b's coordinate system, and A(b) be the bounding box of b in a's coordinate
// system. Let the symbol ^ denote intersection. The thing we need to prove is:
//
// a ^ A(b) && b ^ B(a) => a ^ b
//
// I will discuss the equivalent statement
//
// a ^ A(b) && !(a ^ b) => !(b ^ B(a))
//
// If a intersects b's bounding box, but does not intersect b,
// the intersection of a and A(b) is a rectangle which lies in
// one of the four corners of the region A(b) - b (the set of all
// points which lie in the bounding box, but not in b). Without
// loss of generality, let a ^ A(b) lie in the lower left corner
// of A(b) - b. This is a triangular region, two of whose sides
// are parts of edges of A(b), the third being a side of b.
// Construct a line parallel to the side of b, passing between
// b and a ^ A(b). This line never intersects b, since b is a rectangle.
// It also never intersects a, since it passes above and to the
// right of the upper right corner of a. It also never intersects
// B(a), since the upper right side of B(a) is parallel to the
// line, but passes through the upper right corner of a. Thus,
// this line separates b from B(a), and they do not intersect. QED.

template<>
bool Intersect<2>(const RotBox<2>& r, const AxisBox<2>& b, bool proper)
{
  const AxisBox<2> b2 = r.boundingBox();
  if(!Intersect(b2, b, proper))
    return false;

RotMatrix<2> m = r.m_orient.inverse();

const AxisBox<2> b3 = RotBox<2>(Point<2>(b.m_low).rotate(m, r.m_corner0),
                             b.m_high - b.m_low, m).boundingBox();
  const AxisBox<2> b4(r.m_corner0, r.m_corner0 + r.m_size);
  return Intersect(b3, b4, proper);
}

// The 3d implementation is based on the following theorem:
//
// Theorem:
//
// Two convex polyhedra do not intersect if and only if there exists a separating
// plane which is either parallel to the face of one polyhedron or which is
// parallel to at least one edge of each polyhedron.
//
// Found this in the abstract to the paper:
//
// Surface-to-surface intersection based on triangular parameter domain subdivision
// Ernst Huber
// Institute of Computer Graphics
// Vienna University of Technology
// A-1040 Vienna, Karlsplatz 13/186/1, Austria
//
// online postscript version of the abstract (where I got this from):
//
// http://www.cs.ubc.ca/conferences/CCCG/elec_proc/c48.ps.gz
//
// The paper gives a reference for the theorem (probably the one to really look at
// for proof/details):
//
// S. Gottschalk
// Separating Axis Theorem
// Technical Report TR96-024
// Department of Computer Science
// UNC Chapel Hill
// 1996

template<>
bool Intersect<3>(const RotBox<3>& r, const AxisBox<3>& b, bool proper)
{
  // Checking intersection of each with the bounding box of
  // the other in the coordinate system of the first will take care
  // of the "plane parallel to face" case

const AxisBox<3> b2 = r.boundingBox();
  if(!Intersect(b2, b, proper))
    return false;

RotMatrix<3> minv = r.m_orient.inverse();
  Vector<3> b_size = b.m_high - b.m_low;

const AxisBox<3> b3 = RotBox<3>(Point<3>(b.m_low).rotate(minv, r.m_corner0),
                             b_size, minv).boundingBox();
  const AxisBox<3> b4(r.m_corner0, r.m_corner0 + r.m_size);
  if(!Intersect(b3, b4, proper))
    return false;

// Now for the "plane parallel to at least one edge of each" case

Vector<3> sep =  b.m_low - r.m_corner0;
  const RotMatrix<3> &m = r.m_orient;

// Generate normals to the 9 possible separating planes

for(int i = 0; i < 3; ++i) {
    // Generate edge vectors for the RotBox, ignore size, only care about direction
// Just access m_orient directly below instead of using r_vec
//    Vector<3> r_vec = m.row(i);

for(int j = 0; j < 3; ++j) {
      Vector<3> axis;

// Cross product, ignore size of b since we only care about direction

switch(j) {
        case 0:
          axis[0] = 0;
          axis[1] = -m.elem(i, 2);
          axis[2] =  m.elem(i, 1);
          break;
        case 1:
          axis[0] =  m.elem(i, 2);
          axis[1] = 0;
          axis[2] = -m.elem(i, 0);
          break;
        case 2:
          axis[0] = -m.elem(i, 1);
          axis[1] =  m.elem(i, 0);
          axis[2] = 0;
          break;
        default:
          assert(false);
      }

if(axis.sqrMag() < numeric_constants<CoordType>::epsilon() * numeric_constants<CoordType>::epsilon()) {
        // Parallel edges, this reduces to the 2d case above. We've already
        // checked the bounding box intersections, so we know they intersect.
        // We don't need to scale WFMATH_EPSILON, det(m_orient) = 1
        // essentially takes care of that.
        return true;
      }

// Project both boxes on this axis, check for separating plane.

// We only need to project two axes per box, the one parallel
      // to the plane doesn't contribute

const int next[] = {1, 2, 0};
      CoordType val;
      CoordType b_low, b_high, r_low, r_high, dist;
      int k;

// AxisBox projection

k = next[j];

val = axis[k] * b_size[k];

if(val > 0) {
        b_high = val;
        b_low = 0;
      }
      else {
        b_low = val;
        b_high = 0;
      }

k = next[k];

val = axis[k] * b_size[k];

if(val > 0)
        b_high += val;
      else
        b_low += val;

// RotBox projection

k = next[i];

val = Dot(m.row(k), axis) * r.m_size[k];

if(val > 0) {
        r_high = val;
        r_low = 0;
      }
      else {
        r_low = val;
        r_high = 0;
      }

k = next[k];

val = Dot(m.row(k), axis) * r.m_size[k];

if(val > 0)
        r_high += val;
      else
        r_low += val;

// Distance between basepoints for boxes along this axis

dist = Dot(sep, axis);

if(_Greater(r_low - dist, b_high, proper)
        || _Less(r_high - dist, b_low, proper))
        return false;
    }
  }

return true;
}

// force a bunch of instantiations

template bool Intersect<2>(const Point<2>&, const Point<2>&, bool);
template bool Intersect<3>(const Point<3>&, const Point<3>&, bool);
template bool Contains<2>(const Point<2>&, const Point<2>&, bool);
template bool Contains<3>(const Point<3>&, const Point<3>&, bool);

template bool Intersect<Point<2>,AxisBox<2> >(const Point<2>&, const AxisBox<2>&, bool);
template bool Intersect<Point<3>,AxisBox<3> >(const Point<3>&, const AxisBox<3>&, bool);
template bool Contains<2>(const Point<2>&, const AxisBox<2>&, bool);
template bool Contains<3>(const Point<3>&, const AxisBox<3>&, bool);
template bool Intersect<2>(const AxisBox<2>&, const Point<2>&, bool);
template bool Intersect<3>(const AxisBox<3>&, const Point<3>&, bool);
template bool Contains<2>(const AxisBox<2>&, const Point<2>&, bool);
template bool Contains<3>(const AxisBox<3>&, const Point<3>&, bool);

template bool Intersect<2>(const AxisBox<2>&, const AxisBox<2>&, bool);
template bool Intersect<3>(const AxisBox<3>&, const AxisBox<3>&, bool);
template bool Contains<2>(const AxisBox<2>&, const AxisBox<2>&, bool);
template bool Contains<3>(const AxisBox<3>&, const AxisBox<3>&, bool);

template bool Intersect<Point<2>,Ball<2> >(const Point<2>&, const Ball<2>&, bool);
template bool Intersect<Point<3>,Ball<3> >(const Point<3>&, const Ball<3>&, bool);
template bool Contains<2>(const Point<2>&, const Ball<2>&, bool);
template bool Contains<3>(const Point<3>&, const Ball<3>&, bool);
template bool Intersect<2>(const Ball<2>&, const Point<2>&, bool);
template bool Intersect<3>(const Ball<3>&, const Point<3>&, bool);
template bool Contains<2>(const Ball<2>&, const Point<2>&, bool);
template bool Contains<3>(const Ball<3>&, const Point<3>&, bool);

template bool Intersect<AxisBox<2>,Ball<2> >(const AxisBox<2>&, const Ball<2>&, bool);
template bool Intersect<AxisBox<3>,Ball<3> >(const AxisBox<3>&, const Ball<3>&, bool);
template bool Contains<2>(const AxisBox<2>&, const Ball<2>&, bool);
template bool Contains<3>(const AxisBox<3>&, const Ball<3>&, bool);
template bool Intersect<2>(const Ball<2>&, const AxisBox<2>&, bool);
template bool Intersect<3>(const Ball<3>&, const AxisBox<3>&, bool);
template bool Contains<2>(const Ball<2>&, const AxisBox<2>&, bool);
template bool Contains<3>(const Ball<3>&, const AxisBox<3>&, bool);

template bool Intersect<2>(const Ball<2>&, const Ball<2>&, bool);
template bool Intersect<3>(const Ball<3>&, const Ball<3>&, bool);
template bool Contains<2>(const Ball<2>&, const Ball<2>&, bool);
template bool Contains<3>(const Ball<3>&, const Ball<3>&, bool);

template bool Intersect<Point<2>,Segment<2> >(const Point<2>&, const Segment<2>&, bool);
template bool Intersect<Point<3>,Segment<3> >(const Point<3>&, const Segment<3>&, bool);
template bool Contains<2>(const Point<2>&, const Segment<2>&, bool);
template bool Contains<3>(const Point<3>&, const Segment<3>&, bool);
template bool Intersect<2>(const Segment<2>&, const Point<2>&, bool);
template bool Intersect<3>(const Segment<3>&, const Point<3>&, bool);
template bool Contains<2>(const Segment<2>&, const Point<2>&, bool);
template bool Contains<3>(const Segment<3>&, const Point<3>&, bool);

template bool Intersect<AxisBox<2>,Segment<2> >(const AxisBox<2>&, const Segment<2>&, bool);
template bool Intersect<AxisBox<3>,Segment<3> >(const AxisBox<3>&, const Segment<3>&, bool);
template bool Contains<2>(const AxisBox<2>&, const Segment<2>&, bool);
template bool Contains<3>(const AxisBox<3>&, const Segment<3>&, bool);
template bool Intersect<2>(const Segment<2>&, const AxisBox<2>&, bool);
template bool Intersect<3>(const Segment<3>&, const AxisBox<3>&, bool);
template bool Contains<2>(const Segment<2>&, const AxisBox<2>&, bool);
template bool Contains<3>(const Segment<3>&, const AxisBox<3>&, bool);

template bool Intersect<Ball<2>,Segment<2> >(const Ball<2>&, const Segment<2>&, bool);
template bool Intersect<Ball<3>,Segment<3> >(const Ball<3>&, const Segment<3>&, bool);
template bool Contains<2>(const Ball<2>&, const Segment<2>&, bool);
template bool Contains<3>(const Ball<3>&, const Segment<3>&, bool);
template bool Intersect<2>(const Segment<2>&, const Ball<2>&, bool);
template bool Intersect<3>(const Segment<3>&, const Ball<3>&, bool);
template bool Contains<2>(const Segment<2>&, const Ball<2>&, bool);
template bool Contains<3>(const Segment<3>&, const Ball<3>&, bool);

template bool Intersect<2>(const Segment<2>&, const Segment<2>&, bool);
template bool Intersect<3>(const Segment<3>&, const Segment<3>&, bool);
template bool Contains<2>(const Segment<2>&, const Segment<2>&, bool);
template bool Contains<3>(const Segment<3>&, const Segment<3>&, bool);

template bool Intersect<Point<2>,RotBox<2> >(const Point<2>&, const RotBox<2>&, bool);
template bool Intersect<Point<3>,RotBox<3> >(const Point<3>&, const RotBox<3>&, bool);
template bool Contains<2>(const Point<2>&, const RotBox<2>&, bool);
template bool Contains<3>(const Point<3>&, const RotBox<3>&, bool);
template bool Intersect<2>(const RotBox<2>&, const Point<2>&, bool);
template bool Intersect<3>(const RotBox<3>&, const Point<3>&, bool);
template bool Contains<2>(const RotBox<2>&, const Point<2>&, bool);
template bool Contains<3>(const RotBox<3>&, const Point<3>&, bool);

template bool Intersect<AxisBox<2>,RotBox<2> >(const AxisBox<2>&, const RotBox<2>&, bool);
template bool Intersect<AxisBox<3>,RotBox<3> >(const AxisBox<3>&, const RotBox<3>&, bool);
template bool Contains<2>(const AxisBox<2>&, const RotBox<2>&, bool);
template bool Contains<3>(const AxisBox<3>&, const RotBox<3>&, bool);
template bool Contains<2>(const RotBox<2>&, const AxisBox<2>&, bool);
template bool Contains<3>(const RotBox<3>&, const AxisBox<3>&, bool);

template bool Intersect<Ball<2>,RotBox<2> >(const Ball<2>&, const RotBox<2>&, bool);
template bool Intersect<Ball<3>,RotBox<3> >(const Ball<3>&, const RotBox<3>&, bool);
template bool Contains<2>(const Ball<2>&, const RotBox<2>&, bool);
template bool Contains<3>(const Ball<3>&, const RotBox<3>&, bool);
template bool Intersect<2>(const RotBox<2>&, const Ball<2>&, bool);
template bool Intersect<3>(const RotBox<3>&, const Ball<3>&, bool);
template bool Contains<2>(const RotBox<2>&, const Ball<2>&, bool);
template bool Contains<3>(const RotBox<3>&, const Ball<3>&, bool);

template bool Intersect<Segment<2>,RotBox<2> >(const Segment<2>&, const RotBox<2>&, bool);
template bool Intersect<Segment<3>,RotBox<3> >(const Segment<3>&, const RotBox<3>&, bool);
template bool Contains<2>(const Segment<2>&, const RotBox<2>&, bool);
template bool Contains<3>(const Segment<3>&, const RotBox<3>&, bool);
template bool Intersect<2>(const RotBox<2>&, const Segment<2>&, bool);
template bool Intersect<3>(const RotBox<3>&, const Segment<3>&, bool);
template bool Contains<2>(const RotBox<2>&, const Segment<2>&, bool);
template bool Contains<3>(const RotBox<3>&, const Segment<3>&, bool);

template bool Intersect<2>(const RotBox<2>&, const RotBox<2>&, bool);
template bool Intersect<3>(const RotBox<3>&, const RotBox<3>&, bool);
template bool Contains<2>(const RotBox<2>&, const RotBox<2>&, bool);
template bool Contains<3>(const RotBox<3>&, const RotBox<3>&, bool);

}
0707010000002F000081A40000000200000002000000015D8693EF000038AD000000000000000000000000000000000000002D00000000wfmath-1569100783.d0f8a54/wfmath/intersect.h// intersect.h (Shape intersection functions)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

#ifndef WFMATH_INTERSECT_H
#define WFMATH_INTERSECT_H

#include <wfmath/vector.h>
#include <wfmath/point.h>
#include <wfmath/const.h>
#include <wfmath/intersect_decls.h>
#include <wfmath/axisbox.h>
#include <wfmath/ball.h>
#include <wfmath/segment.h>
#include <wfmath/rotbox.h>

#include <cmath>

namespace WFMath {

// Get the reversed order intersect functions (is this safe? FIXME)
// No it's not. In the case of an unknown intersection we end up in
// a stack crash loop.

template<class S1, class S2>
inline bool Intersect(const S1& s1, const S2& s2, bool proper)
{
  return Intersect(s2, s1, proper);
}

// Point<>

template<int dim>
inline bool Intersect(const Point<dim>& p1, const Point<dim>& p2, bool proper)
{
  return !proper && p1 == p2;
}

template<int dim, class S>
inline bool Contains(const S& s, const Point<dim>& p, bool proper)
{
  return Intersect(p, s, proper);
}

template<int dim>
inline bool Contains(const Point<dim>& p1, const Point<dim>& p2, bool proper)
{
  return !proper && p1 == p2;
}

// AxisBox<>

template<int dim>
inline bool Intersect(const AxisBox<dim>& b, const Point<dim>& p, bool proper)
{
  for(int i = 0; i < dim; ++i)
    if(_Greater(b.m_low[i], p[i], proper) || _Less(b.m_high[i], p[i], proper))
      return false;

return true;
}

template<int dim>
inline bool Contains(const Point<dim>& p, const AxisBox<dim>& b, bool proper)
{
  return !proper && p == b.m_low && p == b.m_high;
}

template<int dim>
inline bool Intersect(const AxisBox<dim>& b1, const AxisBox<dim>& b2, bool proper)
{
  for(int i = 0; i < dim; ++i)
    if(_Greater(b1.m_low[i], b2.m_high[i], proper)
      || _Less(b1.m_high[i], b2.m_low[i], proper))
      return false;

return true;
}

template<int dim>
inline bool Contains(const AxisBox<dim>& outer, const AxisBox<dim>& inner, bool proper)
{
  for(int i = 0; i < dim; ++i)
    if(_Less(inner.m_low[i], outer.m_low[i], proper)
      || _Greater(inner.m_high[i], outer.m_high[i], proper))
      return false;

return true;
}

// Ball<>

template<int dim>
inline bool Intersect(const Ball<dim>& b, const Point<dim>& p, bool proper)
{
  return _LessEq(SquaredDistance(b.m_center, p), b.m_radius * b.m_radius
					   * (1 + numeric_constants<CoordType>::epsilon()), proper);
}

template<int dim>
inline bool Contains(const Point<dim>& p, const Ball<dim>& b, bool proper)
{
  return !proper && b.m_radius == 0 && p == b.m_center;
}

template<int dim>
inline bool Intersect(const Ball<dim>& b, const AxisBox<dim>& a, bool proper)
{
  CoordType dist = 0;

for(int i = 0; i < dim; ++i) {
    CoordType dist_i;
    if(b.m_center[i] < a.m_low[i])
      dist_i = b.m_center[i] - a.m_low[i];
    else if(b.m_center[i] > a.m_high[i])
      dist_i = b.m_center[i] - a.m_high[i];
    else
      continue;
    dist+= dist_i * dist_i;
  }

return _LessEq(dist, b.m_radius * b.m_radius, proper);
}

template<int dim>
inline bool Contains(const Ball<dim>& b, const AxisBox<dim>& a, bool proper)
{
  CoordType sqr_dist = 0;

for(int i = 0; i < dim; ++i) {
    CoordType furthest = FloatMax(std::fabs(b.m_center[i] - a.m_low[i]),
                                  std::fabs(b.m_center[i] - a.m_high[i]));
    sqr_dist += furthest * furthest;
  }

return _LessEq(sqr_dist, b.m_radius * b.m_radius * (1 + numeric_constants<CoordType>::epsilon()), proper);
}

template<int dim>
inline bool Contains(const AxisBox<dim>& a, const Ball<dim>& b, bool proper)
{
  for(int i = 0; i < dim; ++i)
    if(_Less(b.m_center[i] - b.m_radius, a.lowerBound(i), proper)
       || _Greater(b.m_center[i] + b.m_radius, a.upperBound(i), proper))
      return false;

return true;
}

template<int dim>
inline bool Intersect(const Ball<dim>& b1, const Ball<dim>& b2, bool proper)
{
  CoordType sqr_dist = SquaredDistance(b1.m_center, b2.m_center);
  CoordType rad_sum = b1.m_radius + b2.m_radius;

return _LessEq(sqr_dist, rad_sum * rad_sum, proper);
}

template<int dim>
inline bool Contains(const Ball<dim>& outer, const Ball<dim>& inner, bool proper)
{
  CoordType rad_diff = outer.m_radius - inner.m_radius;

if(_Less(rad_diff, 0, proper))
    return false;

CoordType sqr_dist = SquaredDistance(outer.m_center, inner.m_center);

return _LessEq(sqr_dist, rad_diff * rad_diff, proper);
}

// Segment<>

template<int dim>
inline bool Intersect(const Segment<dim>& s, const Point<dim>& p, bool proper)
{
  // This is only true if p lies on the line between m_p1 and m_p2

Vector<dim> v1 = s.m_p1 - p, v2 = s.m_p2 - p;

CoordType proj = Dot(v1, v2);

if(_Greater(proj, 0, proper)) // p is on the same side of both ends, not between them
    return false;

// Check for colinearity
  return Equal(proj * proj, v1.sqrMag() * v2.sqrMag());
}

template<int dim>
inline bool Contains(const Point<dim>& p, const Segment<dim>& s, bool proper)
{
  return !proper && p == s.m_p1 && p == s.m_p2;
}

template<int dim>
bool Intersect(const Segment<dim>& s, const AxisBox<dim>& b, bool proper)
{
  // Use parametric coordinates on the line, where 0 is the location
  // of m_p1 and 1 is the location of m_p2

// Find the parametric coordinates of the portion of the line
  // which lies betweens b.lowerBound(i) and b.upperBound(i) for
  // each i. Find the intersection of those segments and the
  // segment (0, 1), and check if it's nonzero.

CoordType min = 0, max = 1;

for(int i = 0; i < dim; ++i) {
    CoordType dist = s.m_p2[i] - s.m_p1[i];
    if(dist == 0) {
      if(_Less(s.m_p1[i], b.m_low[i], proper)
        || _Greater(s.m_p1[i], b.m_high[i], proper))
        return false;
    }
    else {
      CoordType low = (b.m_low[i] - s.m_p1[i]) / dist;
      CoordType high = (b.m_high[i] - s.m_p1[i]) / dist;
      if(low > high) {
        CoordType tmp = high;
        high = low;
        low = tmp;
      }
      if(low > min)
        min = low;
      if(high < max)
        max = high;
    }
  }

return _LessEq(min, max, proper);
}

template<int dim>
inline bool Contains(const Segment<dim>& s, const AxisBox<dim>& b, bool proper)
{
  // This is only possible for zero width or zero height box,
  // in which case we check for containment of the endpoints.

bool got_difference = false;

for(int i = 0; i < dim; ++i) {
    if(b.m_low[i] == b.m_high[i])
      continue;
    if(got_difference)
      return false;
    else // It's okay to be different on one axis
      got_difference = true;
  }

return Contains(s, b.m_low, proper) &&
        (got_difference ? Contains(s, b.m_high, proper) : true);
}

template<int dim>
inline bool Contains(const AxisBox<dim>& b, const Segment<dim>& s, bool proper)
{
  return Contains(b, s.m_p1, proper) && Contains(b, s.m_p2, proper);
}

template<int dim>
bool Intersect(const Segment<dim>& s, const Ball<dim>& b, bool proper)
{
  Vector<dim> line = s.m_p2 - s.m_p1, offset = b.m_center - s.m_p1;

// First, see if the closest point on the line to the center of
  // the ball lies inside the segment

CoordType proj = Dot(line, offset);

// If the nearest point on the line is outside the segment,
  // intersection reduces to checking the nearest endpoint.

if(proj <= 0)
    return Intersect(b, s.m_p1, proper);

CoordType lineSqrMag = line.sqrMag();

if (proj >= lineSqrMag)
    return Intersect(b, s.m_p2, proper);

Vector<dim> perp_part = offset - line * (proj / lineSqrMag);

return _LessEq(perp_part.sqrMag(), b.m_radius * b.m_radius, proper);
}

template<int dim>
inline bool Contains(const Ball<dim>& b, const Segment<dim>& s, bool proper)
{
  return Contains(b, s.m_p1, proper) && Contains(b, s.m_p2, proper);
}

template<int dim>
inline bool Contains(const Segment<dim>& s, const Ball<dim>& b, bool proper)
{
  return b.m_radius == 0 && Contains(s, b.m_center, proper);
}

template<int dim>
bool Intersect(const Segment<dim>& s1, const Segment<dim>& s2, bool proper)
{
  // Check that the lines that contain the segments intersect, and then check
  // that the intersection point lies within the segments

Vector<dim> v1 = s1.m_p2 - s1.m_p1, v2 = s2.m_p2 - s2.m_p1,
	      deltav = s2.m_p1 - s1.m_p1;

CoordType v1sqr = v1.sqrMag(), v2sqr = v2.sqrMag();
  CoordType proj12 = Dot(v1, v2), proj1delta = Dot(v1, deltav),
	    proj2delta = Dot(v2, deltav);

CoordType denom = v1sqr * v2sqr - proj12 * proj12;

if(dim > 2 && !Equal(v2sqr * proj1delta * proj1delta +
		         v1sqr * proj2delta * proj2delta,
		       2 * proj12 * proj1delta * proj2delta +
		         deltav.sqrMag() * denom))
    return false; // Skew lines; don't intersect

if(denom > 0) {
    // Find the location of the intersection point in parametric coordinates,
    // where one end of the segment is at zero and the other at one

CoordType coord1 = (v2sqr * proj1delta - proj12 * proj2delta) / denom;
    CoordType coord2 = -(v1sqr * proj2delta - proj12 * proj1delta) / denom;

return _LessEq(coord1, 0, proper) && _LessEq(coord1, 1, proper)
           && _GreaterEq(coord2, 0, proper) && _GreaterEq(coord2, 1, proper);
  }
  else {
    // Parallel segments, see if one contains an endpoint of the other
    return Contains(s1, s2.m_p1, proper) || Contains(s1, s2.m_p2, proper)
	|| Contains(s2, s1.m_p1, proper) || Contains(s2, s1.m_p2, proper)
	// Degenerate case (identical segments), nonzero length
	|| ((proper && s1.m_p1 != s1.m_p2)
          && ((s1.m_p1 == s2.m_p1 && s1.m_p2 == s2.m_p2)
              || (s1.m_p1 == s2.m_p2 && s1.m_p2 == s2.m_p1)));
  }
}

template<int dim>
inline bool Contains(const Segment<dim>& s1, const Segment<dim>& s2, bool proper)
{
  return Contains(s1, s2.m_p1, proper) && Contains(s1, s2.m_p2, proper);
}

// RotBox<>

template<int dim>
inline bool Intersect(const RotBox<dim>& r, const Point<dim>& p, bool proper)
{
  // Rotate the point into the internal coordinate system of the box

Vector<dim> shift = ProdInv(p - r.m_corner0, r.m_orient);

for(int i = 0; i < dim; ++i) {
    if(r.m_size[i] < 0) {
      if(_Less(shift[i], r.m_size[i], proper) || _Greater(shift[i], 0, proper))
        return false;
    }
    else {
      if(_Greater(shift[i], r.m_size[i], proper) || _Less(shift[i], 0, proper))
        return false;
    }
  }

return true;
}

template<int dim>
inline bool Contains(const Point<dim>& p, const RotBox<dim>& r, bool proper)
{
  if(proper)
    return false;

for(int i = 0; i < dim; ++i)
    if(r.m_size[i] != 0)
      return false;

return p == r.m_corner0;
}

template<int dim>
bool Intersect(const RotBox<dim>& r, const AxisBox<dim>& b, bool proper);

template<int dim>
inline bool Contains(const RotBox<dim>& r, const AxisBox<dim>& b, bool proper)
{
  RotMatrix<dim> m = r.m_orient.inverse();

return Contains(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
		  RotBox<dim>(Point<dim>(b.m_low).rotate(m, r.m_corner0),
			      b.m_high - b.m_low, m), proper);
}

template<int dim>
inline bool Contains(const AxisBox<dim>& b, const RotBox<dim>& r, bool proper)
{
  return Contains(b, r.boundingBox(), proper);
}

template<int dim>
inline bool Intersect(const RotBox<dim>& r, const Ball<dim>& b, bool proper)
{
  return Intersect(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
		  Ball<dim>(r.m_corner0 + ProdInv(b.m_center - r.m_corner0,
			    r.m_orient), b.m_radius), proper);
}

template<int dim>
inline bool Contains(const RotBox<dim>& r, const Ball<dim>& b, bool proper)
{
  return Contains(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
		  Ball<dim>(r.m_corner0 + ProdInv(b.m_center - r.m_corner0,
			    r.m_orient), b.m_radius), proper);
}

template<int dim>
inline bool Contains(const Ball<dim>& b, const RotBox<dim>& r, bool proper)
{
  return Contains(Ball<dim>(r.m_corner0 + ProdInv(b.m_center - r.m_corner0,
			    r.m_orient), b.m_radius),
		  AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size), proper);
}

template<int dim>
inline bool Intersect(const RotBox<dim>& r, const Segment<dim>& s, bool proper)
{
  Point<dim> p1 = r.m_corner0 + ProdInv(s.m_p1 - r.m_corner0, r.m_orient);
  Point<dim> p2 = r.m_corner0 + ProdInv(s.m_p2 - r.m_corner0, r.m_orient);

return Intersect(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
		   Segment<dim>(p1, p2), proper);
}

template<int dim>
inline bool Contains(const RotBox<dim>& r, const Segment<dim>& s, bool proper)
{
  Point<dim> p1 = r.m_corner0 + ProdInv(s.m_p1 - r.m_corner0, r.m_orient);
  Point<dim> p2 = r.m_corner0 + ProdInv(s.m_p2 - r.m_corner0, r.m_orient);

return Contains(AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size),
		  Segment<dim>(p1, p2), proper);
}

template<int dim>
inline bool Contains(const Segment<dim>& s, const RotBox<dim>& r, bool proper)
{
  Point<dim> p1 = r.m_corner0 + ProdInv(s.m_p1 - r.m_corner0, r.m_orient);
  Point<dim> p2 = r.m_corner0 + ProdInv(s.m_p2 - r.m_corner0, r.m_orient);

return Contains(Segment<dim>(p1, p2),
		  AxisBox<dim>(r.m_corner0, r.m_corner0 + r.m_size), proper);
}

template<int dim>
inline bool Intersect(const RotBox<dim>& r1, const RotBox<dim>& r2, bool proper)
{
  return Intersect(RotBox<dim>(r1).rotatePoint(r2.m_orient.inverse(),
					       r2.m_corner0),
		   AxisBox<dim>(r2.m_corner0, r2.m_corner0 + r2.m_size), proper);
}

template<int dim>
inline bool Contains(const RotBox<dim>& outer, const RotBox<dim>& inner, bool proper)
{
  return Contains(AxisBox<dim>(outer.m_corner0, outer.m_corner0 + outer.m_size),
		  RotBox<dim>(inner).rotatePoint(outer.m_orient.inverse(),
						 outer.m_corner0), proper);
}

// Polygon<> intersection functions are in polygon_funcs.h, to avoid
// unnecessary inclusion of <vector>

} // namespace WFMath

#endif  // WFMATH_INTERSECT_H
07070100000030000081A40000000200000002000000015D8693EF000018D8000000000000000000000000000000000000003300000000wfmath-1569100783.d0f8a54/wfmath/intersect_decls.h// intersect_decls.h (Declarations for "friend" intersection functions)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_INTERSECT_DECLS_H
#define WFMATH_INTERSECT_DECLS_H

#include <wfmath/const.h>

namespace WFMath {

// Some Intersect and Contains helper functions

inline bool _Less(CoordType x1, CoordType x2, bool proper)
{
  return proper ? x1 <= x2 : (x2 - x1) > numeric_constants<CoordType>::epsilon();
}

inline bool _LessEq(CoordType x1, CoordType x2, bool proper)
{
  return !proper ? x1 <= x2 : x1 < x2;
}

inline bool _Greater(CoordType x1, CoordType x2, bool proper)
{
  return proper ? x1 >= x2 : (x1 - x2) > numeric_constants<CoordType>::epsilon();
}

inline bool _GreaterEq(CoordType x1, CoordType x2, bool proper)
{
  return !proper ? x1 >= x2 : x1 > x2;
}

template<int dim>
bool Intersect(const AxisBox<dim>& b, const Point<dim>& p, bool proper);
template<int dim>
bool Contains(const Point<dim>& p, const AxisBox<dim>& b, bool proper);

template<int dim>
bool Intersect(const Ball<dim>& b, const Point<dim>& p, bool proper);
template<int dim>
bool Contains(const Point<dim>& p, const Ball<dim>& b, bool proper);

template<int dim>
bool Intersect(const Segment<dim>& s, const Point<dim>& p, bool proper);
template<int dim>
bool Contains(const Point<dim>& p, const Segment<dim>& s, bool proper);

template<int dim>
bool Intersect(const RotBox<dim>& r, const Point<dim>& p, bool proper);
template<int dim>
bool Contains(const Point<dim>& p, const RotBox<dim>& r, bool proper);

template<int dim>
bool Intersect(const AxisBox<dim>& b1, const AxisBox<dim>& b2, bool proper);
template<int dim>
bool Contains(const AxisBox<dim>& outer, const AxisBox<dim>& inner, bool proper);

template<int dim>
bool Intersect(const Ball<dim>& b, const AxisBox<dim>& a, bool proper);
template<int dim>
bool Contains(const Ball<dim>& b, const AxisBox<dim>& a, bool proper);
template<int dim>
bool Contains(const AxisBox<dim>& a, const Ball<dim>& b, bool proper);

template<int dim>
bool Intersect(const Segment<dim>& s, const AxisBox<dim>& b, bool proper);
template<int dim>
bool Contains(const Segment<dim>& s, const AxisBox<dim>& b, bool proper);
template<int dim>
bool Contains(const AxisBox<dim>& b, const Segment<dim>& s, bool proper);

template<int dim>
bool Intersect(const RotBox<dim>& r, const AxisBox<dim>& b, bool proper);
template<int dim>
bool Contains(const RotBox<dim>& r, const AxisBox<dim>& b, bool proper);
template<int dim>
bool Contains(const AxisBox<dim>& b, const RotBox<dim>& r, bool proper);

template<int dim>
bool Intersect(const Ball<dim>& b1, const Ball<dim>& b2, bool proper);
template<int dim>
bool Contains(const Ball<dim>& outer, const Ball<dim>& inner, bool proper);

template<int dim>
bool Intersect(const Segment<dim>& s, const Ball<dim>& b, bool proper);
template<int dim>
bool Contains(const Ball<dim>& b, const Segment<dim>& s, bool proper);
template<int dim>
bool Contains(const Segment<dim>& s, const Ball<dim>& b, bool proper);

template<int dim>
bool Intersect(const RotBox<dim>& r, const Ball<dim>& b, bool proper);
template<int dim>
bool Contains(const RotBox<dim>& r, const Ball<dim>& b, bool proper);
template<int dim>
bool Contains(const Ball<dim>& b, const RotBox<dim>& r, bool proper);

template<int dim>
bool Intersect(const Segment<dim>& s1, const Segment<dim>& s2, bool proper);
template<int dim>
bool Contains(const Segment<dim>& s1, const Segment<dim>& s2, bool proper);

template<int dim>
bool Intersect(const RotBox<dim>& r, const Segment<dim>& s, bool proper);
template<int dim>
bool Contains(const RotBox<dim>& r, const Segment<dim>& s, bool proper);
template<int dim>
bool Contains(const Segment<dim>& s, const RotBox<dim>& r, bool proper);

template<int dim>
bool Intersect(const RotBox<dim>& r1, const RotBox<dim>& r2, bool proper);
template<int dim>
bool Contains(const RotBox<dim>& outer, const RotBox<dim>& inner, bool proper);

template<int dim>
bool Intersect(const Polygon<dim>& r, const Point<dim>& p, bool proper);
template<int dim>
bool Contains(const Point<dim>& p, const Polygon<dim>& r, bool proper);

template<int dim>
bool Intersect(const Polygon<dim>& p, const AxisBox<dim>& b, bool proper);
template<int dim>
bool Contains(const Polygon<dim>& p, const AxisBox<dim>& b, bool proper);
template<int dim>
bool Contains(const AxisBox<dim>& b, const Polygon<dim>& p, bool proper);

template<int dim>
bool Intersect(const Polygon<dim>& p, const Ball<dim>& b, bool proper);
template<int dim>
bool Contains(const Polygon<dim>& p, const Ball<dim>& b, bool proper);
template<int dim>
bool Contains(const Ball<dim>& b, const Polygon<dim>& p, bool proper);

template<int dim>
bool Intersect(const Polygon<dim>& r, const Segment<dim>& s, bool proper);
template<int dim>
bool Contains(const Polygon<dim>& p, const Segment<dim>& s, bool proper);
template<int dim>
bool Contains(const Segment<dim>& s, const Polygon<dim>& p, bool proper);

template<int dim>
bool Intersect(const Polygon<dim>& p, const RotBox<dim>& r, bool proper);
template<int dim>
bool Contains(const Polygon<dim>& p, const RotBox<dim>& r, bool proper);
template<int dim>
bool Contains(const RotBox<dim>& r, const Polygon<dim>& p, bool proper);

template<int dim>
bool Intersect(const Polygon<dim>& p1, const Polygon<dim>& p2, bool proper);
template<int dim>
bool Contains(const Polygon<dim>& outer, const Polygon<dim>& inner, bool proper);

} // namespace WFMath

#endif  // WFMATH_INTERSECT_DECLS_H
07070100000031000081A40000000200000002000000015D8693EF000006BF000000000000000000000000000000000000003400000000wfmath-1569100783.d0f8a54/wfmath/intstring_test.cpp// intstring_test.cpp (IntToString() test functions)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-1-28

#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include "int_to_string.h"
#include "randgen.h"

#include <climits>
#include <cstdlib>

#include <cassert>

using namespace WFMath;

static void TestConvert()
{
  for(unsigned i = 0; i < 100; ++i) {
    unsigned long val = MTRand::instance.randInt();
    assert(strtoul(IntToString(val).c_str(), 0, 0) == val);
    // This assignment changes the value, but we just want a
    // random number, so we don't care. Large unsigned ints will
    // provide us negative numbers for testing.
    long val2 = (long) val;
    assert(atol(IntToString(val2).c_str()) == val2);
  }
}

int main()
{
  TestConvert();

return 0;
}
07070100000032000081A40000000200000002000000015D8693EF000004B3000000000000000000000000000000000000002A00000000wfmath-1569100783.d0f8a54/wfmath/line.cpp// line.cpp (Line<> implementation)
//
//  The WorldForge Project
//  Copyright (C) 2012  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Alistair Riddoch
// Created: 2011-1-27

#include "line_funcs.h"

#include <wfmath/axisbox.h>
#include <wfmath/ball.h>
#include <wfmath/vector.h>

namespace WFMath {

template class Line<2>;
template class Line<3>;

}
07070100000033000081A40000000200000002000000015D8693EF00001463000000000000000000000000000000000000002800000000wfmath-1569100783.d0f8a54/wfmath/line.h// line.h (A segmented line in n-dimensional space)
//
//  The WorldForge Project
//  Copyright (C) 2012  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_LINE_H
#define WFMATH_LINE_H

#include <wfmath/const.h>
#include <wfmath/point.h>

#include <vector>

namespace WFMath {

/// A dim dimensional line
/**
 * This class implements the full shape interface, as described in
 * the fake class Shape.
 **/
template<int dim = 3>
class Line
{
 public:
  ///
  Line() : m_points() {}
  ///
  Line(const Line<dim>& l) : m_points(l.m_points) {}
  ///
  explicit Line(const AtlasInType& a);
  ///
  ~Line() {}

/// Create an Atlas object from the line
  AtlasOutType toAtlas() const;
  /// Set the line's value to that given by an Atlas object
  void fromAtlas(const AtlasInType& a);

///
  Line& operator=(const Line& a);

/// generic: check if two classes are equal, up to a given tolerance
  bool isEqualTo(const Line& s, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const;
  /// generic: check if two classes are equal, up to tolerance WFMATH_EPSILON
  bool operator==(const Line& s) const	{return isEqualTo(s);}
  /// generic: check if two classes are not equal, up to tolerance WFMATH_EPSILON
  bool operator!=(const Line& s) const	{return !isEqualTo(s);}

/// generic: returns true if the class instance has been initialized
  bool isValid() const {return m_points.size() > 1;}

// Now we begin with the functions in the shape interface

// Descriptive characteristics

/// shape: return the number of corners in the shape.
  /**
   * For many shape classes, this is a fixed constant
   **/
  size_t numCorners() const {return m_points.size();}
  /// shape: return the position of the i'th corner, where 0 <= i < numCorners()
  Point<dim> getCorner(size_t i) const {return m_points[i];}
  /// shape: return the position of the center of the shape
  Point<dim> getCenter() const {return Barycenter(m_points);}

// Add before i'th corner, zero is beginning, numCorners() is end
  bool addCorner(size_t i, const Point<dim>& p, CoordType = numeric_constants<CoordType>::epsilon())
  {m_points.insert(m_points.begin() + i, p); return true;}

// Remove the i'th corner
  void removeCorner(size_t i) {m_points.erase(m_points.begin() + i);}

bool moveCorner(size_t i,
                  const Point<dim>& p,
                  CoordType = numeric_constants<CoordType>::epsilon())
  {m_points[i] = p; return true;}

// Movement functions

/// shape: move the shape by an amount given by the Vector v
  Line& shift(const Vector<dim>& v); // Move the shape a certain distance
  /// shape: move the shape, moving the given corner to the Point p
  /**
   * The corner in question is getCorner(corner).
   **/
  Line& moveCornerTo(const Point<dim>& p, size_t corner)
	{return shift(p - getCorner(corner));}
  /// shape: move the shape, moving the center to the Point p
  /**
   * The center is defined by getCenter()
   **/
  Line& moveCenterTo(const Point<dim>& p)
	{return shift(p - getCenter());}

/// shape: rotate the shape while holding the given corner fixed
  /**
   * The corner in question is getCorner(corner).
   **/
  Line& rotateCorner(const RotMatrix<dim>& m, size_t corner)
	{return rotatePoint(m, getCorner(corner));}
  /// shape: rotate the shape while holding the center fixed
  /**
   * The center is defined by getCenter()
   **/
  Line& rotateCenter(const RotMatrix<dim>& m)
	{return rotatePoint(m, getCenter());}
  /// shape: rotate the shape while holding the Point p fixed.
  /**
   * Note that p can be any Point, it does not have to lie within
   * the shape.
   **/
  Line& rotatePoint(const RotMatrix<dim>& m, const Point<dim>& p);

AxisBox<dim> boundingBox() const {return BoundingBox(m_points);}
  Ball<dim> boundingSphere() const {return BoundingSphere(m_points);}
  Ball<dim> boundingSphereSloppy() const {return BoundingSphereSloppy(m_points);}

private:
  std::vector<Point<dim> > m_points;
  typedef typename std::vector<Point<dim> >::iterator iterator;
  typedef typename std::vector<Point<dim> >::const_iterator const_iterator;
  typedef typename std::vector<Point<dim> >::size_type size_type;
};

template<int dim>
inline Line<dim>& Line<dim>::operator=(const Line& rhs)
{
    m_points = rhs.m_points;
    return *this;
}

} // namespace WFMath

#endif  // WFMATH_LINE_H
07070100000034000081A40000000200000002000000015D8693EF00000793000000000000000000000000000000000000002E00000000wfmath-1569100783.d0f8a54/wfmath/line_funcs.h// line_funcs.h (Line<> implementation)
//
//  The WorldForge Project
//  Copyright (C) 2012  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Al Riddoch

#ifndef WFMATH_LINE_FUNCS_H
#define WFMATH_LINE_FUNCS_H

#include <wfmath/line.h>

namespace WFMath {

template<int dim>
inline bool Line<dim>::isEqualTo(const Line<dim> & l, CoordType epsilon) const
{
  size_type size = m_points.size();
  if (size != l.m_points.size()) {
    return false;
  }

for (size_type i = 0; i < size; ++i) {
    if (!Equal(m_points[i], l.m_points[i], epsilon)) {
      return false;
    }
  }

return true;
}

template<int dim>
inline Line<dim>& Line<dim>::shift(const Vector<dim>& v)
{
  for (iterator i = m_points.begin(); i != m_points.end(); ++i) {
    *i += v;
  }

return *this;
}

template<int dim>
inline Line<dim>& Line<dim>::rotatePoint(const RotMatrix<dim>& m,
                                         const Point<dim>& p)
{
  for (iterator i = m_points.begin(); i != m_points.end(); ++i) {
    i->rotate(m, p);
  }

return *this;
}

} // namespace WFMath

#endif  // WFMATH_LINE_FUNCS_H
07070100000035000081A40000000200000002000000015D8693EF00000B46000000000000000000000000000000000000002F00000000wfmath-1569100783.d0f8a54/wfmath/line_test.cpp// line_test.cpp (Line<> test functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2012-01-26

#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include "const.h"
#include "vector.h"
#include "point.h"
#include "axisbox.h"
#include "ball.h"
#include "stream.h"
#include "line.h"

#include "general_test.h"
#include "shape_test.h"

#include <vector>
#include <list>

using namespace WFMath;

template<int dim>
void test_line(const Line<dim>& p)
{
  std::cout << "Testing line: " << p << std::endl;

// test_general(p);
  // test_shape(p);

assert(p == p);

// FIXME more tests
}

void test_modify()
{
  Line<2> line;
  line.addCorner(0, Point<2>(2, 2));
  line.addCorner(0, Point<2>(0, 0));
  
  assert(line.getCorner(0) == Point<2>(0, 0));

line.moveCorner(0, Point<2>(1, 1));
  assert(line.getCorner(0) == Point<2>(1, 1));
}

int main()
{
  Line<2> line2_1;
  assert(!line2_1.isValid());
  line2_1.addCorner(0, Point<2>(0, 0));
  line2_1.addCorner(0, Point<2>(4, 0));
  line2_1.addCorner(0, Point<2>(4, -4));
  line2_1.addCorner(0, Point<2>(0, -4));
  assert(line2_1.isValid());

test_line(line2_1);

assert(line2_1 == line2_1);

Line<2> line2_2;
  assert(!line2_2.isValid());
  line2_2.addCorner(0, Point<2>(0, 0));
  line2_2.addCorner(0, Point<2>(4, -4));
  line2_2.addCorner(0, Point<2>(4, 0));
  line2_2.addCorner(0, Point<2>(0, -4));
  assert(line2_2.isValid());

// Check in-equality
  assert(line2_1 != line2_2);

// Check assignment
  line2_2 = line2_1;

// Check equality
  assert(line2_1 == line2_2);

Line<2> line2_3;
  assert(!line2_3.isValid());
  assert(line2_3 != line2_1);
  line2_3 = line2_1;
  assert(line2_3 == line2_1);

// Check bounding box calculation
  assert(Equal(line2_1.boundingBox(),
               AxisBox<2>(Point<2>(0, -4), Point<2>(4, 0))));

Line<2> line2_4(line2_1);

assert(line2_1 == line2_4);

Line<3> line3;

test_line(line3);

test_modify();

return 0;
}
07070100000036000081A40000000200000002000000015D8693EF0000123E000000000000000000000000000000000000002C00000000wfmath-1569100783.d0f8a54/wfmath/miniball.h

//    Copright (C) 1999
//    $Revision$
//    $Date$
//
//    This program is free software; you can redistribute it and/or modify
//    it under the terms of the GNU General Public License as published by
//    the Free Software Foundation; either version 2 of the License, or
//    (at your option) any later version.
//
//    This program is distributed in the hope that it will be useful,
//    but WITHOUT ANY WARRANTY; without even the implied warranty of
//    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//    GNU General Public License for more details.
//
//    You should have received a copy of the GNU General Public License
//    along with this program; if not, write to the Free Software
//    Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA,
//    or download the License terms from prep.ai.mit.edu/pub/gnu/COPYING-2.0.
//
//    Contact:
//    --------
//    Bernd Gaertner
//    Institut f. Informatik
//    ETH Zuerich
//    ETH-Zentrum
//    CH-8092 Zuerich, Switzerland
//    http://www.inf.ethz.ch/personal/gaertner
//

// 2001-1-9: included in WFMath backend. Namespace wrapping added
// and filename changed to follow WFMath conventions, but otherwise
// unchanged.

#ifndef WFMATH_MINIBALL_H
#define WFMATH_MINIBALL_H

#include <list>
#include <wfmath/wrapped_array.h>

namespace WFMath { namespace _miniball {

template <int d> class Miniball;
    template <int d> class Basis;

// Miniball
    // --------
    
    template <int d>
    class Miniball {
        public:
            // types
            typedef Wrapped_array<d>                            Point;
            typedef typename std::list<Point>::iterator         It;
            typedef typename std::list<Point>::const_iterator   Cit;
    
        private:
            // data members
            std::list<Point> L;         // STL list keeping the points
            Basis<d>    B;              // basis keeping the current ball
            It          support_end;    // past-the-end iterator of support set
    
            // private methods
            void        mtf_mb (It k);
            void        pivot_mb (It k);
            void        move_to_front (It j);
            double      max_excess (It t, It i, It& pivot) const;
            double      abs (double r) const {return (r>0)? r: (-r);}
            double      sqr (double r) const {return r*r;}
    
        public:
            // construction
            Miniball() : L(), B(), support_end() {}
            void        check_in (const Point& p);
            void        build (bool pivoting = true);
    
            // access
            Point       center() const;
            double      squared_radius () const;
            int         nr_points () const;
            Cit         points_begin () const;
            Cit         points_end () const;
            int         nr_support_points () const;
            Cit         support_points_begin () const;
            Cit         support_points_end () const;
    
            // checking
            double      accuracy (double& slack) const;
            bool        is_valid (double tolerance = 1e-15) const;
     };

// Basis
    // -----
    
    template <int d>
    class Basis {
        private:
            // types
            typedef Wrapped_array<d>            Point;
    
            // data members
            int                 m, s;   // size and number of support points
            double              q0[d];
    
            double              z[d+1];
            double              f[d+1];
            double              v[d+1][d];
            double              a[d+1][d];
    
            double              c[d+1][d];
            double              sqr_r[d+1];
    
            double*             current_c;      // points to some c[j]
            double              current_sqr_r;
    
            double              sqr (double r) const {return r*r;}
    
        public:
            Basis();
    
            // access
            const double*       center() const;
            double              squared_radius() const;
            int                 size() const;
            int                 support_size() const;
            double              excess (const Point& p) const;
    
            // modification
            void                reset(); // generates empty sphere with m=s=0
            bool                push (const Point& p);
            void                pop ();
    
            // checking
            double              slack() const;
    };
    
}} // namespace WFMath::_miniball

#endif // WFMATH_MINIBALL_H
07070100000037000081A40000000200000002000000015D8693EF00001F9F000000000000000000000000000000000000003200000000wfmath-1569100783.d0f8a54/wfmath/miniball_funcs.h

// 2001-1-9: included in WFMath backend. Namespace wrapping added
// and filename changed to follow WFMath conventions, but otherwise
// unchanged.

#ifndef WFMATH_MINIBALL_FUNCS_H
#define WFMATH_MINIBALL_FUNCS_H

#include <cassert>

namespace WFMath { namespace _miniball {

// Miniball
   // --------
   
   template <int d>
   void Miniball<d>::check_in (const Point& p)
   {
       L.push_back(p);
   }
   
   
   template <int d>
   void Miniball<d>::build (bool pivoting)
   {
       B.reset();
       support_end = L.begin();
       if (pivoting)
           pivot_mb (L.end());
       else
           mtf_mb (L.end());
   }
   
   
   template <int d>
   void Miniball<d>::mtf_mb (It i)
   {
       support_end = L.begin();
       if ((B.size())==d+1) return;
       for (It k=L.begin(); k!=i;) {
           It j=k++;
           if (B.excess(*j) > 0) {
               if (B.push(*j)) {
                   mtf_mb (j);
                   B.pop();
                   move_to_front(j);
               }
           }
       }
   }
   
   template <int d>
   void Miniball<d>::move_to_front (It j)
   {
       if (support_end == j)
           support_end++;
       L.splice (L.begin(), L, j);
   }
   
   
   template <int d>
   void Miniball<d>::pivot_mb (It i)
   {
       It t = ++L.begin();
       mtf_mb (t);
       double max_e, old_sqr_r;
       do {
           It pivot;
           max_e = max_excess (t, i, pivot);
           if (max_e <= 0)
               break;
           t = support_end;
           if (t==pivot) ++t;
           old_sqr_r = B.squared_radius();
           B.push (*pivot);
           mtf_mb (support_end);
           B.pop();
           move_to_front (pivot);
       } while (B.squared_radius() > old_sqr_r);
   }
   
   
   template <int d>
   double Miniball<d>::max_excess (It t, It i, It& pivot) const
   {
       const double *c = B.center(), sqr_r = B.squared_radius();
       double e, max_e = 0;
       for (It k=t; k!=i; ++k) {
           const double *p = (*k).begin();
           e = -sqr_r;
           for (int j=0; j<d; ++j)
               e += sqr(p[j]-c[j]);
           if (e > max_e) {
               max_e = e;
               pivot = k;
           }
       }
       return max_e;
    }
   
   
   
   template <int d>
   typename Miniball<d>::Point Miniball<d>::center () const
   {
       return Point(B.center());
   }
   
   template <int d>
   double Miniball<d>::squared_radius () const
   {
       return B.squared_radius();
   }
   
   
   template <int d>
   int Miniball<d>::nr_points () const
   {
       return L.size();
   }
   
   template <int d>
   typename Miniball<d>::Cit Miniball<d>::points_begin () const
   {
       return L.begin();
   }
   
   template <int d>
   typename Miniball<d>::Cit Miniball<d>::points_end () const
   {
       return L.end();
   }
   
   
   template <int d>
   int Miniball<d>::nr_support_points () const
   {
       return B.support_size();
   }
   
   template <int d>
   typename Miniball<d>::Cit Miniball<d>::support_points_begin () const
   {
       return L.begin();
   }
   
   template <int d>
   typename Miniball<d>::Cit Miniball<d>::support_points_end () const
   {
       return support_end;
   }
   
   
   
   template <int d>
   double Miniball<d>::accuracy (double& slack) const
   {
       double e, max_e = 0;
       int n_supp=0;
       Cit i;
       for (i=L.begin(); i!=support_end; ++i,++n_supp)
           if ((e = abs (B.excess (*i))) > max_e)
               max_e = e;
   
       // you've found a non-numerical problem if the following ever fails
       assert (n_supp == nr_support_points());
   
       for (i=support_end; i!=L.end(); ++i)
          if ((e = B.excess (*i)) > max_e)
               max_e = e;
   
       slack = B.slack();
       return (max_e/squared_radius());
   }
   
   
   template <int d>
   bool Miniball<d>::is_valid (double tolerance) const
   {
       double slack;
       return ( (accuracy (slack) < tolerance) && (slack == 0) );
   }

// Basis
   // -----
   
   template <int d>
   const double* Basis<d>::center () const
   {
       return current_c;
   }
   
   template <int d>
   double Basis<d>::squared_radius() const
   {
       return current_sqr_r;
   }
   
   template <int d>
   int Basis<d>::size() const
   {
       return m;
   }
   
   template <int d>
   int Basis<d>::support_size() const
   {
       return s;
   }
   
   template <int d>
   double Basis<d>::excess (const Point& p) const
   {
       double e = -current_sqr_r;
       for (int k=0; k<d; ++k)
          e += sqr(p[k]-current_c[k]);
       return e;
   }
   
   
   
   template <int d>
   void Basis<d>::reset ()
   {
       m = s = 0;
       // we misuse c[0] for the center of the empty sphere
       for (int j=0; j<d; ++j)
           c[0][j]=0;
       current_c = c[0];
       current_sqr_r = -1;
   }
   
   
   template <int d>
   Basis<d>::Basis () : m(0), s(0), current_c(0), current_sqr_r(-1.)
   {
       reset();
   }
   
   
   template <int d>
   void Basis<d>::pop ()
   {
       --m;
   }
   
   
   template <int d>
   bool Basis<d>::push (const Point& p)
   {
       int i, j;
       double eps = 1e-32;
       if (m==0) {
           for (i=0; i<d; ++i)
               q0[i] = p[i];
           for (i=0; i<d; ++i)
               c[0][i] = q0[i];
           sqr_r[0] = 0;
       } else {
          // set v_m to Q_m
          for (i=0; i<d; ++i)
               v[m][i] = p[i]-q0[i];
   
          // compute the a_{m,i}, i< m
          for (i=1; i<m; ++i) {
               a[m][i] = 0;
               for (j=0; j<d; ++j)
                   a[m][i] += v[i][j] * v[m][j];
               a[m][i]*=(2/z[i]);
          }
   
          // update v_m to Q_m-\bar{Q}_m
          for (i=1; i<m; ++i) {
               for (j=0; j<d; ++j)
                   v[m][j] -= a[m][i]*v[i][j];
          }
   
          // compute z_m
          z[m]=0;
          for (j=0; j<d; ++j)
               z[m] += sqr(v[m][j]);
          z[m]*=2;
   
          // reject push if z_m too small
          if (z[m]<eps*current_sqr_r) {
               return false;
          }
   
          // update c, sqr_r
          double e = -sqr_r[m-1];
          for (i=0; i<d; ++i)
               e += sqr(p[i]-c[m-1][i]);
          f[m]=e/z[m];
   
          for (i=0; i<d; ++i)
               c[m][i] = c[m-1][i]+f[m]*v[m][i];
          sqr_r[m] = sqr_r[m-1] + e*f[m]/2;
       }
       current_c = c[m];
       current_sqr_r = sqr_r[m];
       s = ++m;
       return true;
   }
   
   
   
   template <int d>
   double Basis<d>::slack () const
   {
       double l[d+1], min_l=0;
       l[0] = 1;
       for (int i=s-1; i>0; --i) {
           l[i] = f[i];
           for (int k=s-1; k>i; --k)
               l[i]-=a[k][i]*l[k];
           if (l[i] < min_l) min_l = l[i];
           l[0] -= l[i];
       }
       if (l[0] < min_l) min_l = l[0];
       return ( (min_l < 0) ? -min_l : 0);
   }
   
}} // namespace WFMath::_miniball

#endif // WFMATH_MINIBALL_FUNCS_H
07070100000038000081A40000000200000002000000015D8693EF000011BE000000000000000000000000000000000000002B00000000wfmath-1569100783.d0f8a54/wfmath/point.cpp// point.cpp (Point<> backend)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include "point_funcs.h"
#include "axisbox_funcs.h"

#include "basis.h"
#include "quaternion.h"

#include <vector>
#include <list>

namespace WFMath {

template<>
Point<2>& Point<2>::polar(CoordType r, CoordType theta)
{
  CoordType d[2] = {r, theta};
  _PolarToCart(d, m_elem);
  m_valid = true;
  return *this;
}

template<>
void Point<2>::asPolar(CoordType& r, CoordType& theta) const
{
  CoordType d[2];
  _CartToPolar(m_elem, d);
  r = d[0];
  theta = d[1];
}

template<>
Point<3>& Point<3>::polar(CoordType r, CoordType theta, CoordType z)
{
  CoordType d[2] = {r, theta};
  _PolarToCart(d, m_elem);
  m_elem[2] = z;
  m_valid = true;
  return *this;
}

template<>
void Point<3>::asPolar(CoordType& r, CoordType& theta, CoordType& z) const
{
  CoordType d[2];
  _CartToPolar(m_elem, d);
  r = d[0];
  theta = d[1];
  z = m_elem[2];
}

template<>
Point<3>& Point<3>::spherical(CoordType r, CoordType theta, CoordType phi)
{
  CoordType d[3] = {r, theta, phi};
  _SphericalToCart(d, m_elem);
  m_valid = true;
  return *this;
}

template<>
void Point<3>::asSpherical(CoordType& r, CoordType& theta,
				   CoordType& phi) const
{
  CoordType d[3];
  _CartToSpherical(m_elem, d);
  r = d[0];
  theta = d[1];
  phi = d[2];
}

template<>
Point<3>& Point<3>::rotate(const Quaternion& q, const Point<3>& p)
{
  return (*this = p + (*this - p).rotate(q));
}

template<>
Point<3>& Point<3>::rotatePoint(const Quaternion& q, const Point<3>& p)
{
  return rotate(q, p);
}

template<>
Point<3> Point<3>::toLocalCoords(const Point<3>& origin,
                                 const Quaternion& rotation) const
{
  return Point().setToOrigin() + (*this - origin).rotate(rotation.inverse());
}

template<>
Point<3> Point<3>::toParentCoords(const Point<3>& origin,
                                 const Quaternion& rotation) const
{
  return origin + (*this - Point().setToOrigin()).rotate(rotation);
}

template class Point<3>;
template class Point<2>;

template CoordType SquaredDistance<3>(const Point<3> &, const Point<3> &);
template CoordType SquaredDistance<2>(const Point<2> &, const Point<2> &);

template Point<3> Midpoint<3>(const Point<3> &, const Point<3> &, CoordType);
template Point<2> Midpoint<2>(const Point<2> &, const Point<2> &, CoordType);

template Point<3> Barycenter<3, std::vector>(const std::vector<Point<3> > &);
template Point<3> Barycenter<3, std::vector, std::list>(const std::vector<Point<3> > &, const std::list<CoordType> &);

template Point<2> Barycenter<2, std::vector>(const std::vector<Point<2> > &);
template Point<2> Barycenter<2, std::vector, std::list>(const std::vector<Point<2> > &, const std::list<CoordType> &);

template Vector<3> operator-<3>(const Point<3> &, const Point<3> &);
template Vector<2> operator-<2>(const Point<2> &, const Point<2> &);

template Point<3> operator-<3>(const Point<3> &, const Vector<3> &);
template Point<2> operator-<2>(const Point<2> &, const Vector<2> &);

template Point<3>& operator-=<3>(Point<3> &, const Vector<3> &);
template Point<2>& operator-=<2>(Point<2> &, const Vector<2> &);

template Point<3> operator+<3>(const Vector<3> &, const Point<3> &);
template Point<2> operator+<2>(const Vector<2> &, const Point<2> &);

template Point<3> operator+<3>(const Point<3> &, const Vector<3> &);
template Point<2> operator+<2>(const Point<2> &, const Vector<2> &);

template Point<3>& operator+=<3>(Point<3> &, const Vector<3> &);
template Point<2>& operator+=<2>(Point<2> &, const Vector<2> &);

} // namespace WFMath
07070100000039000081A40000000200000002000000015D8693EF000029A9000000000000000000000000000000000000002900000000wfmath-1569100783.d0f8a54/wfmath/point.h// point.h (point class copied from libCoal, subsequently modified)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001, 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_POINT_H
#define WFMATH_POINT_H

#include <wfmath/const.h>

#include <memory>
#include <iosfwd>

#include <cmath>

namespace WFMath {

template<int dim>
Point<dim>& operator+=(Point<dim>& p, const Vector<dim>& v);
template<int dim>
Point<dim>& operator-=(Point<dim>& p, const Vector<dim>& v);

template<int dim>
Vector<dim> operator-(const Point<dim>& c1, const Point<dim>& c2);
template<int dim>
Point<dim> operator+(const Point<dim>& c, const Vector<dim>& v);
template<int dim>
Point<dim> operator+(const Vector<dim>& v, const Point<dim>& c);
template<int dim>
Point<dim> operator-(const Point<dim>& c, const Vector<dim>& v);

template<int dim>
CoordType SquaredDistance(const Point<dim>& p1, const Point<dim>& p2);
template<int dim>
CoordType Distance(const Point<dim>& p1, const Point<dim>& p2)
  {return std::sqrt(SquaredDistance(p1, p2));}
template<int dim>
CoordType SloppyDistance(const Point<dim>& p1, const Point<dim>& p2)
  {return (p1 - p2).sloppyMag();}

/// Find the center of a set of points, all weighted equally
template<int dim, template<class, class> class container>
Point<dim> Barycenter(const container<Point<dim>, std::allocator<Point<dim> > >& c);
/// Find the center of a set of points with the given weights
/**
 * If the number of points and the number of weights are not equal,
 * the excess of either is ignored. The weights (or that subset
 * which is used, if there are more weights than points), must not
 * sum to zero.
 **/
template<int dim, template<class, class> class container,
      template<class, class> class container2>
Point<dim> Barycenter(const container<Point<dim>, std::allocator<Point<dim> > >& c,
          const container2<CoordType, std::allocator<CoordType> >& weights);

// This is used a couple of places in the library
template<int dim>
Point<dim> Midpoint(const Point<dim>& p1, const Point<dim>& p2,
        CoordType dist = 0.5);

template<int dim>
std::ostream& operator<<(std::ostream& os, const Point<dim>& m);
template<int dim>
std::istream& operator>>(std::istream& is, Point<dim>& m);

template<typename Shape>
class ZeroPrimitive;

/// A dim dimensional point
/**
 * This class implements the full shape interface, as described in
 * the fake class Shape.
 **/
template<int dim = 3>
class Point
{
 friend class ZeroPrimitive<Point<dim> >;
 public:
  /// Construct an uninitialized point
  Point () : m_valid(false) {}
  /// Construct a copy of a point
  Point (const Point& p);
  /// Construct a point from an object passed by Atlas
  explicit Point (const AtlasInType& a);
  /// Construct a point from a vector.
  explicit Point(const Vector<dim>& vector);

/**
   * @brief Provides a global instance preset to zero.
   */
  static const Point<dim>& ZERO();

friend std::ostream& operator<< <dim>(std::ostream& os, const Point& p);
  friend std::istream& operator>> <dim>(std::istream& is, Point& p);

/// Create an Atlas object from the point
  AtlasOutType toAtlas() const;
  /// Set the point's value to that given by an Atlas object
  void fromAtlas(const AtlasInType& a);

Point& operator= (const Point& rhs);

bool isEqualTo(const Point &p, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const;
  bool operator== (const Point& rhs) const	{return isEqualTo(rhs);}
  bool operator!= (const Point& rhs) const	{return !isEqualTo(rhs);}

bool isValid() const {return m_valid;}
  /// make isValid() return true if you've initialized the point by hand
  void setValid(bool valid = true) {m_valid = valid;}

/// Set point to (0,0,...,0)
  Point& setToOrigin();

// Operators

// Documented in vector.h
  friend Vector<dim> operator-<dim>(const Point& c1, const Point& c2);
  friend Point operator+<dim>(const Point& c, const Vector<dim>& v);
  friend Point operator-<dim>(const Point& c, const Vector<dim>& v);
  friend Point operator+<dim>(const Vector<dim>& v, const Point& c);

friend Point& operator+=<dim>(Point& p, const Vector<dim>& rhs);
  friend Point& operator-=<dim>(Point& p, const Vector<dim>& rhs);

/// Rotate about point p
  Point& rotate(const RotMatrix<dim>& m, const Point& p)
  {return (*this = p + Prod(*this - p, m));}

// Functions so that Point<> has the generic shape interface

size_t numCorners() const {return 1;}
  Point<dim> getCorner(size_t) const { return *this;}
  Point<dim> getCenter() const {return *this;}

Point shift(const Vector<dim>& v) {return *this += v;}
  Point moveCornerTo(const Point& p, size_t)
  {return operator=(p);}
  Point moveCenterTo(const Point& p) {return operator=(p);}

Point& rotateCorner(const RotMatrix<dim>&, size_t)
  {return *this;}
  Point& rotateCenter(const RotMatrix<dim>&) {return *this;}
  Point& rotatePoint(const RotMatrix<dim>& m, const Point& p) {return rotate(m, p);}

// 3D rotation functions
  Point& rotate(const Quaternion& q, const Point& p);
  Point& rotateCorner(const Quaternion&, size_t)
  { return *this;}
  Point& rotateCenter(const Quaternion&) {return *this;}
  Point& rotatePoint(const Quaternion& q, const Point& p);

// The implementations of these lie in axisbox_funcs.h and
  // ball_funcs.h, to reduce include dependencies
  AxisBox<dim> boundingBox() const;
  Ball<dim> boundingSphere() const;
  Ball<dim> boundingSphereSloppy() const;

Point toParentCoords(const Point& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
  {return origin + (*this - Point().setToOrigin()) * rotation;}
  Point toParentCoords(const AxisBox<dim>& coords) const;
  Point toParentCoords(const RotBox<dim>& coords) const;

// toLocal is just like toParent, expect we reverse the order of
  // translation and rotation and use the opposite sense of the rotation
  // matrix

Point toLocalCoords(const Point& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
  {return Point().setToOrigin() + rotation * (*this - origin);}
  Point toLocalCoords(const AxisBox<dim>& coords) const;
  Point toLocalCoords(const RotBox<dim>& coords) const;

// 3D only
  Point toParentCoords(const Point& origin, const Quaternion& rotation) const;
  Point toLocalCoords(const Point& origin, const Quaternion& rotation) const;

// Member access

/// Access the i'th coordinate of the point
  CoordType operator[](const int i) const {return m_elem[i];}
  /// Access the i'th coordinate of the point
  CoordType& operator[](const int i)	  {return m_elem[i];}

/// Get the square of the distance from p1 to p2
  friend CoordType SquaredDistance<dim>(const Point& p1, const Point& p2);

// FIXME instatiation problem when declared as friend
//  template<template<class> class container>
//  friend Point Barycenter(const container<Point>& c);

/// Find a point on the line containing p1 and p2, by default the midpoint
  /**
   * The default value of 0.5 for dist gives the midpoint. A value of 0 gives
   * p1, and 1 gives p2. Values of dist outside the [0, 1] range are allowed,
   * and give points on the line which are not on the segment bounded by
   * p1 and p2.
   **/
  friend Point<dim> Midpoint<dim>(const Point& p1, const Point& p2, CoordType dist);

// 2D/3D stuff

/// 2D only: construct a point from its (x, y) coordinates
  Point (CoordType x, CoordType y); // 2D only
  /// 3D only: construct a point from its (x, y, z) coordinates
  Point (CoordType x, CoordType y, CoordType z); // 3D only

// Label the first three components of the vector as (x,y,z) for
  // 2D/3D convienience

/// access the first component of a point
  CoordType x() const	{return m_elem[0];}
  /// access the first component of a point
  CoordType& x()	{return m_elem[0];}
  /// access the second component of a point
  CoordType y() const	{return m_elem[1];}
  /// access the second component of a point
  CoordType& y()	{return m_elem[1];}
  /// access the third component of a point
  CoordType z() const;
  /// access the third component of a point
  CoordType& z();

/// 2D only: construct a vector from polar coordinates
  Point& polar(CoordType r, CoordType theta);
  /// 2D only: convert a vector to polar coordinates
  void asPolar(CoordType& r, CoordType& theta) const;

/// 3D only: construct a vector from polar coordinates
  Point& polar(CoordType r, CoordType theta, CoordType z);
  /// 3D only: convert a vector to polar coordinates
  void asPolar(CoordType& r, CoordType& theta, CoordType& z) const;
  /// 3D only: construct a vector from spherical coordinates
  Point& spherical(CoordType r, CoordType theta, CoordType phi);
  /// 3D only: convert a vector to spherical coordinates
  void asSpherical(CoordType& r, CoordType& theta, CoordType& phi) const;

const CoordType* elements() const {return m_elem;}

private:
  CoordType m_elem[dim];
  bool m_valid;
};

template<>
inline CoordType Point<3>::z() const
{
  return m_elem[2];
}

template<>
inline CoordType& Point<3>::z()
{
  return m_elem[2];
}

template<int dim>
inline Point<dim> operator+(const Point<dim>& c, const Vector<dim>& v)
{
  Point<dim> out(c);

out += v;

return out;
}

template<int dim>
inline Point<dim> operator+(const Vector<dim>& v, const Point<dim>& c)
{
  Point<dim> out(c);

out += v;

return out;
}

template<int dim>
inline Point<dim> operator-(const Point<dim>& c, const Vector<dim>& v)
{
  Point<dim> out(c);

out -= v;

return out;
}

template<>
inline Point<2>::Point(CoordType x, CoordType y) : m_valid(true)
{
  m_elem[0] = x;
  m_elem[1] = y;
}

template<>
inline Point<3>::Point(CoordType x, CoordType y, CoordType z) : m_valid(true)
{
  m_elem[0] = x;
  m_elem[1] = y;
  m_elem[2] = z;
}

} // namespace WFMath

#endif  // WFMATH_POINT_H
0707010000003A000081A40000000200000002000000015D8693EF0000193D000000000000000000000000000000000000002F00000000wfmath-1569100783.d0f8a54/wfmath/point_funcs.h// point_funcs.h (point class copied from libCoal, subsequently modified)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001, 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_POINT_FUNCS_H
#define WFMATH_POINT_FUNCS_H

#include <wfmath/point.h>

#include <wfmath/vector.h>
#include <wfmath/zero.h>

#include <cmath>

namespace WFMath {

template<int dim>
inline Point<dim>::Point(const Point<dim>& p) : m_valid(p.m_valid)
{
  for(int i = 0; i < dim; ++i) {
    m_elem[i] = p.m_elem[i];
  }
}

template<int dim>
inline Point<dim>::Point(const Vector<dim>& v) : m_valid(v.isValid())
{
  for(int i = 0; i < dim; ++i) {
    m_elem[i] = v.elements()[i];
  }
}

template<int dim>
const Point<dim>& Point<dim>::ZERO()
{
  static ZeroPrimitive<Point<dim> > zeroPoint(dim);
  return zeroPoint.getShape();
}

template<int dim>
inline Point<dim>& Point<dim>::setToOrigin()
{
  for(int i = 0; i < dim; ++i) {
    m_elem[i] = 0;
  }

m_valid = true;

return *this;
}

template<int dim>
inline bool Point<dim>::isEqualTo(const Point<dim> &p, CoordType epsilon) const
{
  CoordType delta = _ScaleEpsilon(m_elem, p.m_elem, dim, epsilon);

//If anyone is invalid they are never equal
  if (!p.m_valid || !m_valid) {
    return false;
  }

for(int i = 0; i < dim; ++i) {
    if(std::fabs(m_elem[i] - p.m_elem[i]) > delta) {
      return false;
    }
  }

return true;
}

template<int dim>
inline Vector<dim> operator-(const Point<dim>& c1, const Point<dim>& c2)
{
  Vector<dim> out;

for(int i = 0; i < dim; ++i) {
    out.m_elem[i] = c1.m_elem[i] - c2.m_elem[i];
  }

out.m_valid = c1.m_valid && c2.m_valid;

return out;
}

template<int dim>
inline Point<dim>& operator+=(Point<dim>& p, const Vector<dim> &rhs)
{
    for(int i = 0; i < dim; ++i) {
      p.m_elem[i] += rhs.m_elem[i];
    }

p.m_valid = p.m_valid && rhs.m_valid;

return p;
}

template<int dim>
inline Point<dim>& operator-=(Point<dim>& p, const Vector<dim> &rhs)
{
    for(int i = 0; i < dim; ++i) {
      p.m_elem[i] -= rhs.m_elem[i];
    }

p.m_valid = p.m_valid && rhs.m_valid;

return p;
}

template<int dim>
inline Point<dim>& Point<dim>::operator=(const Point<dim>& rhs)
{
    // Compare pointer addresses
    if (this == &rhs) {
      return *this;
    }

for(int i = 0; i < dim; ++i) {
      m_elem[i] = rhs.m_elem[i];
    }

m_valid = rhs.m_valid;

return *this;
}

template<int dim>
inline CoordType SquaredDistance(const Point<dim>& p1, const Point<dim>& p2)
{
  CoordType ans = 0;

for(int i = 0; i < dim; ++i) {
    CoordType diff = p1.m_elem[i] - p2.m_elem[i];
    ans += diff * diff;
  }

return (std::fabs(ans) >= _ScaleEpsilon(p1.m_elem, p2.m_elem, dim)) ? ans : 0;
}

template<int dim, template<class, class> class container,
			template<class, class> class container2>
Point<dim> Barycenter(const container<Point<dim>, std::allocator<Point<dim> > >& c,
		      const container2<CoordType, std::allocator<CoordType> >& weights)
{
  // FIXME become friend

typename container<Point<dim>, std::allocator<Point<dim> > >::const_iterator c_i = c.begin(), c_end = c.end();
  typename container2<CoordType, std::allocator<CoordType> >::const_iterator w_i = weights.begin(),
						 w_end = weights.end();

Point<dim> out;

if (c_i == c_end || w_i == w_end) {
    return out;
  }

bool valid = c_i->isValid();

CoordType tot_weight = *w_i, max_weight = std::fabs(*w_i);
  for(int j = 0; j < dim; ++j) {
    out[j] = (*c_i)[j] * *w_i;
  }

while(++c_i != c_end && ++w_i != w_end) {
    tot_weight += *w_i;
    CoordType val = std::fabs(*w_i);
    if(val > max_weight)
      max_weight = val;
    if(!c_i->isValid())
      valid = false;
    for(int j = 0; j < dim; ++j)
      out[j] += (*c_i)[j] * *w_i;
  }

// Make sure the weights don't add up to zero
  if (max_weight <= 0 || std::fabs(tot_weight) <= max_weight * numeric_constants<CoordType>::epsilon()) {
    return out;
  }

for(int j = 0; j < dim; ++j) {
    out[j] /= tot_weight;
  }

out.setValid(valid);

return out;
}

template<int dim, template<class, class> class container>
Point<dim> Barycenter(const container<Point<dim>, std::allocator<Point<dim> > >& c)
{
  // FIXME become friend

typename container<Point<dim>, std::allocator<Point<dim> > >::const_iterator i = c.begin(), end = c.end();

if (i == end) {
    return Point<dim>();
  }

Point<dim> out = *i;
  float num_points = 1;

bool valid = i->isValid();

while(++i != end) {
    ++num_points;
    if(!i->isValid())
      valid = false;
    for(int j = 0; j < dim; ++j)
      out[j] += (*i)[j];
  }

for(int j = 0; j < dim; ++j) {
    out[j] /= num_points;
  }

out.setValid(valid);

return out;
}

template<int dim>
inline Point<dim> Midpoint(const Point<dim>& p1, const Point<dim>& p2, CoordType dist)
{
  Point<dim> out;
  CoordType conj_dist = 1 - dist;

for(int i = 0; i < dim; ++i) {
    out.m_elem[i] = p1.m_elem[i] * conj_dist + p2.m_elem[i] * dist;
  }

out.m_valid = p1.m_valid && p2.m_valid;

return out;
}

template<> Point<2>& Point<2>::polar(CoordType r, CoordType theta);
template<> void Point<2>::asPolar(CoordType& r, CoordType& theta) const;

template<> Point<3>& Point<3>::polar(CoordType r, CoordType theta,
				     CoordType z);
template<> void Point<3>::asPolar(CoordType& r, CoordType& theta,
				  CoordType& z) const;
template<> Point<3>& Point<3>::spherical(CoordType r, CoordType theta,
					 CoordType phi);
template<> void Point<3>::asSpherical(CoordType& r, CoordType& theta,
				      CoordType& phi) const;

} // namespace WFMath

#endif  // WFMATH_POINT_FUNCS_H
0707010000003B000081A40000000200000002000000015D8693EF00000A72000000000000000000000000000000000000003000000000wfmath-1569100783.d0f8a54/wfmath/point_test.cpp// point_test.cpp (Point<> test functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-12

#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include "const.h"
#include "vector.h"
#include "point.h"
#include "axisbox.h"
#include "ball.h"
#include "stream.h"

#include "general_test.h"
#include "shape_test.h"

#include <vector>
#include <list>

using namespace WFMath;

template<int dim>
void test_point(const Point<dim>& p)
{
  std::cout << "Testing point: " << p << std::endl;

test_general(p);
  test_shape(p);

std::vector<Point<dim> > pvec;
  std::list<CoordType> clist;

assert(!Barycenter(pvec).isValid());

assert(!Barycenter(pvec, clist).isValid());

pvec.push_back(p);
  assert(p == Barycenter(pvec));
  clist.push_back(5);
  assert(p == Barycenter(pvec, clist));

// Barycenter fails if sum of weights is 0
  pvec.push_back(p);
  assert(Barycenter(pvec).isValid());
  clist.push_back(-5);
  assert(!Barycenter(pvec, clist).isValid());

assert(p == p + (p - p));

//Check that an invalid point isn't equal to a valid point, even if the values are equal
  Point<dim> invalid_point_1;
  Point<dim> invalid_point_2;
  for (size_t i = 0; i < dim; ++i) {
      invalid_point_1[i] = 0.0;
      invalid_point_2[i] = 0.0;
  }
  assert(invalid_point_1 != Point<dim>::ZERO());

//Two invalid points are never equal
  assert(invalid_point_1 != invalid_point_2);

// FIXME more tests
}

int main()
{
  test_point(Point<2>(1, -1));
  test_point(Point<3>(1, -1, numeric_constants<CoordType>::sqrt2()));

Point<2> zero2 = Point<2>::ZERO();
  assert(zero2.x() == 0 && zero2.y() == 0);
  Point<3> zero3 = Point<3>::ZERO();
  assert(zero3.x() == 0 && zero3.y() == 0 && zero3.z() == 0);

return 0;
}
0707010000003C000081A40000000200000002000000015D8693EF00001285000000000000000000000000000000000000002D00000000wfmath-1569100783.d0f8a54/wfmath/polygon.cpp// polygon.cpp (Polygon<> implementation)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-1-4

#include "polygon_funcs.h"
#include "rotbox.h"

namespace WFMath {

void _Poly2Reorient::reorient(Polygon<2>& poly, size_t skip) const
{
  size_t end = poly.numCorners();

switch(m_type) {
    case _WFMATH_POLY2REORIENT_NONE:
      return;
    case _WFMATH_POLY2REORIENT_CLEAR_AXIS2:
      for(size_t i = 0; i != end; ++i) {
        if(i == skip)
          continue;
        (poly[i])[1] = 0;
      }
      return;
    case _WFMATH_POLY2REORIENT_CLEAR_BOTH_AXES:
      for(size_t i = 0; i != end; ++i) {
        if(i == skip)
          continue;
        (poly[i])[0] = 0;
        (poly[i])[1] = 0;
      }
      return;
    case _WFMATH_POLY2REORIENT_MOVE_AXIS2_TO_AXIS1:
      for(size_t i = 0; i != end; ++i) {
        if(i == skip)
           continue;
        (poly[i])[0] = (poly[i])[1];
        (poly[i])[1] = 0;
      }
      return;
    case _WFMATH_POLY2REORIENT_SCALE1_CLEAR2:
      for(size_t i = 0; i != end; ++i) {
        if(i == skip)
          continue;
        (poly[i])[0] *= m_scale;
        (poly[i])[1] = 0;
      }
      return;
    default:
      assert(false);
      return;
  }
}

//template<>
bool Polygon<2>::isEqualTo(const Polygon<2>& p, CoordType epsilon) const
{
  if(m_points.size() != p.m_points.size())
    return false;

Polygon<2>::theConstIter i1 = m_points.begin(), i2 = p.m_points.begin(),
			   end = m_points.end();

while(i1 != end) {
    if(!Equal(*i1, *i2, epsilon))
      return false;
    ++i1;
    ++i2;
  }

return true;
}

bool Polygon<2>::isValid() const
{
  for(theConstIter i = m_points.begin(); i != m_points.end(); ++i)
    if(!i->isValid())
      return false;

return true;
}

//template<>
Polygon<2>& Polygon<2>::shift(const Vector<2>& v)
{
  for(theIter i = m_points.begin(); i != m_points.end(); ++i)
    *i += v;

return *this;
}

//template<>
Polygon<2>& Polygon<2>::rotatePoint(const RotMatrix<2>& m, const Point<2>& p)
{
  for(theIter i = m_points.begin(); i != m_points.end(); ++i)
    i->rotate(m, p);

return *this;
}

//template<>
Polygon<2> Polygon<2>::toParentCoords(const Point<2>& origin,
    const RotMatrix<2>& rotation) const
{
  Polygon out;
  out.m_points.resize(m_points.size());
  for(unsigned i = 0; i < m_points.size(); ++i)
    out.m_points[i] = m_points[i].toParentCoords(origin, rotation);
  return out;
}

//template<>
Polygon<2> Polygon<2>::toParentCoords(const AxisBox<2>& coords) const
{
  Polygon out;
  out.m_points.resize(m_points.size());
  for(unsigned i = 0; i < m_points.size(); ++i)
    out.m_points[i] = m_points[i].toParentCoords(coords);
  return out;
}

//template<>
Polygon<2> Polygon<2>::toParentCoords(const RotBox<2>& coords) const
{
  Polygon out;
  out.m_points.resize(m_points.size());
  for(unsigned i = 0; i < m_points.size(); ++i)
    out.m_points[i] = m_points[i].toParentCoords(coords);
  return out;
}

//template<>
Polygon<2> Polygon<2>::toLocalCoords(const Point<2>& origin,
    const RotMatrix<2>& rotation) const
{
  Polygon out;
  out.m_points.resize(m_points.size());
  for(unsigned i = 0; i < m_points.size(); ++i)
    out.m_points[i] = m_points[i].toLocalCoords(origin, rotation);
  return out;
}

//template<>
Polygon<2> Polygon<2>::toLocalCoords(const AxisBox<2>& coords) const
{
  Polygon out;
  out.m_points.resize(m_points.size());
  for(unsigned i = 0; i < m_points.size(); ++i)
    out.m_points[i] = m_points[i].toLocalCoords(coords);
  return out;
}

//template<>
Polygon<2> Polygon<2>::toLocalCoords(const RotBox<2>& coords) const
{
  Polygon out;
  out.m_points.resize(m_points.size());
  for(unsigned i = 0; i < m_points.size(); ++i)
    out.m_points[i] = m_points[i].toLocalCoords(coords);
  return out;
}

template class Polygon<3>;
template class _Poly2Orient<3>;

}
0707010000003D000081A40000000200000002000000015D8693EF00004949000000000000000000000000000000000000002B00000000wfmath-1569100783.d0f8a54/wfmath/polygon.h// polygon.h (A 2D polygon embeded in a <dim> dimensional space)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_POLYGON_H
#define WFMATH_POLYGON_H

#include <wfmath/const.h>
#include <wfmath/axisbox.h>
#include <wfmath/ball.h>
#include <wfmath/quaternion.h>

#include <vector>

namespace WFMath {

template<int dim> class Polygon;

template<int dim>
std::ostream& operator<<(std::ostream& os, const Polygon<dim>& r);
template<int dim>
std::istream& operator>>(std::istream& is, Polygon<dim>& r);

/// The 2D specialization of the Polygon<> template
template<>
class Polygon<2>
{
 public:
  Polygon() : m_points() {}
  Polygon(const Polygon& p) = default;
  /// Construct a polygon from an object passed by Atlas
  explicit Polygon(const AtlasInType& a) : m_points() {fromAtlas(a);}

~Polygon() = default;

friend std::ostream& operator<< <2>(std::ostream& os, const Polygon& p);
  friend std::istream& operator>> <2>(std::istream& is, Polygon& p);

/// Create an Atlas object from the box
  AtlasOutType toAtlas() const;
  /// Set the box's value to that given by an Atlas object
  void fromAtlas(const AtlasInType& a);
  
  Polygon& operator=(const Polygon& p) = default;

bool isEqualTo(const Polygon& p, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const;

bool operator==(const Polygon& p) const	{return isEqualTo(p);}
  bool operator!=(const Polygon& p) const	{return !isEqualTo(p);}

bool isValid() const;

// Descriptive characteristics

size_t numCorners() const {return m_points.size();}
  Point<2> getCorner(size_t i) const {return m_points[i];}
  Point<2> getCenter() const {return Barycenter(m_points);}

// For a Polygon<2>, addCorner() and moveCorner() always succeed.
  // The return values are present for the sake of a unified template
  // interface, and the epsilon argument is ignored

// Add before i'th corner, zero is beginning, numCorners() is end
  bool addCorner(size_t i, const Point<2>& p, CoordType = numeric_constants<CoordType>::epsilon())
  {m_points.insert(m_points.begin() + i, p); return true;}

// Remove the i'th corner
  void removeCorner(size_t i) {m_points.erase(m_points.begin() + i);}

// Move the i'th corner to p
  bool moveCorner(size_t i, const Point<2>& p, CoordType = numeric_constants<CoordType>::epsilon())
  {m_points[i] = p; return true;}

// Remove all points
  void clear()	{m_points.clear();}

const Point<2>& operator[](size_t i) const {return m_points[i];}
  Point<2>& operator[](size_t i)		  {return m_points[i];}

void resize(std::vector<Point<2> >::size_type size) {m_points.resize(size);}

// Movement functions

Polygon& shift(const Vector<2>& v);
  Polygon& moveCornerTo(const Point<2>& p, size_t corner)
  {return shift(p - getCorner(corner));}
  Polygon& moveCenterTo(const Point<2>& p)
  {return shift(p - getCenter());}

Polygon& rotateCorner(const RotMatrix<2>& m, size_t corner)
  {rotatePoint(m, getCorner(corner)); return *this;}
  Polygon& rotateCenter(const RotMatrix<2>& m)
  {rotatePoint(m, getCenter()); return *this;}
  Polygon& rotatePoint(const RotMatrix<2>& m, const Point<2>& p);

// Intersection functions

AxisBox<2> boundingBox() const {return BoundingBox(m_points);}
  Ball<2> boundingSphere() const {return BoundingSphere(m_points);}
  Ball<2> boundingSphereSloppy() const {return BoundingSphereSloppy(m_points);}

Polygon toParentCoords(const Point<2>& origin,
      const RotMatrix<2>& rotation = RotMatrix<2>().identity()) const;
  Polygon toParentCoords(const AxisBox<2>& coords) const;
  Polygon toParentCoords(const RotBox<2>& coords) const;

// toLocal is just like toParent, expect we reverse the order of
  // translation and rotation and use the opposite sense of the rotation
  // matrix

Polygon toLocalCoords(const Point<2>& origin,
      const RotMatrix<2>& rotation = RotMatrix<2>().identity()) const;
  Polygon toLocalCoords(const AxisBox<2>& coords) const;
  Polygon toLocalCoords(const RotBox<2>& coords) const;

friend bool Intersect<2>(const Polygon& r, const Point<2>& p, bool proper);
  friend bool Contains<2>(const Point<2>& p, const Polygon& r, bool proper);

friend bool Intersect<2>(const Polygon& p, const AxisBox<2>& b, bool proper);
  friend bool Contains<2>(const Polygon& p, const AxisBox<2>& b, bool proper);
  friend bool Contains<2>(const AxisBox<2>& b, const Polygon& p, bool proper);

friend bool Intersect<2>(const Polygon& p, const Ball<2>& b, bool proper);
  friend bool Contains<2>(const Polygon& p, const Ball<2>& b, bool proper);
  friend bool Contains<2>(const Ball<2>& b, const Polygon& p, bool proper);

friend bool Intersect<2>(const Polygon& r, const Segment<2>& s, bool proper);
  friend bool Contains<2>(const Polygon& p, const Segment<2>& s, bool proper);
  friend bool Contains<2>(const Segment<2>& s, const Polygon& p, bool proper);

friend bool Intersect<2>(const Polygon& p, const RotBox<2>& r, bool proper);
  friend bool Contains<2>(const Polygon& p, const RotBox<2>& r, bool proper);
  friend bool Contains<2>(const RotBox<2>& r, const Polygon& p, bool proper);

friend bool Intersect<2>(const Polygon& p1, const Polygon& p2, bool proper);
  friend bool Contains<2>(const Polygon& outer, const Polygon& inner, bool proper);

private:
  std::vector<Point<2> > m_points;
  typedef std::vector<Point<2> >::iterator theIter;
  typedef std::vector<Point<2> >::const_iterator theConstIter;

};

// Helper classes, to keep track of the orientation of
// a 2D polygon in dim dimensions

typedef enum {
  _WFMATH_POLY2REORIENT_NONE,
  _WFMATH_POLY2REORIENT_CLEAR_AXIS2,
  _WFMATH_POLY2REORIENT_CLEAR_BOTH_AXES,
  _WFMATH_POLY2REORIENT_MOVE_AXIS2_TO_AXIS1,
  _WFMATH_POLY2REORIENT_SCALE1_CLEAR2
} _Poly2ReorientType;

// Reorient a 2D polygon to match a change in the basis
// used by _Poly2Orient
class _Poly2Reorient
{
public:
  _Poly2Reorient(_Poly2ReorientType type, CoordType scale = 0.0)
  : m_type(type), m_scale(scale) {}
  ~_Poly2Reorient() = default;

void reorient(Polygon<2>& poly, size_t skip = std::numeric_limits<size_t>::max()) const;

private:
  _Poly2ReorientType m_type;
  CoordType m_scale;
};

template<int dim> class _Poly2Orient;

struct _Poly2OrientIntersectData {
  int dim;
  Point<2> p1, p2;
  Vector<2> v1, v2, off;
  bool o1_is_line, o2_is_line;
};

// Finds the intersection of the two planes, returns the
// dimension of the intersection space, the rest of the arguments
// are various information returned depending on the dimension of
// the intersection
template<int dim>
int  _Intersect(const _Poly2Orient<dim> &, const _Poly2Orient<dim> &,
    _Poly2OrientIntersectData &);

// Keep track of the orientation of a 2D polygon in dim dimensions
template<int dim>
class _Poly2Orient
{
public:
  _Poly2Orient() : m_origin() {}
  _Poly2Orient(const _Poly2Orient& p) : m_origin() {operator=(p);}
  ~_Poly2Orient() = default;

_Poly2Orient& operator=(const _Poly2Orient& p);

// Convert a point in the 2D polygon to a point in dim dimensional space
  Point<dim> convert(const Point<2>& p) const;

// Try to convert a point from dim dimensions into 2D, expanding the
  // basis if necessary. Returns true on success. On failure, the
  // basis is unchanged.
  bool expand(const Point<dim>& pd, Point<2>& p2, CoordType epsilon = numeric_constants<CoordType>::epsilon());

// Reduce the basis to the minimum necessary to span the points in
  // poly (with the exception of skip). Returns _Poly2Reorient, which needs
  // to be used to reorient the points to match the new basis.
  _Poly2Reorient reduce(const Polygon<2>& poly, size_t skip = std::numeric_limits<size_t>::max());

void shift(const Vector<dim>& v) {if(m_origin.isValid()) m_origin += v;}
  void rotate(const RotMatrix<dim>& m, const Point<dim>& p);
  // Rotates about the point which corresponds to "p" in the oriented plane
  void rotate2(const RotMatrix<dim>& m, const Point<2>& p);

//3D only
  void rotate(const Quaternion& q, const Point<3>& p);
  // Rotates about the point which corresponds to "p" in the oriented plane
  void rotate2(const Quaternion& q, const Point<2>& p);

_Poly2Orient toParentCoords(const Point<dim>& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
  {_Poly2Orient p(*this); p.m_origin = m_origin.toParentCoords(origin, rotation);
    p.m_axes[0].rotate(rotation); p.m_axes[1].rotate(rotation); return p;}
  _Poly2Orient toParentCoords(const AxisBox<dim>& coords) const
  {_Poly2Orient p(*this); p.m_origin = m_origin.toParentCoords(coords); return p;}
  _Poly2Orient toParentCoords(const RotBox<dim>& coords) const
  {_Poly2Orient p(*this); p.m_origin = m_origin.toParentCoords(coords);
    p.m_axes[0].rotate(coords.orientation());
    p.m_axes[1].rotate(coords.orientation()); return p;}

// toLocal is just like toParent, expect we reverse the order of
  // translation and rotation and use the opposite sense of the rotation
  // matrix

_Poly2Orient toLocalCoords(const Point<dim>& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
  {_Poly2Orient p(*this); p.m_origin = m_origin.toLocalCoords(origin, rotation);
    p.m_axes[0] = rotation * p.m_axes[0];
    p.m_axes[1] = rotation * p.m_axes[1]; return p;}
  _Poly2Orient toLocalCoords(const AxisBox<dim>& coords) const
  {_Poly2Orient p(*this); p.m_origin = m_origin.toLocalCoords(coords); return p;}
  _Poly2Orient toLocalCoords(const RotBox<dim>& coords) const
  {_Poly2Orient p(*this); p.m_origin = m_origin.toLocalCoords(coords);
    p.m_axes[0] = coords.orientation() * p.m_axes[0];
    p.m_axes[1] = coords.orientation() * p.m_axes[1]; return p;}

// 3D only
  _Poly2Orient<3> toParentCoords(const Point<3>& origin, const Quaternion& rotation) const
  {_Poly2Orient p(*this); p.m_origin = m_origin.toParentCoords(origin, rotation);
    p.m_axes[0].rotate(rotation); p.m_axes[0].rotate(rotation); return p;}
  _Poly2Orient<3> toLocalCoords(const Point<3>& origin, const Quaternion& rotation) const
  {_Poly2Orient p(*this); p.m_origin = m_origin.toLocalCoords(origin, rotation);
    p.m_axes[0].rotate(rotation.inverse());
    p.m_axes[0].rotate(rotation.inverse()); return p;}

// Gives the offset from pd to the space spanned by
  // the basis, and puts the nearest point in p2.
  Vector<dim> offset(const Point<dim>& pd, Point<2>& p2) const;

// Like offset, but returns true if the point is in the plane
  bool checkContained(const Point<dim>& pd, Point<2> & p2) const;

// Check if the AxisBox intersects the spanned space, and if so
  // return a point in the intersection.
  bool checkIntersect(const AxisBox<dim>& b, Point<2>& p2, bool proper) const;

friend int  _Intersect<dim>(const _Poly2Orient<dim> &, const _Poly2Orient<dim> &,
            _Poly2OrientIntersectData &);

private:
  // special case of the above when both axes are valid
  bool checkIntersectPlane(const AxisBox<dim>& b, Point<2>& p2, bool proper) const;

Point<dim> m_origin;
  Vector<dim> m_axes[2]; // Normalized to unit length
};

/// A polygon, all of whose points lie in a plane, embedded in dim dimensions
template<int dim = 3>
class Polygon
{
public:
  Polygon() : m_orient(), m_poly() {}
  Polygon(const Polygon& p) : m_orient(p.m_orient), m_poly(p.m_poly) {}

~Polygon() = default;

friend std::ostream& operator<< <dim>(std::ostream& os, const Polygon& p);
  friend std::istream& operator>> <dim>(std::istream& is, Polygon& p);

Polygon& operator=(const Polygon& p)
  {m_orient = p.m_orient; m_poly = p.m_poly; return *this;}

bool isEqualTo(const Polygon& p2, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const;

bool operator==(const Polygon& p) const	{return isEqualTo(p);}
  bool operator!=(const Polygon& p) const	{return !isEqualTo(p);}

bool isValid() const {return m_poly.isValid();}

// Descriptive characteristics

size_t numCorners() const {return m_poly.numCorners();}
  Point<dim> getCorner(size_t i) const {return m_orient.convert(m_poly[i]);}
  Point<dim> getCenter() const {return m_orient.convert(m_poly.getCenter());}

// The failure of the following functions does not invalidate the
  // polygon, but merely leaves it unchaged.

// Add before i'th corner, zero is beginning, numCorners() is end
  // Only succeeds if p lies in a plane with all current points
  bool addCorner(size_t i, const Point<dim>& p, CoordType epsilon = numeric_constants<CoordType>::epsilon());

// Remove the i'th corner
  void removeCorner(size_t i);

// Move the i'th corner to p, only succeeds if new location
  // lies in the same plane as all the other points. Note that,
  // under certain circumstances, this plane may not contain the
  // original location of the point.
  bool moveCorner(size_t i, const Point<dim>& p, CoordType epsilon = numeric_constants<CoordType>::epsilon());

// Remove all points
  void clear()	{m_poly.clear(); m_orient = _Poly2Orient<dim>();}

// Movement functions

Polygon& shift(const Vector<dim>& v)
  {m_orient.shift(v); return *this;}
  Polygon& moveCornerTo(const Point<dim>& p, size_t corner)
  {return shift(p - getCorner(corner));}
  Polygon& moveCenterTo(const Point<dim>& p)
  {return shift(p - getCenter());}

Polygon& rotateCorner(const RotMatrix<dim>& m, size_t corner)
  {m_orient.rotate2(m, m_poly[corner]); return *this;}
  Polygon& rotateCenter(const RotMatrix<dim>& m)
  {if(m_poly.numCorners() > 0)
    m_orient.rotate2(m, m_poly.getCenter());
  return *this;}
  Polygon& rotatePoint(const RotMatrix<dim>& m, const Point<dim>& p)
  {m_orient.rotate(m, p); return *this;}

// 3D rotation functions
  Polygon<3>& rotateCorner(const Quaternion& q, size_t corner)
  {m_orient.rotate2(q, m_poly[corner]); return *this;}
  Polygon<3>& rotateCenter(const Quaternion& q)
  {if(m_poly.numCorners() > 0)
    m_orient.rotate2(q, m_poly.getCenter());
  return *this;}
  Polygon<3>& rotatePoint(const Quaternion& q, const Point<3>& p)
  {m_orient.rotate(q, p); return *this;}

// Intersection functions

AxisBox<dim> boundingBox() const;
  Ball<dim> boundingSphere() const;
  Ball<dim> boundingSphereSloppy() const;

Polygon toParentCoords(const Point<dim>& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
        {Polygon p(*this); p.m_orient = m_orient.toParentCoords(origin, rotation); return p;}
  Polygon toParentCoords(const AxisBox<dim>& coords) const
        {Polygon p(*this); p.m_orient = m_orient.toParentCoords(coords); return p;}
  Polygon toParentCoords(const RotBox<dim>& coords) const
        {Polygon p(*this); p.m_orient = m_orient.toParentCoords(coords); return p;}

// toLocal is just like toParent, expect we reverse the order of
  // translation and rotation and use the opposite sense of the rotation
  // matrix

Polygon toLocalCoords(const Point<dim>& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
        {Polygon p(*this); p.m_orient = m_orient.toLocalCoords(origin, rotation); return p;}
  Polygon toLocalCoords(const AxisBox<dim>& coords) const
        {Polygon p(*this); p.m_orient = m_orient.toLocalCoords(coords); return p;}
  Polygon toLocalCoords(const RotBox<dim>& coords) const
        {Polygon p(*this); p.m_orient = m_orient.toLocalCoords(coords); return p;}

// 3D only
  Polygon<3> toParentCoords(const Point<3>& origin, const Quaternion& rotation) const
        {Polygon<3> p(*this); p.m_orient = m_orient.toParentCoords(origin, rotation); return p;}
  Polygon<3> toLocalCoords(const Point<3>& origin, const Quaternion& rotation) const
        {Polygon<3> p(*this); p.m_orient = m_orient.toLocalCoords(origin, rotation); return p;}

friend bool Intersect<dim>(const Polygon& r, const Point<dim>& p, bool proper);
  friend bool Contains<dim>(const Point<dim>& p, const Polygon& r, bool proper);

friend bool Intersect<dim>(const Polygon& p, const AxisBox<dim>& b, bool proper);
  friend bool Contains<dim>(const Polygon& p, const AxisBox<dim>& b, bool proper);
  friend bool Contains<dim>(const AxisBox<dim>& b, const Polygon& p, bool proper);

friend bool Intersect<dim>(const Polygon& p, const Ball<dim>& b, bool proper);
  friend bool Contains<dim>(const Polygon& p, const Ball<dim>& b, bool proper);
  friend bool Contains<dim>(const Ball<dim>& b, const Polygon& p, bool proper);

friend bool Intersect<dim>(const Polygon& r, const Segment<dim>& s, bool proper);
  friend bool Contains<dim>(const Polygon& p, const Segment<dim>& s, bool proper);
  friend bool Contains<dim>(const Segment<dim>& s, const Polygon& p, bool proper);

friend bool Intersect<dim>(const Polygon& p, const RotBox<dim>& r, bool proper);
  friend bool Contains<dim>(const Polygon& p, const RotBox<dim>& r, bool proper);
  friend bool Contains<dim>(const RotBox<dim>& r, const Polygon& p, bool proper);

friend bool Intersect<dim>(const Polygon& p1, const Polygon& p2, bool proper);
  friend bool Contains<dim>(const Polygon& outer, const Polygon& inner, bool proper);

private:

_Poly2Orient<dim> m_orient;
  Polygon<2> m_poly;
};

template<int dim>
inline bool Polygon<dim>::addCorner(size_t i, const Point<dim>& p, CoordType epsilon)
{
  Point<2> p2;
  bool succ = m_orient.expand(p, p2, epsilon);
  if(succ)
    m_poly.addCorner(i, p2, epsilon);
  return succ;
}

template<int dim>
inline void Polygon<dim>::removeCorner(size_t i)
{
  m_poly.removeCorner(i);
  _Poly2Reorient r = m_orient.reduce(m_poly);
  r.reorient(m_poly);
}

template<int dim>
inline bool Polygon<dim>::moveCorner(size_t i, const Point<dim>& p, CoordType epsilon)
{
  _Poly2Orient<dim> try_orient = m_orient;
  _Poly2Reorient r = try_orient.reduce(m_poly, i);
  Point<2> p2;

if(!try_orient.expand(p, p2, epsilon))
    return false;

r.reorient(m_poly, i);
  m_poly[i] = p2;
  m_orient = try_orient;

return true;
}

} // namespace WFMath

#endif  // WFMATH_POLYGON_H
0707010000003E000081A40000000200000002000000015D8693EF00002474000000000000000000000000000000000000003100000000wfmath-1569100783.d0f8a54/wfmath/polygon_funcs.h// polygon_funcs.h (line polygon implementation)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_POLYGON_FUNCS_H
#define WFMATH_POLYGON_FUNCS_H

#include <wfmath/polygon.h>

#include <wfmath/vector.h>
#include <wfmath/point.h>
#include <wfmath/ball.h>

#include <cmath>

#include <cassert>
#include <limits>

namespace WFMath {

template<int dim>
inline _Poly2Orient<dim>& _Poly2Orient<dim>::operator=(const _Poly2Orient<dim>& a)
{
  m_origin = a.m_origin;

for(int i = 0; i < 2; ++i)
    m_axes[i] = a.m_axes[i];

return *this;
}

template<int dim>
inline bool Polygon<dim>::isEqualTo(const Polygon<dim>& p, CoordType epsilon) const
{
  // The same polygon can be expressed in different ways in the interal
  // format, so we have to call getCorner();

size_t size = m_poly.numCorners();
  if(size != p.m_poly.numCorners())
    return false;

for(size_t i = 0; i < size; ++i)
    if(!Equal(getCorner(i), p.getCorner(i), epsilon))
      return false;

return true;
}

template<int dim>
inline Point<dim> _Poly2Orient<dim>::convert(const Point<2>& p) const
{
  assert(m_origin.isValid());

Point<dim> out = m_origin;

for(int j = 0; j < 2; ++j) {
    if(m_axes[j].isValid())
      out += m_axes[j] * p[j];
    else
      assert(p[j] == 0);
  }

out.setValid(p.isValid());

return out;
}

template<int dim>
bool _Poly2Orient<dim>::expand(const Point<dim>& pd, Point<2>& p2, CoordType epsilon)
{
  p2[0] = p2[1] = 0; // initialize
  p2.setValid();

if(!m_origin.isValid()) { // Adding to an empty list
    m_origin = pd;
    m_origin.setValid();
    return true;
  }

Vector<dim> shift = pd - m_origin, start_shift = shift;

CoordType bound = shift.sqrMag() * epsilon;

int j = 0;

while(true) {
    if(Dot(shift, start_shift) <= bound) // shift is effectively zero
      return true;

if(j == 2) { // Have two axes, shift doesn't lie in their plane
      p2.setValid(false);
      return false;
    }

if(!m_axes[j].isValid()) { // Didn't span this previously, now we do
      p2[j] = shift.mag();
      m_axes[j] = shift / p2[j];
      m_axes[j].setValid();
      return true;
   }

p2[j] = Dot(shift, m_axes[j]);
   shift -= m_axes[j] * p2[j]; // shift is now perpendicular to m_axes[j]
   ++j;
  }
}

template<int dim>
_Poly2Reorient _Poly2Orient<dim>::reduce(const Polygon<2>& poly, size_t skip)
{
  if(poly.numCorners() <= ((skip == 0) ? 1 : 0)) { // No corners left
    m_origin.setValid(false);
    m_axes[0].setValid(false);
    m_axes[1].setValid(false);
    return _WFMATH_POLY2REORIENT_NONE;
  }

assert(m_origin.isValid());

if(!m_axes[0].isValid())
    return _WFMATH_POLY2REORIENT_NONE;

// Check that we still span both axes

bool still_valid[2] = {false,}, got_ratio = false;
  CoordType ratio = std::numeric_limits<CoordType>::max();
  CoordType size = std::numeric_limits<CoordType>::max();
  CoordType epsilon;
  size_t i, end = poly.numCorners();

// scale epsilon
  for(i = 0; i < end; ++i) {
    if(i == skip)
      continue;
    const Point<2> &p = poly[i];
    CoordType x = std::fabs(p[0]),
              y = std::fabs(p[1]),
              max = (x > y) ? x : y;
    if(i == 0 || max < size)
      size = max;
  }
  int exponent;
  (void) std::frexp(size, &exponent);
  epsilon = std::ldexp(numeric_constants<CoordType>::epsilon(), exponent);

i = 0;
  if(skip == 0)
    ++i;
  assert(i != end);
  Point<2> first_point = poly[i];
  first_point.setValid(); // in case someone stuck invalid points in the poly

while(++i != end) {
    if(i == skip)
      continue;

Vector<2> diff = poly[i] - first_point;
    if(diff.sqrMag() < epsilon * epsilon) // No addition to span
      continue;
    if(!m_axes[1].isValid()) // We span 1D
      return _WFMATH_POLY2REORIENT_NONE;
    for(int j = 0; j < 2; ++j) {
      if(std::fabs(diff[j]) < epsilon) {
        assert(diff[j ? 0 : 1] >= epsilon); // because diff != 0
        if(still_valid[j ? 0 : 1] || got_ratio) // We span a 2D space
          return _WFMATH_POLY2REORIENT_NONE;
        still_valid[j] = true;
      }
    }
    // The point has both elements nonzero
    if(still_valid[0] || still_valid[1]) // We span a 2D space
      return _WFMATH_POLY2REORIENT_NONE;
    CoordType new_ratio = diff[1] / diff[0];
    if(!got_ratio) {
      ratio = new_ratio;
      got_ratio = true;
      continue;
    }
    if(!Equal(ratio, new_ratio)) // We span a 2D space
      return _WFMATH_POLY2REORIENT_NONE;
  }

// Okay, we don't span both vectors. What now?

if(still_valid[0]) {
    assert(m_axes[1].isValid());
    assert(!still_valid[1]);
    assert(!got_ratio);
    // This is easy, m_axes[1] is just invalid
    m_origin += m_axes[1] * first_point[1];
    m_axes[1].setValid(false);
    return _WFMATH_POLY2REORIENT_CLEAR_AXIS2;
  }

if(still_valid[1]) {
    assert(m_axes[1].isValid());
    assert(!got_ratio);
    // This is a little harder, m_axes[0] is invalid, must swap axes
    m_origin += m_axes[0] * first_point[0];
    m_axes[0] = m_axes[1];
    m_axes[1].setValid(false);
    return _WFMATH_POLY2REORIENT_MOVE_AXIS2_TO_AXIS1;
  }

// The !m_axes[1].isValid() case reducing to a point falls into here
  if(!got_ratio) { // Nothing's valid, all points are equal
    m_origin += m_axes[0] * first_point[0];
    if(m_axes[1].isValid())
      m_origin += m_axes[1] * first_point[1];
    m_axes[0].setValid(false);
    m_axes[1].setValid(false);
    return _WFMATH_POLY2REORIENT_CLEAR_BOTH_AXES;
  }

assert(m_axes[1].isValid());

// All the points are colinear, along some line which is not parallel
  // to either of the original axes

Vector<dim> new0;
  new0 = m_axes[0] + m_axes[1] * ratio;
  CoordType norm = new0.mag();
  new0 /= norm;

//  Vector diff = m_axes[0] * first_point[0] + m_axes[1] * first_point[1];
//  // Causes Dot(diff, m_axes[0]) to vanish, so the point on the line
//  // with x coordinate zero is the new origin
//  diff -= new0 * (first_point[0] * norm);
//  m_origin += diff;
  // or, equivalently
    m_origin += m_axes[1] * (first_point[1] - ratio * first_point[0]);

m_axes[0] = new0;
  m_axes[1].setValid(false);
  return _Poly2Reorient(_WFMATH_POLY2REORIENT_SCALE1_CLEAR2, norm);
}

template<int dim>
inline void _Poly2Orient<dim>::rotate(const RotMatrix<dim>& m, const Point<dim>& p)
{
  m_origin.rotate(m, p);

for(int j = 0; j < 2; ++j)
    m_axes[j] = Prod(m_axes[j], m);
}

template<int dim>
void _Poly2Orient<dim>::rotate2(const RotMatrix<dim>& m, const Point<2>& p)
{
  assert(m_origin.isValid());

if(!m_axes[0].isValid()) {
    assert(p[0] == 0 && p[1] == 0);
    return;
  }

Vector<dim> shift = m_axes[0] * p[0];
  m_axes[0] = Prod(m_axes[0], m);

if(m_axes[1].isValid()) {
    shift += m_axes[1] * p[1];
    m_axes[1] = Prod(m_axes[1], m);
  }
  else
    assert(p[1] == 0);

m_origin += shift - Prod(shift, m);
}

template<>
inline void _Poly2Orient<3>::rotate(const Quaternion& q, const Point<3>& p)
{
  m_origin.rotate(q, p);

for(int j = 0; j < 2; ++j)
    m_axes[j].rotate(q);
}

template<>
inline void _Poly2Orient<3>::rotate2(const Quaternion& q, const Point<2>& p)
{
  assert(m_origin.isValid());

if(!m_axes[0].isValid()) {
    assert(p[0] == 0 && p[1] == 0);
    return;
  }

Vector<3> shift = m_axes[0] * p[0];
  m_axes[0].rotate(q);

if(m_axes[1].isValid()) {
    shift += m_axes[1] * p[1];
    m_axes[1].rotate(q);
  }
  else
    assert(p[1] == 0);

m_origin += shift - shift.rotate(q);
}

template<int dim>
AxisBox<dim> Polygon<dim>::boundingBox() const
{
  assert(m_poly.numCorners() > 0);

Point<dim> min = m_orient.convert(m_poly[0]), max = min;
  bool valid = min.isValid();

for(size_t i = 1; i != m_poly.numCorners(); ++i) {
    Point<dim> p = m_orient.convert(m_poly[i]);
    valid = valid && p.isValid();
    for(int j = 0; j < dim; ++j) {
      if(p[j] < min[j])
        min[j] = p[j];
      if(p[j] > max[j])
        max[j] = p[j];
    }
  }

min.setValid(valid);
  max.setValid(valid);

return AxisBox<dim>(min, max, true);
}

template<int dim>
inline Ball<dim> Polygon<dim>::boundingSphere() const
{
  Ball<2> b = m_poly.boundingSphere();

return Ball<dim>(m_orient.convert(b.center()), b.radius());
}

template<int dim>
inline Ball<dim> Polygon<dim>::boundingSphereSloppy() const
{
  Ball<2> b = m_poly.boundingSphereSloppy();

return Ball<dim>(m_orient.convert(b.center()), b.radius());
}

} // namespace WFMath

#endif  // WFMATH_POLYGON_FUNCS_H
0707010000003F000081A40000000200000002000000015D8693EF000089A1000000000000000000000000000000000000003700000000wfmath-1569100783.d0f8a54/wfmath/polygon_intersect.cpp// polygon_intersect.cpp (Polygon<2> intersection functions)
//
//  The WorldForge Project
//  Copyright (C) 2002  Ron Steinke and The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-2-20

#include "polygon_intersect.h"

#include "segment.h"
#include "rotbox.h"

#include <algorithm>
#include <list>

namespace WFMath {

// instantiations, only need 3d because 2d is a specialization,
// except for the reverse-order intersect

template bool Intersect<Point<2>,Polygon<2> >(const Point<2>&, const Polygon<2>&, bool);
template bool Intersect<Point<3>,Polygon<3> >(const Point<3>&, const Polygon<3>&, bool);
template bool Contains<3>(const Point<3>&, const Polygon<3>&, bool);
template bool Intersect<3>(const Polygon<3>&, const Point<3>&, bool);
template bool Contains<3>(const Polygon<3>&, const Point<3>&, bool);

template bool Intersect<AxisBox<2>,Polygon<2> >(const AxisBox<2>&, const Polygon<2>&, bool);
template bool Intersect<AxisBox<3>,Polygon<3> >(const AxisBox<3>&, const Polygon<3>&, bool);
template bool Contains<3>(const AxisBox<3>&, const Polygon<3>&, bool);
template bool Intersect<3>(const Polygon<3>&, const AxisBox<3>&, bool);
template bool Contains<3>(const Polygon<3>&, const AxisBox<3>&, bool);

template bool Intersect<Ball<2>,Polygon<2> >(const Ball<2>&, const Polygon<2>&, bool);
template bool Intersect<Ball<3>,Polygon<3> >(const Ball<3>&, const Polygon<3>&, bool);
template bool Contains<3>(const Ball<3>&, const Polygon<3>&, bool);
template bool Intersect<3>(const Polygon<3>&, const Ball<3>&, bool);
template bool Contains<3>(const Polygon<3>&, const Ball<3>&, bool);

template bool Intersect<Segment<2>,Polygon<2> >(const Segment<2>&, const Polygon<2>&, bool);
template bool Intersect<Segment<3>,Polygon<3> >(const Segment<3>&, const Polygon<3>&, bool);
template bool Contains<3>(const Segment<3>&, const Polygon<3>&, bool);
template bool Intersect<3>(const Polygon<3>&, const Segment<3>&, bool);
template bool Contains<3>(const Polygon<3>&, const Segment<3>&, bool);

template bool Intersect<RotBox<2>,Polygon<2> >(const RotBox<2>&, const Polygon<2>&, bool);
template bool Intersect<RotBox<3>,Polygon<3> >(const RotBox<3>&, const Polygon<3>&, bool);
template bool Contains<3>(const RotBox<3>&, const Polygon<3>&, bool);
template bool Intersect<3>(const Polygon<3>&, const RotBox<3>&, bool);
template bool Contains<3>(const Polygon<3>&, const RotBox<3>&, bool);

template bool Intersect<3>(const Polygon<3>&, const Polygon<3>&, bool);
template bool Contains<3>(const Polygon<3>&, const Polygon<3>&, bool);

template<>
bool _Poly2Orient<3>::checkIntersectPlane(const AxisBox<3>& b, Point<2>& p2,
					  bool proper) const
{
  assert("This function should only be called if the orientation represents a plane" &&
         m_origin.isValid() && m_axes[0].isValid() && m_axes[1].isValid());

Vector<3> normal = Cross(m_axes[0], m_axes[1]); // normal to the plane

//  enum {
//    AXIS_UP,
//    AXIS_DOWN,
//    AXIS_FLAT
//  } axis_direction[3];

CoordType normal_mag = normal.sloppyMag();
  int high_corner_num = 0;

for(int i = 0; i < 3; ++i) {
    if(std::fabs(normal[i]) < normal_mag * numeric_constants<CoordType>::epsilon()) {
//      axis_direction[i] = AXIS_FLAT;
    } else if(normal[i] > 0) {
//      axis_direction[i] = AXIS_UP;
      high_corner_num |= (1 << i);
    }
//    else
//      axis_direction[i] = AXIS_DOWN;
  }

int low_corner_num = high_corner_num ^ 7;

Point<3> high_corner = b.getCorner(high_corner_num);
  Point<3> low_corner = b.getCorner(low_corner_num);

// If these are on opposite sides of the plane, we have an intersection

CoordType perp_size = Dot(normal, high_corner - low_corner) / normal_mag;
  assert(perp_size >= 0);

if(perp_size < normal_mag * numeric_constants<CoordType>::epsilon()) {
    // We have a very flat box, lying parallel to the plane
    return !proper && checkContained(Midpoint(high_corner, low_corner), p2);
  }

if(_Less(Dot(high_corner - m_origin, normal), 0, proper)
     || _Less(Dot(low_corner - m_origin, normal), 0, proper))
    return false; // box lies above or below the plane

// Find the intersection of the line through the corners with the plane

Point<2> p2_high, p2_low;

CoordType high_dist = offset(high_corner, p2_high).mag();
  CoordType low_dist = offset(low_corner, p2_low).mag();

p2 = Midpoint(p2_high, p2_low, high_dist / (high_dist + low_dist));

return true;
}

// This assumes the y coordinates of the points are all zero
static void _LinePolyGetBounds(const Polygon<2> &poly, CoordType &low, CoordType &high)
{
	low = high = poly[0][0];

for(size_t i = 0; i < poly.numCorners(); ++i) {
          CoordType val = poly[i][0];
          if(val < low)
            low = val;
          if(val > high)
            high = val;
        }
}

// For use in _GetCrossings()
struct LinePointData {
  CoordType low, high;
  bool cross;
};

// This finds the intervals where the polygon intersects the line
// through p parallel to v, and puts the endpoints of those
// intervals in the vector "cross"
static bool _GetCrossings(const Polygon<2> &poly, const Point<2> &p,
			  const Vector<2> &v, std::vector<CoordType> &cross,
			  bool proper)
{
  assert(poly.numCorners() == cross.size()); // Already allocated
  assert(Equal(v.sqrMag(), 1));

// The sign of the cross product changes when you cross the line
  Point<2> old_p = poly.getCorner(poly.numCorners() - 1);
  bool old_below = (Cross(v, old_p - p) < 0);
  int next_cross = 0;

// Stuff for when multiple sequential corners lie on the line
  std::list<LinePointData> line_point_data;

for(size_t i = 0; i < poly.numCorners(); ++i) {
    Point<2> p_i =  poly.getCorner(i);
    Vector<2> v_i = p_i - p;

CoordType v_i_sqr_mag = v_i.sqrMag(), proj = Dot(v_i, v);

if(Equal(v_i_sqr_mag, proj * proj)) { // corner lies on line
      Point<2> p_j;
      Vector<2> v_j;
      CoordType proj_j, low_proj = proj, high_proj = proj;
      size_t j;
      for(j = i + 1; j != i; j == poly.numCorners() - 1 ? j = 0 : ++j) {
        p_j = poly.getCorner(j);
	v_j = p_j - p;
        proj_j = Dot(v_j, v);

if(!Equal(v_j.sqrMag(), proj_j * proj_j))
          break;

if(proj_j < low_proj)
          low_proj = proj_j;
        if(proj_j > high_proj)
          high_proj = proj_j;
      }

assert(j != i); // We know that the polygon spans a 2d space

bool below = (Cross(v, v_j) < 0);

if(below == old_below && proper) {
        old_p = p_j;
        continue;
      }

if(j == i + 1) { // just one point on the line

if(below != old_below) {
          old_below = below;
          cross[next_cross++] = proj;
        }
        else {
          assert(!proper);
          // Just touches, adding it twice will give a zero length "hit" region
          cross[next_cross++] = proj;
          cross[next_cross++] = proj;
        }

old_p = p_j;
        continue;
      }

LinePointData data = {low_proj, high_proj, below != old_below};

std::list<LinePointData>::iterator I;

for(I = line_point_data.begin(); I != line_point_data.end(); ++I) {
        if(data.low > I->high)
          continue;

if(data.high < I->low) {
          line_point_data.insert(I, data);
          break;
        }

// overlap

I->low = (I->low < data.low) ? I->low : data.low;
        I->high = (I->high > data.high) ? I->high : data.high;
        I->cross = (I->cross != data.cross);

std::list<LinePointData>::iterator J = I;

++J;

if(J->low < I->high) {
          I->high = J->high;
          I->cross = (I->cross != J->cross);
	  line_point_data.erase(J);
        }
      }

if(I == line_point_data.end())
        line_point_data.push_back(data);

old_below = below;
      old_p = p_j;
      continue;
    }

// the corner doesn't lie on the line, compute the intersection point

bool below = (Cross(v, v_i) < 0);

if(below != old_below) {
      old_below = below;
      Vector<2> dist = p - old_p;
      CoordType dist_sqr_mag = dist.sqrMag();
      CoordType dist_proj = Dot(dist, v);

CoordType denom = dist_proj * dist_proj - dist_sqr_mag;

assert(denom != 0); // We got a crossing, the vectors can't be parallel

CoordType line_pos = (dist_proj * Dot(v_i, dist) + dist_sqr_mag * proj) / denom;

cross[next_cross++] = line_pos;
    }

old_p = p;
  }

cross.resize(next_cross);
  std::sort(cross.begin(), cross.end());

if(!line_point_data.empty()) {
    std::list<LinePointData>::iterator I = line_point_data.begin();
    std::vector<CoordType>::iterator cross_num = cross.begin();
    bool hit = false;

while(cross_num != cross.end() && I != line_point_data.end()) {
      if(*cross_num < I->low) {
        ++cross_num;
	hit = !hit;
        continue;
      }

bool hit_between;
      if(*cross_num > I->high) {
        hit_between = I->cross;
      }
      else {
        std::vector<CoordType>::iterator high_cross_num = cross_num;

do {
          ++high_cross_num;
        } while(*high_cross_num < I->high);

hit_between = (((high_cross_num - cross_num) % 2) != 0) != I->cross;

cross_num = cross.erase(cross_num, high_cross_num);
      }
      
      if(hit_between) {
        cross_num = cross.insert(cross_num, proper == hit ? I->low : I->high);
        ++cross_num;
        hit = !hit;
      }
      else if(!proper) {
        cross_num = cross.insert(cross_num, I->low);
        ++cross_num;
        cross_num = cross.insert(cross_num, I->high);
        ++cross_num;
      }
      ++I;
    }

while(I != line_point_data.end()) {
      if(I->cross) {
        cross.push_back(proper == hit ? I->low : I->high);
        hit = !hit;
      }
      else if(!proper) {
        cross.push_back(I->low);
        cross.push_back(I->high);
      }
      ++I;
    }

assert(!hit); // end outside the polygon
  }

return cross.size() != 0;
}

bool _PolyPolyIntersect(const Polygon<2> &poly1, const Polygon<2> &poly2,
			const int intersect_dim,
			const _Poly2OrientIntersectData &data, bool proper)
{
  switch(intersect_dim) {
    case -1:
      return false;
    case 0:
      return Intersect(poly1, data.p1, proper)
	  && Intersect(poly2, data.p2, proper);
    case 1:
      if(proper && (data.o1_is_line || data.o2_is_line))
        return false;

if(data.o1_is_line && data.o2_is_line) {
        assert(!proper);
	CoordType low1, low2, high1, high2;

_LinePolyGetBounds(poly1, low1, high1);

low1 -= data.p1[0];
	high1 -= data.p1[0];

if(data.v1[0] < 0) { // v1 = (-1, 0)
          CoordType tmp = low1;
          low1 = -high1;
          high1 = -tmp;
        }

_LinePolyGetBounds(poly2, low2, high2);

low2 -= data.p2[0];
	high2 -= data.p2[0];

if(data.v2[0] < 0) { // v2 = (-1, 0)
          CoordType tmp = low2;
          low2 = -high2;
          high2 = -tmp;
        }

return high1 >= low2 && high2 >= low1;
      }

if(data.o1_is_line) {
	assert(!proper);
	CoordType min, max;
	_LinePolyGetBounds(poly1, min, max);

min -= data.p1[0];
	max -= data.p1[0];

if(data.v1[0] < 0) { // v1 = (-1, 0)
          CoordType tmp = min;
          min = -max;
          max = -tmp;
        }

Segment<2> s(data.p2 + min * data.v2, data.p1 + max * data.v2);

return Intersect(poly2, s, false);
      }

if(data.o2_is_line) {
	assert(!proper);
	CoordType min, max;
	_LinePolyGetBounds(poly2, min, max);

min -= data.p2[0];
	max -= data.p2[0];

if(data.v2[0] < 0) { // v2 = (-1, 0)
          CoordType tmp = min;
          min = -max;
          max = -tmp;
        }

Segment<2> s(data.p1 + min * data.v1, data.p1 + max * data.v1);

return Intersect(poly1, s, false);
      }

{
	std::vector<CoordType> cross1(poly1.numCorners());
	if(!_GetCrossings(poly1, data.p1, data.v1, cross1, proper))
	  return false; // line misses polygon

std::vector<CoordType> cross2(poly2.numCorners());
	if(!_GetCrossings(poly2, data.p2, data.v2, cross2, proper))
	  return false; // line misses polygon

std::vector<CoordType>::iterator i1 = cross1.begin(), i2 = cross2.begin();
	bool hit1 = false, hit2 = false;

while(i1 != cross1.end() && i2 != cross2.end()) {
	  if(Equal(*i1, *i2)) {
	    if(!proper)
	      return true;

hit1 = !hit1;
	    ++i1;
	    hit2 = !hit2;
	    ++i2;
	  }

if(*i1 < *i2) {
	    hit1 = !hit1;
	    ++i1;
	  }
	  else {
	    hit2 = !hit2;
	    ++i2;
	  }

if(hit1 && hit2)
	    return true;
	}

return false;
      }
    case 2:
      // Shift one polygon into the other's coordinates.
      // Perhaps not the most efficient, but this is a
      // rare special case.
      {
        Polygon<2> tmp_poly(poly2);

for(size_t i = 0; i < tmp_poly.numCorners(); ++i) {
          Point<2> &p = tmp_poly[i];
          Point<2> shift_p = p + data.off;

p[0] = shift_p[0] * data.v1[0] + shift_p[1] * data.v2[0];
          p[1] = shift_p[0] * data.v1[1] + shift_p[1] * data.v2[1];
        }

return Intersect(poly1, tmp_poly, proper);
      }
    default:
      assert(false);
      return false;
  }
}

bool _PolyPolyContains(const Polygon<2> &outer, const Polygon<2> &inner,
		       const int intersect_dim,
		       const _Poly2OrientIntersectData &data, bool proper)
{
  switch(intersect_dim) {
    case -1:
      return false;
    case 0:
      return Contains(data.p2, inner, false)
	  && Contains(outer, data.p1, proper);
    case 1:
      if(!data.o2_is_line) // The inner poly isn't contained by the intersect line
        return false;

// The inner poly lies on a line, so it reduces to a line segment
      {
	CoordType min, max;
	_LinePolyGetBounds(inner, min, max);

min -= data.p2[0];
	max -= data.p2[0];

if(data.v2[0] < 0) { // v2 = (-1, 0)
          CoordType tmp = min;
          min = -max;
          max = -tmp;
        }

Segment<2> s(data.p1 + min * data.v1, data.p1 + max * data.v1);

return Contains(outer, s, proper);
      }
    case 2:
      // Shift one polygon into the other's coordinates.
      // Perhaps not the most efficient, but this is a
      // rare special case.
      {
        Polygon<2> tmp_poly(inner);

for(size_t i = 0; i < tmp_poly.numCorners(); ++i) {
          Point<2> &p = tmp_poly[i];
          Point<2> shift_p = p + data.off;

p[0] = shift_p[0] * data.v1[0] + shift_p[1] * data.v2[0];
          p[1] = shift_p[0] * data.v1[1] + shift_p[1] * data.v2[1];
        }

return Contains(outer, tmp_poly, proper);
      }
    default:
      assert(false);
      return false;
  }
}

// Polygon<2> intersection functions

// FIXME deal with round off error in _all_ these intersection functions

// The Polygon<2>/Point<2> intersection function was stolen directly
// from shape.cpp in libCoal

template<>
bool Intersect<2>(const Polygon<2>& r, const Point<2>& p, bool proper)
{
  const Polygon<2>::theConstIter begin = r.m_points.begin(), end = r.m_points.end();
  bool hit = false;

for (Polygon<2>::theConstIter i = begin, j = end - 1; i != end; j = i++) {
    bool vertically_between =
        (((*i)[1] <= p[1] && p[1] < (*j)[1]) ||
         ((*j)[1] <= p[1] && p[1] < (*i)[1]));

if (!vertically_between)
      continue;

CoordType x_intersect = (*i)[0] + ((*j)[0] - (*i)[0])
			    * (p[1] - (*i)[1]) / ((*j)[1] - (*i)[1]);

if(Equal(p[0], x_intersect))
      return !proper;

if(p[0] < x_intersect)
            hit = !hit;
  }

return hit;
}

template<>
bool Contains<2>(const Point<2>& p, const Polygon<2>& r, bool proper)
{
  if(proper) // Weird degenerate case
    return r.numCorners() == 0;

for(unsigned int i = 0; i < r.m_points.size(); ++i)
    if(p != r.m_points[i])
      return false;

return true;
}

template<>
bool Intersect<2>(const Polygon<2>& p, const AxisBox<2>& b, bool proper)
{
  const Polygon<2>::theConstIter begin = p.m_points.begin(), end = p.m_points.end();
  bool hit = false;

for (Polygon<2>::theConstIter i = begin, j = end - 1; i != end; j = i++) {
    bool low_vertically_between =
        (((*i)[1] <= b.m_low[1] && b.m_low[1] < (*j)[1]) ||
         ((*j)[1] <= b.m_low[1] && b.m_low[1] < (*i)[1]));
    bool low_horizontally_between =
        (((*i)[0] <= b.m_low[0] && b.m_low[0] < (*j)[0]) ||
         ((*j)[0] <= b.m_low[0] && b.m_low[0] < (*i)[0]));
    bool high_vertically_between =
        (((*i)[1] <= b.m_high[1] && b.m_high[1] < (*j)[1]) ||
         ((*j)[1] <= b.m_high[1] && b.m_high[1] < (*i)[1]));
    bool high_horizontally_between =
        (((*i)[0] <= b.m_high[0] && b.m_high[0] < (*j)[0]) ||
         ((*j)[0] <= b.m_high[0] && b.m_high[0] < (*i)[0]));

CoordType xdiff = ((*j)[0] - (*i)[0]);
    CoordType ydiff = ((*j)[1] - (*i)[1]);

if(low_vertically_between) { // Check for edge intersect
      CoordType x_intersect = (*i)[0] + (b.m_low[1] - (*i)[1])
			      * xdiff / ydiff;

if(Equal(b.m_low[0], x_intersect) || Equal(b.m_high[0], x_intersect))
        return !proper;
      if(b.m_low[0] < x_intersect && b.m_high[0] > x_intersect)
        return true;

// Also check for point inclusion here, only need to do this for one point
      if(b.m_low[0] < x_intersect)
        hit = !hit;
    }

if(low_horizontally_between) { // Check for edge intersect
      CoordType y_intersect = (*i)[1] + (b.m_low[0] - (*i)[0])
			      * ydiff / xdiff;

if(Equal(b.m_low[1], y_intersect) || Equal(b.m_high[1], y_intersect))
        return !proper;
      if(b.m_low[1] < y_intersect && b.m_high[1] > y_intersect)
        return true;
    }

if(high_vertically_between) { // Check for edge intersect
      CoordType x_intersect = (*i)[0] + (b.m_high[1] - (*i)[1])
			      * xdiff / ydiff;

if(Equal(b.m_low[0], x_intersect) || Equal(b.m_high[0], x_intersect))
        return !proper;
      if(b.m_low[0] < x_intersect && b.m_high[0] > x_intersect)
        return true;
    }

if(high_horizontally_between) { // Check for edge intersect
      CoordType y_intersect = (*i)[1] + (b.m_high[0] - (*i)[0])
			      * ydiff / xdiff;

if(Equal(b.m_low[1], y_intersect) || Equal(b.m_high[1], y_intersect))
        return !proper;
      if(b.m_low[1] < y_intersect && b.m_high[1] > y_intersect)
        return true;
    }
  }

return hit;
}

template<>
bool Contains<2>(const Polygon<2>& p, const AxisBox<2>& b, bool proper)
{
  const Polygon<2>::theConstIter begin = p.m_points.begin(), end = p.m_points.end();
  bool hit = false;

CoordType xdiff = ((*j)[0] - (*i)[0]);
    CoordType ydiff = ((*j)[1] - (*i)[1]);

if(low_vertically_between) { // Check for edge intersect
      CoordType x_intersect = (*i)[0] + (b.m_low[1] - (*i)[1])
			      * xdiff / ydiff;

bool on_corner = Equal(b.m_low[0], x_intersect)
			|| Equal(b.m_high[0], x_intersect);

if(on_corner && proper)
        return false;

if(!on_corner && b.m_low[0] < x_intersect && b.m_high[0] > x_intersect)
        return false;

// Also check for point inclusion here, only need to do this for one point
      if(!on_corner && b.m_low[0] < x_intersect)
        hit = !hit;
    }

if(low_horizontally_between) { // Check for edge intersect
      CoordType y_intersect = (*i)[1] + (b.m_low[0] - (*i)[0])
			      * ydiff / xdiff;

bool on_corner = Equal(b.m_low[1], y_intersect)
			|| Equal(b.m_high[1], y_intersect);

if(on_corner && proper)
        return false;

if(!on_corner && b.m_low[1] < y_intersect && b.m_high[1] > y_intersect)
        return false;
    }

if(high_vertically_between) { // Check for edge intersect
      CoordType x_intersect = (*i)[0] + (b.m_high[1] - (*i)[1])
			      * xdiff / ydiff;

bool on_corner = Equal(b.m_low[0], x_intersect)
			|| Equal(b.m_high[0], x_intersect);

if(on_corner && proper)
        return false;

if(!on_corner && b.m_low[0] < x_intersect && b.m_high[0] > x_intersect)
        return false;
    }

if(high_horizontally_between) { // Check for edge intersect
      CoordType y_intersect = (*i)[1] + (b.m_high[0] - (*i)[0])
			      * ydiff / xdiff;

bool on_corner = Equal(b.m_low[1], y_intersect)
			|| Equal(b.m_high[1], y_intersect);

if(on_corner && proper)
        return false;

if(!on_corner && b.m_low[1] < y_intersect && b.m_high[1] > y_intersect)
        return false;
    }
  }

return hit;
}

template<>
bool Contains<2>(const AxisBox<2>& b, const Polygon<2>& p, bool proper)
{
  for(Polygon<2>::theConstIter i = p.m_points.begin(); i != p.m_points.end(); ++i)
    if(!Contains(b, *i, proper))
      return false;

return true;
}

template<>
bool Intersect<2>(const Polygon<2>& p, const Ball<2>& b, bool proper)
{
  if(Contains(p, b.m_center, proper))
    return true;

Segment<2> s2;
  s2.endpoint(0) = p.m_points.back();
  int next_end = 1;

for(Polygon<2>::theConstIter i = p.m_points.begin(); i != p.m_points.end(); ++i) {
    s2.endpoint(next_end) = *i;
    if(Intersect(s2, b, proper))
      return true;
    next_end = next_end ? 0 : 1;
  }

return false;
}

template<>
bool Contains<2>(const Polygon<2>& p, const Ball<2>& b, bool proper)
{
  if(!Contains(p, b.m_center, proper))
    return false;

Segment<2> s2;
  s2.endpoint(0) = p.m_points.back();
  int next_end = 1;

for(Polygon<2>::theConstIter i = p.m_points.begin(); i != p.m_points.end(); ++i) {
    s2.endpoint(next_end) = *i;
    if(Intersect(s2, b, !proper))
      return false;
    next_end = next_end ? 0 : 1;
  }

return true;
}

template<>
bool Contains<2>(const Ball<2>& b, const Polygon<2>& p, bool proper)
{
  CoordType sqr_dist = b.m_radius * b.m_radius;

for(Polygon<2>::theConstIter i = p.m_points.begin(); i != p.m_points.end(); ++i)
    if(_Greater(SquaredDistance(b.m_center, *i), sqr_dist, proper))
      return false;

return true;
}

template<>
bool Intersect<2>(const Polygon<2>& p, const Segment<2>& s, bool proper)
{
  if(Contains(p, s.endpoint(0), proper))
    return true;

const Polygon<2>::theConstIter begin = p.m_points.begin(), end = p.m_points.end();

Segment<2> s2;

s2.endpoint(0) = p.m_points.back();
  int next_point = 1;

for(Polygon<2>::theConstIter i = begin; i != end; ++i) {
    s2.endpoint(next_point) = *i;
    if(Intersect(s, s2, proper))
      return true;
    next_point = next_point ? 0 : 1;
  }

return false;
}

template<>
bool Contains<2>(const Polygon<2>& p, const Segment<2>& s, bool proper)
{
  if(proper && !Contains(p, s.endpoint(0), true))
    return false;

const Polygon<2>::theConstIter begin = p.m_points.begin(), end = p.m_points.end();

Segment<2> s2;

s2.endpoint(0) = p.m_points.back();
  int next_point = 1;
  bool hit = false;

for(Polygon<2>::theConstIter i = begin; i != end; ++i) {
    s2.endpoint(next_point) = *i;
    if(Intersect(s2, s, !proper))
      return false;
    bool this_point = next_point;
    next_point = next_point ? 0 : 1;
    if(proper)
      continue;

// Check for crossing at an endpoint
    if(Contains(s, *i, false) && (*i != s.m_p2)) {
      Vector<2> segment = s.m_p2 - s.m_p1;
      Vector<2> edge1 = *i - s2.endpoint(next_point); // Gives prev point in this case
      Vector<2> edge2 = *i - *(i + 1);

CoordType c1 = Cross(segment, edge1), c2 = Cross(segment, edge2);

if(c1 * c2 < 0) { // opposite sides
        if(*i == s.m_p1) { // really a containment issue
          if(edge1[1] * edge2[1] > 0 // Edges either both up or both down
            || ((edge1[1] > 0) ? c1 : c2) < 0) // segment lies to the left
            hit = !hit;
          continue; // Already checked containment for this point
        }
        else
          return false;
      }
    }

// Check containment of one endpoint

// next_point also gives prev_point
    bool vertically_between =
        ((s2.endpoint(this_point)[1] <= s.m_p1[1]
       && s.m_p1[1] < s2.endpoint(next_point)[1]) ||
         (s2.endpoint(next_point)[1] <= s.m_p1[1]
       && s.m_p1[1] < s2.endpoint(this_point)[1]));

if (!vertically_between)
      continue;

CoordType x_intersect = s2.m_p1[0] + (s2.m_p2[0] - s2.m_p1[0])
			    * (s.m_p1[1] - s2.m_p1[1])
			    / (s2.m_p2[1] - s2.m_p1[1]);

if(Equal(s.m_p1[0], x_intersect)) { // Figure out which side the segment's on

// Equal points are handled in the crossing routine above
      if(s2.endpoint(next_point) == s.m_p1)
        continue;
      assert(s2.endpoint(this_point) != s.m_p1);

Vector<2> poly_edge = (s2.m_p1[1] < s2.m_p2[1]) ? (s2.m_p2 - s2.m_p1)
						      : (s2.m_p1 - s2.m_p2);
      Vector<2> segment = s.m_p2 - s.m_p1;

if(Cross(segment, poly_edge) < 0)
        hit = !hit;
    }
    else if(s.m_p1[0] < x_intersect)
      hit = !hit;
  }

return proper || hit;
}

template<>
bool Contains<2>(const Segment<2>& s, const Polygon<2>& p, bool proper)
{
  for(Polygon<2>::theConstIter i = p.m_points.begin(); i != p.m_points.end(); ++i)
    if(!Contains(s, *i, proper))
      return false;

return true;
}

template<>
bool Intersect<2>(const Polygon<2>& p, const RotBox<2>& r, bool proper)
{
  CoordType m_low[2], m_high[2];

for(int j = 0; j < 2; ++j) {
    if(r.m_size[j] > 0) {
      m_low[j] = r.m_corner0[j];
      m_high[j] = r.m_corner0[j] + r.m_size[j];
    }
    else {
      m_high[j] = r.m_corner0[j];
      m_low[j] = r.m_corner0[j] + r.m_size[j];
    }
  }

Point<2> ends[2];
  ends[0] = p.m_points.back();
  // FIXME Point<>::rotateInverse()
  ends[0].rotate(r.m_orient.inverse(), r.m_corner0);
  int next_end = 1;

const Polygon<2>::theConstIter begin = p.m_points.begin(), end = p.m_points.end();
  bool hit = false;

for (Polygon<2>::theConstIter i = begin; i != end; ++i) {
    ends[next_end] = *i;
    // FIXME Point<>::rotateInverse()
    ends[next_end].rotate(r.m_orient.inverse(), r.m_corner0);
    next_end = next_end ? 0 : 1;

bool low_vertically_between =
        (((ends[0])[1] <= m_low[1] && m_low[1] < (ends[1])[1]) ||
         ((ends[1])[1] <= m_low[1] && m_low[1] < (ends[0])[1]));
    bool low_horizontally_between =
        (((ends[0])[0] <= m_low[0] && m_low[0] < (ends[1])[0]) ||
         ((ends[1])[0] <= m_low[0] && m_low[0] < (ends[0])[0]));
    bool high_vertically_between =
        (((ends[0])[1] <= m_high[1] && m_high[1] < (ends[1])[1]) ||
         ((ends[1])[1] <= m_high[1] && m_high[1] < (ends[0])[1]));
    bool high_horizontally_between =
        (((ends[0])[0] <= m_high[0] && m_high[0] < (ends[1])[0]) ||
         ((ends[1])[0] <= m_high[0] && m_high[0] < (ends[0])[0]));

CoordType xdiff = (ends[1])[0] - (ends[0])[0];
    CoordType ydiff = (ends[1])[1] - (ends[0])[1];

if(low_vertically_between) { // Check for edge intersect
      CoordType x_intersect = (ends[0])[0] + (m_low[1] - (ends[0])[1])
			      * xdiff / ydiff;

if(Equal(m_low[0], x_intersect) || Equal(m_high[0], x_intersect))
        return !proper;
      if(m_low[0] < x_intersect && m_high[0] > x_intersect)
        return true;

// Also check for point inclusion here, only need to do this for one point
      if(m_low[0] < x_intersect)
        hit = !hit;
    }

if(low_horizontally_between) { // Check for edge intersect
      CoordType y_intersect = (ends[0])[1] + (m_low[0] - (ends[0])[0])
			      * ydiff / xdiff;

if(Equal(m_low[1], y_intersect) || Equal(m_high[1], y_intersect))
        return !proper;
      if(m_low[1] < y_intersect && m_high[1] > y_intersect)
        return true;
    }

if(high_vertically_between) { // Check for edge intersect
      CoordType x_intersect = (ends[0])[0] + (m_high[1] - (ends[0])[1])
			      * xdiff / ydiff;

if(Equal(m_low[0], x_intersect) || Equal(m_high[0], x_intersect))
        return !proper;
      if(m_low[0] < x_intersect && m_high[0] > x_intersect)
        return true;
    }

if(high_horizontally_between) { // Check for edge intersect
      CoordType y_intersect = (ends[0])[1] + (m_high[0] - (ends[0])[0])
			      * ydiff / xdiff;

if(Equal(m_low[1], y_intersect) || Equal(m_high[1], y_intersect))
        return !proper;
      if(m_low[1] < y_intersect && m_high[1] > y_intersect)
        return true;
    }
  }

return hit;
}

template<>
bool Contains<2>(const Polygon<2>& p, const RotBox<2>& r, bool proper)
{
  CoordType m_low[2], m_high[2];

Point<2> ends[2];
  ends[0] = p.m_points.back();
  // FIXME Point<>::rotateInverse()
  ends[0].rotate(r.m_orient.inverse(), r.m_corner0);
  int next_end = 1;

const Polygon<2>::theConstIter begin = p.m_points.begin(), end = p.m_points.end();
  bool hit = false;

CoordType xdiff = (ends[1])[0] - (ends[0])[0];
    CoordType ydiff = (ends[1])[1] - (ends[0])[1];

if(low_vertically_between) { // Check for edge intersect
      CoordType x_intersect = (ends[0])[0] + (m_low[1] - (ends[0])[1])
			      * xdiff / ydiff;

bool on_corner = Equal(m_low[0], x_intersect)
			|| Equal(m_high[0], x_intersect);

if(on_corner && proper)
        return false;

if(!on_corner && m_low[0] < x_intersect && m_high[0] > x_intersect)
        return false;

// Also check for point inclusion here, only need to do this for one point
      if(!on_corner && m_low[0] < x_intersect)
        hit = !hit;
    }

if(low_horizontally_between) { // Check for edge intersect
      CoordType y_intersect = (ends[0])[1] + (m_low[0] - (ends[0])[0])
			      * ydiff / xdiff;

bool on_corner = Equal(m_low[1], y_intersect)
			|| Equal(m_high[1], y_intersect);

if(on_corner && proper)
        return false;

if(!on_corner && m_low[1] < y_intersect && m_high[1] > y_intersect)
        return false;
    }

if(high_vertically_between) { // Check for edge intersect
      CoordType x_intersect = (ends[0])[0] + (m_high[1] - (ends[0])[1])
			      * xdiff / ydiff;

bool on_corner = Equal(m_low[0], x_intersect)
			|| Equal(m_high[0], x_intersect);

if(on_corner && proper)
        return false;

if(!on_corner && m_low[0] < x_intersect && m_high[0] > x_intersect)
        return false;
    }

if(high_horizontally_between) { // Check for edge intersect
      CoordType y_intersect = (ends[0])[1] + (m_high[0] - (ends[0])[0])
			      * ydiff / xdiff;

bool on_corner = Equal(m_low[1], y_intersect)
			|| Equal(m_high[1], y_intersect);

if(on_corner && proper)
        return false;

if(!on_corner && m_low[1] < y_intersect && m_high[1] > y_intersect)
        return false;
    }
  }

return hit;
}

template<>
bool Contains<2>(const RotBox<2>& r, const Polygon<2>& p, bool proper)
{
  for(Polygon<2>::theConstIter i = p.m_points.begin(); i != p.m_points.end(); ++i)
    if(!Contains(r, *i, proper))
      return false;

return true;
}

template<>
bool Intersect<2>(const Polygon<2>& p1, const Polygon<2>& p2, bool proper)
{
  Polygon<2>::theConstIter begin1 = p1.m_points.begin(), end1 = p1.m_points.end();
  Polygon<2>::theConstIter begin2 = p2.m_points.begin(), end2 = p2.m_points.end();
  Segment<2> s1, s2;
  int next_end1, next_end2;

s1.endpoint(0) = p1.m_points.back();
  s2.endpoint(0) = p2.m_points.back();
  next_end1 = next_end2 = 1;
  for(Polygon<2>::theConstIter i1 = begin1; i1 != end1; ++i1) {
    s1.endpoint(next_end1) = *i1;
    next_end1 = next_end1 ? 0 : 1;

for(Polygon<2>::theConstIter i2 = begin2; i2 != end2; ++i2) {
      s2.endpoint(next_end2) = *i2;
      next_end2 = next_end2 ? 0 : 1;

if(Intersect(s1, s2, proper))
        return true;
    }
  }

return Contains(p1, p2.m_points.front(), proper)
      || Contains(p2, p1.m_points.front(), proper);
}

template<>
bool Contains<2>(const Polygon<2>& outer, const Polygon<2>& inner, bool proper)
{
  if(proper && !Contains(outer, inner.m_points.front(), true))
    return false;

Polygon<2>::theConstIter begin = inner.m_points.begin(), end = inner.m_points.end();
  Segment<2> s;
  s.endpoint(0) = inner.m_points.back();
  int next_end = 1;

for(Polygon<2>::theConstIter i = begin; i != end; ++i) {
    s.endpoint(next_end) = *i;
    next_end = next_end ? 0 : 1;
    if(!proper) {
      if(!Contains(outer, s, false))
        return false;
    }
    else {
      Polygon<2>::theConstIter begin2 = outer.m_points.begin(),
				end2 = outer.m_points.end();
      Segment<2> s2;
      s2.endpoint(0) = outer.m_points.back();
      int next_end2 = 1;
      for(Polygon<2>::theConstIter i2 = begin2; i2 != end2; ++i2) {
        s2.endpoint(next_end2) = *i2;
        next_end2 = next_end2 ? 0 : 1;
  
        if(Intersect(s, s2, false))
          return false;
      }
    }
  }

return true;
}

}
07070100000040000081A40000000200000002000000015D8693EF00004B50000000000000000000000000000000000000003500000000wfmath-1569100783.d0f8a54/wfmath/polygon_intersect.h// polygon_funcs.h (Polygon<> intersection functions)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke
// Created: 2002-2-20

#ifndef WFMATH_POLYGON_INTERSECT_H
#define WFMATH_POLYGON_INTERSECT_H

#include <wfmath/axisbox.h>
#include <wfmath/ball.h>
#include <wfmath/polygon.h>
#include <wfmath/intersect.h>
#include <wfmath/error.h>

#include <cmath>

#include <cassert>

// FIXME Work is needed on this code. At very least the following notes
// from the original author apply:
// "The Intersect() and Contains() functions involving WFMath::Polygon<>"
// "are still under development, and probably shouldn't be used yet."

namespace WFMath {

template<int dim>
inline Vector<dim> _Poly2Orient<dim>::offset(const Point<dim>& pd, Point<2>& p2) const
{
  assert(m_origin.isValid()); // Check for empty polygon before calling this

Vector<dim> out = pd - m_origin;

for(int j = 0; j < 2; ++j) {
    p2[j] = Dot(out, m_axes[j]);
    out -= p2[j] * m_axes[j];
  }

return out;
}

template<int dim>
inline bool _Poly2Orient<dim>::checkContained(const Point<dim>& pd, Point<2> & p2) const
{
  Vector<dim> off = offset(pd, p2);

CoordType sqrsum = 0;
  for(int i = 0; i < dim; ++i)
    sqrsum += pd[i] * pd[i];

return off.sqrMag() < numeric_constants<CoordType>::epsilon() * sqrsum;
}

template<>
bool _Poly2Orient<3>::checkIntersectPlane(const AxisBox<3>& b, Point<2>& p2,
					  bool proper) const;

template<int dim>
bool _Poly2Orient<dim>::checkIntersect(const AxisBox<dim>& b, Point<2>& p2,
				       bool proper) const
{
  assert(m_origin.isValid());

if(!m_axes[0].isValid()) {
    // Single point
    p2[0] = p2[1] = 0;
    return Intersect(b, convert(p2), proper);
  }

if(m_axes[1].isValid()) {
    // A plane

// I only know how to do this in 3D, so write a function which will
    // specialize to different dimensions

return checkIntersectPlane(b, p2, proper);
  }

// A line

// This is a modified version of AxisBox<>/Segment<> intersection

CoordType min = 0, max = 0; // Initialize to avoid compiler warnings
  bool got_bounds = false;

for(int i = 0; i < dim; ++i) {
    const CoordType dist = (m_axes[0])[i]; // const may optimize away better
    if(dist == 0) {
      if(_Less(m_origin[i], b.lowCorner()[i], proper)
        || _Greater(m_origin[i], b.highCorner()[i], proper))
        return false;
    }
    else {
      CoordType low = (b.lowCorner()[i] - m_origin[i]) / dist;
      CoordType high = (b.highCorner()[i] - m_origin[i]) / dist;
      if(low > high) {
        CoordType tmp = high;
        high = low;
        low = tmp;
      }
      if(got_bounds) {
        if(low > min)
          min = low;
        if(high < max)
          max = high;
      }
      else {
        min = low;
        max = high;
        got_bounds = true;
      }
    }
  }

assert(got_bounds); // We can't be parallel in _all_ dimensions

if(_LessEq(min, max, proper)) {
    p2[0] = (max - min) / 2;
    p2[1] = 0;
    return true;
  }
  else
    return false;
}

template<int dim>
int  _Intersect(const _Poly2Orient<dim> &o1, const _Poly2Orient<dim> &o2,
	        _Poly2OrientIntersectData &data)
{
  if(!o1.m_origin.isValid() || !o2.m_origin.isValid()) { // No points
    return -1;
  }

// Check for single point basis

if(!o1.m_axes[0].isValid()) {
    if(!o2.checkContained(o1.m_origin, data.p2))
      return -1; // no intersect

//_Poly2OrientIntersectData data;

data.p1[0] = data.p1[1] = 0;

return 0; // point intersect
  }

if(!o2.m_axes[0].isValid()) {
    if(!o1.checkContained(o2.m_origin, data.p1))
      return -1; // no intersect

data.p2[0] = data.p2[1] = 0;

return 0; // point intersect
  }

// Find a common basis for the plane's orientations
  // by projecting out the part of o1's basis that lies
  // in o2's basis

Vector<dim> basis1, basis2;
  CoordType sqrmag1, sqrmag2;
  int basis_size = 0;

basis1 = o2.m_axes[0] * Dot(o2.m_axes[0], o1.m_axes[0]);
  if(o2.m_axes[1].isValid())
    basis1 += o2.m_axes[1] * Dot(o2.m_axes[1], o1.m_axes[0]);

// Don't need to scale, the m_axes are unit vectors
  sqrmag1 = basis1.sqrMag();
  if(sqrmag1 > numeric_constants<CoordType>::epsilon() * numeric_constants<CoordType>::epsilon())
    basis_size = 1;

if(o1.m_axes[1].isValid()) {
    basis2 = o2.m_axes[0] * Dot(o2.m_axes[0], o1.m_axes[1]);
    if(o2.m_axes[1].isValid())
      basis2 += o2.m_axes[1] * Dot(o2.m_axes[1], o1.m_axes[1]);

// Project out part parallel to basis1
    if(basis_size == 1)
      basis2 -= basis1 * (Dot(basis1, basis2) / sqrmag1);

sqrmag2 = basis2.sqrMag();
    if(sqrmag2 > numeric_constants<CoordType>::epsilon() * numeric_constants<CoordType>::epsilon()) {
      if(basis_size++ == 0) {
        basis1 = basis2;
        sqrmag1 = sqrmag2;
      }
    }
  }

Vector<dim> off = o2.m_origin - o1.m_origin;

switch(basis_size) {
    case 0:
      {
      // All vectors are orthogonal, check for a common point in the plane
      // This can happen even in 3d for degenerate bases

data.p1[0] = Dot(o1.m_axes[0], off);
      Vector<dim> off1 = o1.m_axes[0] * data.p1[0];
      if(o1.m_axes[1].isValid()) {
        data.p1[1] = Dot(o1.m_axes[1], off);
        off1 += o1.m_axes[1] * data.p1[1];
      }
      else
        data.p1[1] = 0;

data.p2[0] = -Dot(o2.m_axes[0], off);
      Vector<dim> off2 = o2.m_axes[0] * data.p2[0];
      if(o1.m_axes[1].isValid()) {
        data.p2[1] = -Dot(o2.m_axes[1], off);
        off2 += o1.m_axes[1] * data.p2[1];
      }
      else
        data.p2[1] = 0;

if(off1 - off2 != off) // No common point
        return -1;
      else  // Got a point
        return 1;
      }
    case 1:
      {
      // Check for an intersection line

data.o1_is_line = !o1.m_axes[1].isValid();
      data.o2_is_line = !o2.m_axes[1].isValid();

if(!o1.m_axes[1].isValid() && !o2.m_axes[1].isValid()) {
        CoordType proj = Dot(off, o2.m_axes[0]);
        if(off != o2.m_axes[0] * proj)
          return -1;

data.v1[0] = 1;
        data.v1[1] = 0;
        data.p1[0] = data.p1[1] = 0;
        data.v2[0] = (Dot(o1.m_axes[0], o2.m_axes[0]) > 0) ? 1 : -1;
        data.v2[1] = 0;
        data.p2[0] = -proj;
        data.p2[1] = 0;

return 1;
      }

if(!o1.m_axes[1].isValid()) {
        data.p2[0] = -Dot(off, o2.m_axes[0]);
        data.p2[1] = -Dot(off, o2.m_axes[1]);

if(off != - data.p2[0] * o2.m_axes[0] - data.p2[1] * o2.m_axes[1])
          return -1;

data.v1[0] = 1;
        data.v1[1] = 0;
        data.p1[0] = data.p1[1] = 0;
        data.v2[0] = Dot(o1.m_axes[0], o2.m_axes[0]);
        data.v2[1] = Dot(o1.m_axes[0], o2.m_axes[1]);

return 1;
      }

if(!o2.m_axes[1].isValid()) {
        data.p1[0] = Dot(off, o1.m_axes[0]);
        data.p1[1] = Dot(off, o1.m_axes[1]);

if(off != data.p1[0] * o1.m_axes[0] + data.p1[1] * o1.m_axes[1])
          return -1;

data.v2[0] = 1;
        data.v2[1] = 0;
        data.p2[0] = data.p2[1] = 0;
        data.v1[0] = Dot(o1.m_axes[0], o2.m_axes[0]);
        data.v1[1] = Dot(o1.m_axes[1], o2.m_axes[0]);

return 1;
      }

data.p1[0] = Dot(off, o1.m_axes[0]);
      data.p1[1] = Dot(off, o1.m_axes[1]);
      data.p2[0] = -Dot(off, o2.m_axes[0]);
      data.p2[1] = -Dot(off, o2.m_axes[1]);

if(off != data.p1[0] * o1.m_axes[0] + data.p1[1] * o1.m_axes[1]
        - data.p2[0] * o2.m_axes[0] - data.p2[1] * o2.m_axes[1])
        return -1;

basis1 /= std::sqrt(sqrmag1);

data.v1[0] = Dot(o1.m_axes[0], basis1);
      data.v1[1] = Dot(o1.m_axes[1], basis1);
      data.v2[0] = Dot(o2.m_axes[0], basis1);
      data.v2[1] = Dot(o2.m_axes[1], basis1);

return 1;
      }
    case 2:
      {
      assert(o1.m_axes[1].isValid() && o2.m_axes[1].isValid());

// The planes are parallel, check if they are the same plane
      CoordType off_sqr_mag = data.off.sqrMag();

// Find the offset between the origins in o2's coordnates

if(off_sqr_mag != 0) { // The offsets aren't identical
        Vector<dim> off_copy = off;

data.off[0] = Dot(o2.m_axes[0], off);
        off_copy -= o1.m_axes[0] * data.off[0];
        data.off[1] = Dot(o2.m_axes[1], off);
        off_copy -= o1.m_axes[1] * data.off[1];

if(off_copy.sqrMag() > off_sqr_mag * numeric_constants<CoordType>::epsilon())
          return -1; // The planes are different
      }
      else
        data.off[0] = data.off[1] = 0;

// Define o2's basis vectors in o1's coordinates
      data.v1[0] = Dot(o2.m_axes[0], o1.m_axes[0]);
      data.v1[1] = Dot(o2.m_axes[0], o1.m_axes[1]);
      data.v2[0] = Dot(o2.m_axes[1], o1.m_axes[0]);
      data.v2[1] = Dot(o2.m_axes[1], o1.m_axes[1]);

return 2;
      }
    default:
      assert(false);
      return -1;
  }
}

template<int dim>
inline bool Intersect(const Polygon<dim>& r, const Point<dim>& p, bool proper)
{
  Point<2> p2;

return r.m_poly.numCorners() > 0 && r.m_orient.checkContained(p, p2)
	 && Intersect(r.m_poly, p2, proper);
}

template<int dim>
inline bool Contains(const Point<dim>& p, const Polygon<dim>& r, bool proper)
{
  if(r.m_poly.numCorners() == 0)
    return true;

if(proper)
    return false;

for(size_t i = 1; i < r.m_poly.numCorners(); ++i)
    if(r.m_poly[i] != r.m_poly[0])
      return false;

Point<2> p2;

return r.m_orient.checkContained(p, p2) && p2 == r.m_poly[0];
}

template<int dim>
bool Intersect(const Polygon<dim>& p, const AxisBox<dim>& b, bool proper)
{
  size_t corners = p.m_poly.numCorners();

if(corners == 0)
    return false;

Point<2> p2;

if(!p.m_orient.checkIntersect(b, p2, proper))
    return false;

Segment<dim> s;
  s.endpoint(0) = p.m_orient.convert(p.m_poly.getCorner(corners-1));
  int next_end = 1;

for(size_t i = 0; i < corners; ++i) {
    s.endpoint(next_end) = p.m_orient.convert(p.m_poly.getCorner(i));
    if(Intersect(b, s, proper))
      return true;
    next_end = next_end ? 0 : 1;
  }

return Contains(p, p2, proper);
}

template<int dim>
bool _PolyContainsBox(const _Poly2Orient<dim> &orient, const Polygon<2> &poly,
		  const Point<dim> &corner, const Vector<dim> &size, bool proper)
{
  int num_dim = 0, nonzero_dim = -1;

for(int i = 0; i < dim; ++i) {
    if(size[i] == 0)
      continue;
    if(num_dim == 2)
      return false;
    if(nonzero_dim == -1 || std::fabs(size[nonzero_dim]) < std::fabs(size[i]))
      nonzero_dim = i;
    ++num_dim;
  }

Point<2> corner1;

if(!orient.checkContained(corner, corner1))
    return false;

if(num_dim == 0)
    return Contains(poly, corner1, proper);

Point<2> corner2;

if(!orient.checkContained(corner + size, corner2))
    return false;

if(num_dim == 1)
    return Contains(poly, Segment<2>(corner1, corner2), proper);

Point<dim> other_corner = corner;
  other_corner[nonzero_dim] += size[nonzero_dim];

Point<2> corner3;
  if(!orient.checkContained(other_corner, corner3))
    return false;

// Create a RotBox<2>

Vector<2> vec1(corner2 - corner1), vec2(corner3 - corner1);

RotMatrix<2> m; // A matrix which gives the rotation from the x-axis to vec1

try {
    m.rotation(Vector<2>(1, 0), vec1);
  }
  catch(const ColinearVectors<2>&) { // vec1 is parallel to (-1, 0), so we're fine
    m.identity();
  }

RotBox<2> box(corner1, ProdInv(vec2, m), m);

return Contains(poly, box, proper);
}

template<int dim>
inline bool Contains(const Polygon<dim>& p, const AxisBox<dim>& b, bool proper)
{
  return _PolyContainsBox(p.m_orient, p.m_poly, b.m_low, b.m_high - b.m_low, proper);
}

template<int dim>
inline bool Contains(const AxisBox<dim>& b, const Polygon<dim>& p, bool proper)
{
  for(size_t i = 0; i < p.m_poly.numCorners(); ++i)
    if(!Contains(b, p.getCorner(i), proper))
      return false;

return true;
}

template<int dim>
inline bool Intersect(const Polygon<dim>& p, const Ball<dim>& b, bool proper)
{
  if(p.m_poly.numCorners() == 0)
    return false;

Point<2> c2;
  CoordType dist;

dist = b.m_radius * b.m_radius - p.m_orient.offset(b.m_center, c2).sqrMag();

if(_Less(dist, 0, proper))
    return false;

return Intersect(p.m_poly, Ball<2>(c2, std::sqrt(dist)), proper);
}

template<int dim>
inline bool Contains(const Polygon<dim>& p, const Ball<dim>& b, bool proper)
{
  if(p.m_poly.numCorners() == 0)
    return false;

if(b.m_radius > 0)
    return false;

Point<2> c2;

if(!p.m_orient.checkContained(b.m_center, c2))
    return false;

return Contains(p.m_poly, c2, proper);
}

template<int dim>
inline bool Contains(const Ball<dim>& b, const Polygon<dim>& p, bool proper)
{
  if(p.m_poly.numCorners() == 0)
    return true;

Point<2> c2;
  CoordType dist;

dist = b.m_radius * b.m_radius - p.m_orient.offset(b.m_center, c2).sqrMag();

if(_Less(dist, 0, proper))
    return false;

for(size_t i = 0; i != p.m_poly.numCorners(); ++i)
    if(_Less(dist, SquaredDistance(c2, p.m_poly[i]), proper))
      return false;

return true;
}

template<int dim>
bool Intersect(const Polygon<dim>& p, const Segment<dim>& s, bool proper)
{
  if(p.m_poly.numCorners() == 0)
    return false;

Point<2> p1, p2;
  CoordType d1, d2;
  Vector<dim> v1, v2;

v1 = p.m_orient.offset(s.m_p1, p1);
  v2 = p.m_orient.offset(s.m_p2, p2);

if(Dot(v1, v2) > 0) // Both points on same side of sheet
    return false;

d1 = v1.mag();
  d2 = v2.mag();
  Point<2> p_intersect;

if(d1 + d2 == 0) // Avoid divide by zero later
    return Intersect(p.m_poly, Segment<2>(p1, p2), proper);

for(int i = 0; i < 2; ++i)
    p_intersect[i] = (p1[i] * d2 + p2[i] * d1) / (d1 + d2);

return Intersect(p.m_poly, p_intersect, proper);
}

template<int dim>
inline bool Contains(const Polygon<dim>& p, const Segment<dim>& s, bool proper)
{
  if(p.m_poly.numCorners() == 0)
    return false;

Segment<2> s2;

if(!p.m_orient.checkContained(s.m_p1, s2.endpoint(0)))
    return false;
  if(!p.m_orient.checkContained(s.m_p2, s2.endpoint(1)))
    return false;

return Contains(p.m_poly, s2, proper);
}

template<int dim>
inline bool Contains(const Segment<dim>& s, const Polygon<dim>& p, bool proper)
{
  if(p.m_poly.numCorners() == 0)
    return true;

// Expand the basis to include the segment, this deals well with
  // degenerate polygons

Segment<2> s2;
  _Poly2Orient<dim> orient(p.m_orient);

for(int i = 0; i < 2; ++i)
    if(!orient.expand(s.endpoint(i), s2.endpoint(i)))
      return false;

return Contains(s2, p.m_poly, proper);
}

template<int dim>
bool Intersect(const Polygon<dim>& p, const RotBox<dim>& r, bool proper)
{
  size_t corners = p.m_poly.numCorners();

if(corners == 0)
    return false;

_Poly2Orient<dim> orient(p.m_orient);
  // FIXME rotateInverse()
  orient.rotate(r.m_orient.inverse(), r.m_corner0);

AxisBox<dim> b(r.m_corner0, r.m_corner0 + r.m_size);

Point<2> p2;

if(!orient.checkIntersect(b, p2, proper))
    return false;

Segment<dim> s;
  s.endpoint(0) = orient.convert(p.m_poly.getCorner(corners-1));
  int next_end = 1;

for(size_t i = 0; i < corners; ++i) {
    s.endpoint(next_end) = orient.convert(p.m_poly.getCorner(i));
    if(Intersect(b, s, proper))
      return true;
    next_end = next_end ? 0 : 1;
  }

return Contains(p, p2, proper);
}

template<int dim>
inline bool Contains(const Polygon<dim>& p, const RotBox<dim>& r, bool proper)
{
  _Poly2Orient<dim> orient(p.m_orient);
  orient.rotate(r.m_orient.inverse(), r.m_corner0);

return _PolyContainsBox(orient, p.m_poly, r.m_corner0, r.m_size, proper);
}

template<int dim>
inline bool Contains(const RotBox<dim>& r, const Polygon<dim>& p, bool proper)
{
  if(p.m_poly.numCorners() == 0)
    return true;

AxisBox<dim> b(r.m_corner0, r.m_corner0 + r.m_size);

_Poly2Orient<dim> orient(p.m_orient);
  orient.rotate(r.m_orient.inverse(), r.m_corner0);

for(size_t i = 0; i < p.m_poly.numCorners(); ++i)
    if(!Contains(b, orient.convert(p.m_poly[i]), proper))
      return false;

return true;
}

bool _PolyPolyIntersect(const Polygon<2> &poly1, const Polygon<2> &poly2,
			const int intersect_dim,
			const _Poly2OrientIntersectData &data, bool proper);

template<int dim>
inline bool Intersect(const Polygon<dim>& p1, const Polygon<dim>& p2, bool proper)
{
  _Poly2OrientIntersectData data;

int intersect_dim = _Intersect(p1.m_orient, p2.m_orient, data);

return _PolyPolyIntersect(p1.m_poly, p2.m_poly, intersect_dim, data, proper);
}

bool _PolyPolyContains(const Polygon<2> &outer, const Polygon<2> &inner,
		       const int intersect_dim,
		       const _Poly2OrientIntersectData &data, bool proper);

template<int dim>
inline bool Contains(const Polygon<dim>& outer, const Polygon<dim>& inner, bool proper)
{
  if(outer.m_poly.numCorners() == 0)
    return !proper && inner.m_poly.numCorners() == 0;

if(inner.m_poly.numCorners() == 0)
    return true;

_Poly2OrientIntersectData data;

int intersect_dim = _Intersect(outer.m_orient, inner.m_orient, data);

return _PolyPolyContains(outer.m_poly, inner.m_poly, intersect_dim, data, proper);
}

template<>
bool Intersect(const Polygon<2>& r, const Point<2>& p, bool proper);
template<>
bool Contains(const Point<2>& p, const Polygon<2>& r, bool proper);

template<>
bool Intersect(const Polygon<2>& p, const AxisBox<2>& b, bool proper);
template<>
bool Contains(const Polygon<2>& p, const AxisBox<2>& b, bool proper);
template<>
bool Contains(const AxisBox<2>& b, const Polygon<2>& p, bool proper);

template<>
bool Intersect(const Polygon<2>& p, const Ball<2>& b, bool proper);
template<>
bool Contains(const Polygon<2>& p, const Ball<2>& b, bool proper);
template<>
bool Contains(const Ball<2>& b, const Polygon<2>& p, bool proper);

template<>
bool Intersect(const Polygon<2>& r, const Segment<2>& s, bool proper);
template<>
bool Contains(const Polygon<2>& p, const Segment<2>& s, bool proper);
template<>
bool Contains(const Segment<2>& s, const Polygon<2>& p, bool proper);

template<>
bool Intersect(const Polygon<2>& p, const RotBox<2>& r, bool proper);
template<>
bool Contains(const Polygon<2>& p, const RotBox<2>& r, bool proper);
template<>
bool Contains(const RotBox<2>& r, const Polygon<2>& p, bool proper);

template<>
bool Intersect(const Polygon<2>& p1, const Polygon<2>& p2, bool proper);
template<>
bool Contains(const Polygon<2>& outer, const Polygon<2>& inner, bool proper);

} // namespace WFMath

#endif  // WFMATH_POLYGON_INTERSECT_H
07070100000041000081A40000000200000002000000015D8693EF00001697000000000000000000000000000000000000003200000000wfmath-1569100783.d0f8a54/wfmath/polygon_test.cpp// polygon_test.cpp (Polygon<> test functions)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-1-20

#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include "const.h"
#include "vector.h"
#include "rotmatrix.h"
#include "point.h"
#include "polygon.h"
#include "polygon_intersect.h"
#include "stream.h"
#include <vector>

#include "general_test.h"
#include "shape_test.h"

using namespace WFMath;

template<int dim>
void test_polygon(const Polygon<dim>& p)
{
  std::cout << "Testing " << p << std::endl;

test_general(p);
  test_shape(p);

// FIXME more tests

// Just check that these compile
  Point<dim> point;
  point.setToOrigin();
  AxisBox<dim> a(point, point, true);
  Vector<dim> vec;
  vec.zero();
  RotMatrix<dim> mat;
  mat.identity();
  RotBox<dim> r(point, vec, mat);

Intersect(p, a, false);
  Intersect(p, r, false);
}

/**
 * Test intersection between a square polygon and axis boxes at each of its four sides.
 */
void test_intersect()
{

Polygon<2> p;

p.addCorner(0, Point<2>(0, 0));
  p.addCorner(0, Point<2>(4, 0));
  p.addCorner(0, Point<2>(4, -4));
  p.addCorner(0, Point<2>(0, -4));
  p.isValid();

AxisBox<2> a1(Point<2>(-1, -1), Point<2>(1, -3));
  std::cout << "Testing intersection of " << p << " and " << a1 << std::endl;
  assert(Intersect(p, a1, false));

AxisBox<2> a2(Point<2>(1, -5), Point<2>(2, -3));
  std::cout << "Testing intersection of " << p << " and " << a2 << std::endl;
  assert(Intersect(p, a2, false));

AxisBox<2> a3(Point<2>(5, -1), Point<2>(3, -3));
  std::cout << "Testing intersection of " << p << " and " << a3 << std::endl;
  assert(Intersect(p, a3, false));

AxisBox<2> a4(Point<2>(1, 1), Point<2>(2, -1));
  std::cout << "Testing intersection of " << p << " and " << a4 << std::endl;
  assert(Intersect(p, a4, false));

RotBox<2> r1(Point<2>(-1, -1), Vector<2>(2, -2), RotMatrix<2>().identity());
  std::cout << "Testing intersection of " << p << " and " << r1 << std::endl;
  assert(Intersect(p, r1, false));

RotBox<2> r2(Point<2>(1, -5), Vector<2>(1, 2), RotMatrix<2>().identity());
  std::cout << "Testing intersection of " << p << " and " << r2 << std::endl;
  assert(Intersect(p, r2, false));

RotBox<2> r3(Point<2>(5, -1), Vector<2>(-2, -2), RotMatrix<2>().identity());
  std::cout << "Testing intersection of " << p << " and " << r3 << std::endl;
  assert(Intersect(p, r3, false));

RotBox<2> r4(Point<2>(1, 1), Vector<2>(1, -2), RotMatrix<2>().identity());
  std::cout << "Testing intersection of " << p << " and " << r4 << std::endl;
  assert(Intersect(p, r4, false));

}

/**
 * Test contains between a square polygon and axis boxes at each of its four sides.
 */
void test_contains()
{

Polygon<2> p;

p.addCorner(0, Point<2>(0, 0));
  p.addCorner(0, Point<2>(4, 0));
  p.addCorner(0, Point<2>(4, -4));
  p.addCorner(0, Point<2>(0, -4));
  p.isValid();

AxisBox<2> a1(Point<2>(0.1f, -3.9f), Point<2>(0.2f, -3.8f));
  std::cout << "Testing " << p << " contains " << a1 << std::endl;
  assert(Contains(p, a1, false));

AxisBox<2> a2(Point<2>(3.8f, -3.9f), Point<2>(3.9f, -3.8f));
  std::cout << "Testing " << p << " contains " << a2 << std::endl;
  assert(Contains(p, a2, false));

AxisBox<2> a3(Point<2>(0.1f, -0.2f), Point<2>(0.2f, -0.1f));
  std::cout << "Testing " << p << " contains " << a3 << std::endl;
  assert(Contains(p, a3, false));

AxisBox<2> a4(Point<2>(3.8f, -0.2f), Point<2>(3.9f, -0.1f));
  std::cout << "Testing " << p << " contains " << a4 << std::endl;
  assert(Contains(p, a4, false));

RotBox<2> r1(Point<2>(0.1f, -3.9f), Vector<2>(0.1f, 0.1f), RotMatrix<2>().identity());
  std::cout << "Testing " << p << " contains " << r1 << std::endl;
  assert(Contains(p, r1, false));

RotBox<2> r2(Point<2>(3.8f, -3.9f), Vector<2>(0.1f, 0.1f), RotMatrix<2>().identity());
  std::cout << "Testing " << p << " contains " << r2 << std::endl;
  assert(Contains(p, r2, false));

RotBox<2> r3(Point<2>(0.1f, -0.2f), Vector<2>(0.1f, 0.1f), RotMatrix<2>().identity());
  std::cout << "Testing " << p << " contains " << r3 << std::endl;
  assert(Contains(p, r3, false));

RotBox<2> r4(Point<2>(3.8f, -0.2f), Vector<2>(0.1f, 0.1f), RotMatrix<2>().identity());
  std::cout << "Testing " << p << " contains " << r4 << std::endl;
  assert(Contains(p, r4, false));

}

int main()
{
  bool succ;

Polygon<2> p2;

succ = p2.addCorner(0, Point<2>(1, -1));
  assert(succ);
  succ = p2.addCorner(0, Point<2>(2, -1));
  assert(succ);
  succ = p2.addCorner(0, Point<2>(1, -3));
  assert(succ);

test_polygon(p2);

Polygon<3> p3;

succ = p3.addCorner(0, Point<3>(1, -1, 5));
  assert(succ);
  succ = p3.addCorner(0, Point<3>(2, -1, std::sqrt(3.0f/2)));
  assert(succ);
  succ = p3.addCorner(0, Point<3>(1, -3, 2.0f/3));
  assert(succ);

test_polygon(p3);

test_intersect();

test_contains();

return 0;
}
07070100000042000081A40000000200000002000000015D8693EF0000299E000000000000000000000000000000000000003100000000wfmath-1569100783.d0f8a54/wfmath/probability.cpp// probability.cpp (probability and statistics implementation)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-1-23

#include <wfmath/probability.h>

#include <wfmath/const.h>

#include <cmath>

#include <cassert>

namespace WFMath {

template<typename FloatT>
static FloatT LogPoisson(FloatT mean, unsigned int step);
template<typename FloatT>
static FloatT IncompleteGamma(FloatT a, FloatT z);
template<typename FloatT>
static FloatT IncompleteGammaNoPrefactor(FloatT a, FloatT z);
template<typename FloatT>
static FloatT IncompleteGammaComplement(FloatT a, FloatT z);
template<typename FloatT>
static FloatT IncompleteGammaComplementNoPrefactor(FloatT a, FloatT z);

// Making this an int makes LogFactorial faster
static const unsigned int GammaCutoff = 10;

template<typename FloatT>
FloatT GaussianConditional(FloatT mean, FloatT stddev, FloatT val)
{
  assert(stddev != 0);

FloatT diff = val - mean;
  FloatT diffnorm = diff / stddev;
  FloatT diffsqr_over_two = diffnorm * diffnorm / 2;

/* Make sure round off error in Sqrt3 doesn't hit
   * assert() in IncompleteGammaComplementNoPrefactor()
   */
  static const FloatT half = 0.5;
  if(diffnorm < numeric_constants<FloatT>::sqrt3() +
                10 * std::numeric_limits<FloatT>::epsilon()) {
    FloatT erfc_norm = IncompleteGammaComplement(half, diffsqr_over_two);

FloatT normalization = (diffnorm > 0) ? (erfc_norm / 2) : (1 - erfc_norm / 2);

return Gaussian(mean, stddev, val) / normalization;
  }
  static const FloatT two = 2.0;

return two / (std::fabs(diff)
	 * IncompleteGammaComplementNoPrefactor<FloatT>(half, diffsqr_over_two));
}

template<typename FloatT>
FloatT Gaussian(FloatT mean, FloatT stddev, FloatT val)
{
  assert(stddev != 0);

FloatT diff = (mean - val) / stddev;

return std::exp(-(diff * diff) / 2) / (std::fabs(stddev) *
         (numeric_constants<FloatT>::sqrt_pi() *
          numeric_constants<FloatT>::sqrt2()));
}

template<typename FloatT>
FloatT PoissonConditional(FloatT mean, unsigned int step)
{
  assert(mean >= 0);

if(mean == 0) // Funky limit, but allow it
    return (step == 0) ? 1 : 0;

if(step == 0)
    return std::exp(-mean);

if(mean > step + 1)
    return Poisson(mean, step) /
           IncompleteGamma(static_cast<FloatT>(step), mean);

static const FloatT one = 1.0;
  return one / IncompleteGammaNoPrefactor(static_cast<FloatT>(step), mean);
}

template<typename FloatT>
FloatT Poisson(FloatT mean, unsigned int step)
{
  assert(mean >= 0);

if(mean == 0) // Funky limit, but allow it
    return (step == 0) ? 1 : 0;

return std::exp(LogPoisson(mean, step));
}

template<typename FloatT>
static FloatT LogPoisson(FloatT mean, unsigned int step)
{
  assert(mean > 0);

if(step == 0)
    return -mean;

FloatT first = static_cast<FloatT>(step) * std::log(mean);
  FloatT second = mean +  LogFactorial<FloatT>(step);

assert("LogFactorial() always returns positive" && second > 0);

FloatT ans = first - second;

// can only get probability == 1 for step == mean == 0
  assert("must get probability < 1" && ans < 0);

return ans;
}

template<typename FloatT>
FloatT Factorial(unsigned int n)
{
  if(n == 0 || n == 1)
    return 1;

if(n < GammaCutoff) {
    FloatT ans = static_cast<FloatT>(n);
    while(--n > 1) // Don't need to multiply by 1
      ans *= static_cast<FloatT>(n);
    return ans;
  }
  else
    return std::exp(LogGamma(static_cast<FloatT>(n + 1)));
}

template<typename FloatT>
FloatT LogFactorial(unsigned int n)
{
  if(n == 0 || n == 1)
    return 0; // ln(0!) = ln(1!) = ln(1) = 0

if(n < GammaCutoff) {
    FloatT ans = static_cast<FloatT>(n);
    while(--n > 1) // Don't need to multiply by 1
      ans *= static_cast<FloatT>(n);
    return std::log(ans);
  }
  else
    return LogGamma(static_cast<FloatT>(n + 1));
}

template<typename FloatT>
FloatT Gamma(FloatT z)
{
  if(z >= 0.5)
    return std::exp(LogGamma(z));
  else
    return numeric_constants<FloatT>::pi() *
           std::exp(-LogGamma(1 - z)) /
           std::sin(numeric_constants<FloatT>::pi() * z);
}

template<typename FloatT>
FloatT LogGamma(FloatT z)
{
  /* This will return nan or something when z is a non-positive
   * integer (from trying to take log(0)), but that's what
   * should happen anyway.
   */
  static const FloatT one = 1.0;

if(z < 0.5)
    return numeric_constants<FloatT>::log_pi() -
           LogGamma<FloatT>(one - z) -
           std::log(std::fabs(std::sin(numeric_constants<FloatT>::pi() * z)));

if(z == 0.5) // special case for Gaussian
    return numeric_constants<FloatT>::log_pi() / 2;

if(z == 1 || z == 2) // 0! and 1!
    return 0;

FloatT log_shift;

if(z < GammaCutoff) {
    FloatT shift = 1;
    while(z < GammaCutoff)
      shift *= z++;
    log_shift = std::log(std::fabs(shift));
  }
  else
    log_shift = 0;

// Stirling approximation (see Gradshteyn + Ryzhik, Table of Integrals,
  // Series, and Products, fifth edition, formula 8.344 for a specific formula)

static const FloatT half = 0.5, two = 2.0;

FloatT ans = (z - half) * std::log(z) - log_shift - z +
               (numeric_constants<FloatT>::log_pi() +
                numeric_constants<FloatT>::log2()) / two;

// coeffs[i] is the 2*(i+1)th Bernoulli number, divided by (2i + 1)*(2i + 2)
  static const FloatT coeffs[] = 	{1.0/12.0,		-1.0/360.0,
	 1.0/1260.0,		-1.0/1620.0,		 5.0/5940.0,
	-691.0/360360.0,	 7.0/1092.0,		-3617.0/122400.0,
	 43867.0/244188.0,	-174661.0/125400.0,	 854513.0/63756.0,};
  static const int num_coeffs = sizeof(coeffs) / sizeof(FloatT);

FloatT z_power = 1/z;
  FloatT z_to_minus_two = z_power * z_power;
  FloatT small_enough = std::fabs(ans) * std::numeric_limits<FloatT>::epsilon();
  int i;

for(i = 0; i < num_coeffs; ++i) {
    FloatT next_term = coeffs[i] * z_power;
    ans += next_term;
    if(std::fabs(next_term) < small_enough)
      break;
    z_power *= z_to_minus_two;
  }

assert(i < num_coeffs); // If someone hits this, tell me and I'll add more terms,
			  // worst case is for n = cutoff = 10, which should work
			  // for DBL_EPSILON > 1.048e-21

return ans;
}

template<typename FloatT>
static FloatT IncompleteGamma(FloatT a, FloatT z)
{
  assert(z >= 0 && a >= 0); // We only use this part of the parameter space

if(a == 0)
    return 1;
  else if(z == 0)
    return 0;

if(z > a + 1)
    return 1 - IncompleteGammaComplement(a, z);

FloatT prefactor = std::exp(a * (std::log(z) + 1) - z - LogGamma(a));

return IncompleteGammaNoPrefactor(a, z) * prefactor;
}

template<typename FloatT>
static FloatT IncompleteGammaNoPrefactor(FloatT a, FloatT z)
{
  assert(z <= a + 1 && z > 0 && a > 0);

// Power series

FloatT term = 1;
  FloatT dividend = a;

FloatT ans = term;
  while(std::fabs(term / ans) > std::numeric_limits<FloatT>::epsilon()) {
    term *= z / ++dividend;
    ans += term;
  }

return ans;
}

template<typename FloatT>
static FloatT IncompleteGammaComplement(FloatT a, FloatT z)
{
  assert(z >= 0 && a >= 0); // We only use this part of the parameter space

if(a == 0)
    return 0;
  else if(z == 0)
    return 1;

if(z < a + 1)
    return 1 - IncompleteGamma(a, z);

FloatT prefactor = std::exp(a * std::log(z) - z - LogGamma(a));

return IncompleteGammaComplementNoPrefactor(a, z) * prefactor;
}

template<typename FloatT>
static FloatT IncompleteGammaComplementNoPrefactor(FloatT a, FloatT z)
{
  assert(z >= a + 1 && a > 0);

// Continued fraction

static const FloatT fudge = 1000;

FloatT b_contrib = z + 1 - a;
  FloatT a_last, b_last, a_next, b_next;
  FloatT term = 1;
  bool last_zero,
       next_zero = (std::fabs(b_contrib) <= std::numeric_limits<FloatT>::min()
                                            * fudge);

if(next_zero) {
    a_last = 0;
    b_last = 1;
    a_next = 1;
    b_next = b_contrib;
  }
  else {
    a_last = 0;
    b_last = 1 / b_contrib;
    a_next = b_last;
    b_next = 1;
  }

while(true) {
    FloatT a_tmp = a_next, b_tmp = b_next;

FloatT a_contrib = term * (a - term);
    ++term;
    b_contrib += 2;

a_next = b_contrib * a_tmp + a_contrib * a_last;
    b_next = b_contrib * b_tmp + a_contrib * b_last;

a_last = a_tmp;
    b_last = b_tmp;

last_zero = next_zero;
    next_zero = (std::fabs(b_next) <=
                 std::fabs(a_next) * (std::numeric_limits<FloatT>::min() *
                                      fudge));

if(next_zero)
      continue; // b_next is about zero

a_next /= b_next;

if(!last_zero &&
       std::fabs(a_next - a_last) < std::fabs(a_last) *
                                    std::numeric_limits<FloatT>::epsilon())
      return a_next; // Can't compare if b_last was zero

a_last /= b_next;
    b_last /= b_next;
    b_next = 1;
  }
}

template
float GaussianConditional<float>(float mean, float stddev, float val);
template
float Gaussian<float>(float mean, float stddev, float val);
template
float PoissonConditional<float>(float mean, unsigned int step);
template
float Poisson<float>(float mean, unsigned int step);
template
float LogFactorial<float>(unsigned int n);
template
float Factorial<float>(unsigned int n);
template
float LogGamma<float>(float z);
template
float Gamma<float>(float z);

template
double GaussianConditional<double>(double mean, double stddev, double val);
template
double Gaussian<double>(double mean, double stddev, double val);
template
double PoissonConditional<double>(double mean, unsigned int step);
template
double Poisson<double>(double mean, unsigned int step);
template
double LogFactorial<double>(unsigned int n);
template
double Factorial<double>(unsigned int n);
template
double LogGamma<double>(double z);
template
double Gamma<double>(double z);

} // namespace WFMath
07070100000043000081A40000000200000002000000015D8693EF00000A2C000000000000000000000000000000000000002F00000000wfmath-1569100783.d0f8a54/wfmath/probability.h// probability.h (probability and statistics functions)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-1-23

// These functions will use double instead of CoordType, for accuracy

#ifndef WFMATH_PROBABILTIY_H
#define WFMATH_PROBABILTIY_H

namespace WFMath {

/// Gives the conditional probability of the Gaussian distribution at position val
/**
 * The probability that a Gaussian random variable will fall between
 * val and val + delta, given that it is already known to be not
 * less than val, is given by this function multiplied by delta
 * (for small delta).
 **/
template<typename FloatT>
FloatT GaussianConditional(FloatT mean, FloatT stddev, FloatT val);
/// Gives the value of the Gaussian distribution at position val
template<typename FloatT>
FloatT Gaussian(FloatT mean, FloatT stddev, FloatT val);

/// Gives the conditional probability of the Poisson distribution at position step
/**
 * Returns the probability that a Poisson random variable will have value
 * step, given that it is already known not to be less than step.
 **/
template<typename FloatT>
FloatT PoissonConditional(FloatT mean, unsigned int step);
/// Gives the value of the Poisson distribution at position step
template<typename FloatT>
FloatT Poisson(FloatT mean, unsigned int step);

/// Gives the natural log of n!
template<typename FloatT>
FloatT LogFactorial(unsigned int n);
/// Gives n!
template<typename FloatT>
FloatT Factorial(unsigned int n);

/// The natural log of Euler's Gamma function
template<typename FloatT>
FloatT LogGamma(FloatT z);
/// Euler's Gamma function
template<typename FloatT>
FloatT Gamma(FloatT z);

} // namespace WFMath

#endif  // WFMATH_PROBABILITY_H
07070100000044000081A40000000200000002000000015D8693EF000010E6000000000000000000000000000000000000003600000000wfmath-1569100783.d0f8a54/wfmath/probability_test.cpp// probability_test.cpp (probability and statistics test functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-1-24

#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include "const.h"
#include "probability.h"
#include "shuffle.h"
#include <iostream>
#include <vector>

#include <cassert>

using namespace WFMath;

const double fudge = 3000;
const double use_epsilon = fudge * std::numeric_limits<double>::epsilon();

void test_probability(double mean, double std_dev, double step)
{
  assert(step > 0);
  assert(mean > 0);

double one_minus_gauss_sum = 0.5, poisson_sum = 0;
  bool gauss_done = false, poisson_done = false, past_poisson_peak = false;
//  double my_fudge = 1;

for(unsigned int num_step = 0; !gauss_done || !poisson_done; ++num_step) {
//    std::cout << "Step " << num_step << std::endl;
    if(!gauss_done) {
      double val = Gaussian(mean, std_dev, mean + step * num_step);
//      std::cout << "val = " << val << std::endl;
      double cond = GaussianConditional(mean, std_dev, mean + step * num_step);
//      std::cout << "cond = " << cond << std::endl;
      double cond_conj = GaussianConditional(mean, std_dev, mean - step * num_step);
//      std::cout << "cond_conj = " << cond_conj << std::endl;

if(val > fudge * std::numeric_limits<double>::min()) {
        if(cond_conj != 0) {
//          double first_frac = val / cond, second_frac = val / cond_conj;
//          double sum = first_frac + second_frac;
//          std::cout << first_frac << ',' << second_frac << ',' << sum - 1 << std::endl;
//          assert(Equal(sum, 1, use_epsilon));
//          while(!Equal(sum, 1, my_fudge * std::numeric_limits<double>::epsilon()))
//            my_fudge *= 1.1;
        }

if(num_step != 0) {
//          std::cout << "one_minus_gauss_sum = " << one_minus_gauss_sum << std::endl;
          assert(Equal(val, one_minus_gauss_sum * cond, fudge * step / mean));
          one_minus_gauss_sum = val / cond - val * step;
          assert(one_minus_gauss_sum > -use_epsilon); // Avoid cumulative roundoff errors
        }
      }
      else
        gauss_done = true;
    }
    if(!poisson_done) {
      double val = Poisson(mean / step, num_step);
//      std::cout << "val = " << val << std::endl;
      double cond = PoissonConditional(mean / step, num_step);
//      std::cout << "cond = " << cond << std::endl;
//      std::cout << "poisson_sum = " << poisson_sum << std::endl;

assert(val <= 1 + use_epsilon);
      assert(cond <= 1 + use_epsilon);
      assert(Equal(val + poisson_sum * cond, cond, use_epsilon));

poisson_sum += val;
      assert(poisson_sum <= 1 + use_epsilon);

if(val > fudge * std::numeric_limits<double>::min() && past_poisson_peak)
        poisson_done = true;
      else if(val > std::numeric_limits<double>::epsilon())
        past_poisson_peak = true;
    }
  }
//  std::cout << "my_fudge = " << my_fudge << std::endl;
}

// just a simple test, to make sure it's not really broken
void test_shuffle()
{
  const int nums[] = {0, 4, 1, -5, 7, 3};
  unsigned num_nums = sizeof(nums)/sizeof(nums[0]);
  std::vector<int> foo(nums, nums + num_nums);
  Shuffle(foo);
//  for(unsigned i = 0; i < foo.size(); ++i)
//    std::cerr << foo[i] << ' ';
//  std::cerr << std::endl;
}

int main()
{
  test_probability(2.0, 0.5, 0.001);

test_probability(0.3, 2.0, 0.001);

return 0;
}
07070100000045000081A40000000200000002000000015D8693EF00002248000000000000000000000000000000000000003000000000wfmath-1569100783.d0f8a54/wfmath/quaternion.cpp// quaternion.cpp (Quaternion implementation)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

// Some code here was taken from the quaternion implementation is
// eris. Some of the other algorithms are based on information
// found here <http://www.cs.ualberta.ca/~andreas/math/matrfaq_latest.html>
// and here <http://www.cs.berkeley.edu/~laura/cs184/quat/quaternion.html>.

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include "quaternion.h"
#include "error.h"
#include "rotmatrix.h"

#include <cmath>

#include <cassert>

namespace WFMath {

Quaternion::Quaternion (CoordType w_in,
                        CoordType x_in,
                        CoordType y_in,
                        CoordType z_in)
	: m_w(0), m_vec(), m_valid(true), m_age(1)
{
  CoordType norm = std::sqrt(w_in*w_in + x_in*x_in + y_in*y_in + z_in*z_in);

m_w = w_in / norm;
  m_vec[0] = x_in / norm;
  m_vec[1] = y_in / norm;
  m_vec[2] = z_in / norm;
  m_vec.setValid();
}

const Quaternion& Quaternion::IDENTITY()
{
  static Quaternion ident = Quaternion(Identity());
  return ident;
}

// The equality functions regard q and -q as equal, since they
// correspond to the same rotation matrix. We consider the form
// of the quaternion with w > 0 canonical.

bool Quaternion::isEqualTo(const Quaternion &q, float epsilon) const
{
  // Since the sum of squares is 1, the magnitude of the largest
  // element must be between 1 and 0.5, so we don't need to scale epsilon.

assert(epsilon > 0);

//If anyone is invalid they are never equal
  if (!q.m_valid || !m_valid) {
    return false;
  }

if(std::fabs(m_w - q.m_w) <= epsilon) {
    int i;
    for(i = 0; i < 3; ++i)
      if(std::fabs(m_vec[i] - q.m_vec[i]) > epsilon)
        break; // try again with swapped signs
    if(i == 3) // got through the loop
      return true;
  }

// This makes q == -q true
  if(std::fabs(m_w + q.m_w) <= epsilon) {
    for(int i = 0; i < 3; ++i)
      if(std::fabs(m_vec[i] + q.m_vec[i]) > epsilon)
        return false;
    return true;
  }

return false;
}

// order of multiplication vs sense of rotation
//
// v.rotate(q1).rotate(q2) is the same as v.rotate(q1 * q2),
// the same as with matrices

Quaternion& Quaternion::operator*= (const Quaternion& rhs)
{
  m_valid = m_valid && rhs.m_valid;
  m_age = m_age + rhs.m_age;
  checkNormalization();

CoordType old_w = m_w;
  m_w = m_w * rhs.m_w - Dot(m_vec, rhs.m_vec);
  m_vec = old_w * rhs.m_vec + rhs.m_w * m_vec - Cross(m_vec, rhs.m_vec);

return *this;
}

Quaternion& Quaternion::operator/= (const Quaternion& rhs)
{
  m_valid = m_valid && rhs.m_valid;
  m_age = m_age + rhs.m_age;
  checkNormalization();

CoordType old_w = m_w;
  m_w = m_w * rhs.m_w + Dot(m_vec, rhs.m_vec);
  m_vec = rhs.m_w * m_vec - old_w * rhs.m_vec + Cross(m_vec, rhs.m_vec);

return *this;
}

bool Quaternion::fromRotMatrix(const RotMatrix<3>& m)
{
  RotMatrix<3> m_tmp;
  bool not_flip = !m.parity();

m_valid = m.isValid();
  m_vec.setValid(m.isValid());

if(!not_flip)
    m_tmp = Prod(m, RotMatrix<3>().mirrorX());

const RotMatrix<3> &m_ref = not_flip ? m : m_tmp;

CoordType s;
  const int nxt[3] = {1, 2, 0};
  CoordType tr = m_ref.trace();

// check the diagonal
  if (tr > 0.0) {
    s = std::sqrt(tr + 1.0f);
    m_w = (s / 2.0f);
    s = (0.5f / s);

m_vec[0] = (m_ref.elem(2, 1) - m_ref.elem(1, 2)) * s;
    m_vec[1] = (m_ref.elem(0, 2) - m_ref.elem(2, 0)) * s;
    m_vec[2] = (m_ref.elem(1, 0) - m_ref.elem(0, 1)) * s;
  } else {
    // diagonal is negative
    int i = 0;

if (m_ref.elem(1, 1) > m_ref.elem(0, 0)) i = 1;
    if (m_ref.elem(2, 2) > m_ref.elem(i, i)) i = 2;

int j = nxt[i], k = nxt[j];

s = std::sqrt (1.0f + m_ref.elem(i, i) - m_ref.elem(j, j) - m_ref.elem(k, k));
    m_vec[i] = -(s * 0.5f);

assert("sqrt() returns positive" && s > 0.0);
    s = (0.5f / s);

m_w = (m_ref.elem(k, j) - m_ref.elem(j, k)) * s;
    m_vec[j] = (m_ref.elem(i, j) + m_ref.elem(j, i)) * s;
    m_vec[k] = (m_ref.elem(i, k) + m_ref.elem(k, i)) * s;
  }

m_age = m.age();

return not_flip;
}

Quaternion Quaternion::inverse() const
{
  Quaternion q(m_valid);
  q.m_w = m_w;
  q.m_vec = -m_vec;
  q.m_age = m_age; // no multiplication was done, so roundoff error does not increase
  return q;
}

Quaternion& Quaternion::rotate(const RotMatrix<3>& m)
{
  // FIXME find a more efficient way to do this
  Quaternion tmp;
  tmp.fromRotMatrix(m);
  *this *= tmp;
  return *this;
}

Quaternion& Quaternion::rotation(int axis, CoordType angle)
{
  if (axis < 0 || axis > 2) {
    m_valid = false;
    return *this;
  }

CoordType half_angle = angle / 2;

m_w = std::cos(half_angle);
  for(int i = 0; i < 3; ++i)
    // Note sin() only called once
    m_vec[i] = (i == axis) ? std::sin(half_angle) : 0;
  m_vec.setValid();

m_valid = true;
  m_age = 1;

return *this;
}

Quaternion& Quaternion::rotation(const Vector<3>& axis, CoordType angle)
{
  CoordType axis_mag = axis.mag();
  CoordType half_angle = angle / 2;

if (axis_mag < numeric_constants<CoordType>::epsilon()) {
    m_valid = false;
    return *this;
  }

m_w = std::cos(half_angle);
  m_vec = axis * (std::sin(half_angle) / axis_mag);

m_valid = axis.isValid();
  m_age = 1;

return *this;
}

Quaternion& Quaternion::rotation(const Vector<3>& axis)
{
  CoordType axis_mag = axis.mag();
  CoordType half_angle = axis_mag / 2;

if (axis_mag < numeric_constants<CoordType>::epsilon()) {
    m_valid = false;
    return *this;
  }

m_w = std::cos(half_angle);
  m_vec = axis * (std::sin(half_angle) / axis_mag);

m_valid = axis.isValid();
  m_age = 1;

return *this;
}

Quaternion& Quaternion::rotation(const Vector<3>& from, const Vector<3>& to)
{
  CoordType mag_prod = std::sqrt(from.sqrMag() * to.sqrMag());
  CoordType ctheta_plus_1 = Dot(from, to) / mag_prod + 1;

if (mag_prod < numeric_constants<CoordType>::epsilon()) {
    m_valid = false;
    return *this;
  }

// antiparallel vectors
  if(ctheta_plus_1 < numeric_constants<CoordType>::epsilon()) // same check as used in the RotMatrix function
    throw ColinearVectors<3>(from, to);

// cosine of half the angle
  m_w = std::sqrt(ctheta_plus_1 / 2.f);

// vector in direction of axis, magnitude of cross product is proportional to
  // the sin of the angle, divide to make the magnitude the sin of half the angle,
  // sin(x) = 2sin(x/2)cos(x/2), so sin(x/2) = sin(x)/(2cos(x/2))
  m_vec = Cross(from, to) / (2 * mag_prod * m_w);

m_valid = from.isValid() && to.isValid();
  m_age = 1;

return *this;
}

Quaternion& Quaternion::rotation(const Vector<3>& from, const Vector<3>& to, const Vector<3>& fallbackAxis)
{
  CoordType mag_prod = std::sqrt(from.sqrMag() * to.sqrMag());
  CoordType ctheta_plus_1 = Dot(from, to) / mag_prod + 1;

if (mag_prod < numeric_constants<CoordType>::epsilon()) {
    m_valid = false;
    return *this;
  }

// antiparallel vectors
  if(ctheta_plus_1 < numeric_constants<CoordType>::epsilon()) { // same check as used in the RotMatrix function
      rotation(fallbackAxis, numeric_constants<CoordType>::pi());
  } else {
    // cosine of half the angle
    m_w = std::sqrt(ctheta_plus_1 / 2.f);

// vector in direction of axis, magnitude of cross product is proportional to
    // the sin of the angle, divide to make the magnitude the sin of half the angle,
    // sin(x) = 2sin(x/2)cos(x/2), so sin(x/2) = sin(x)/(2cos(x/2))
    m_vec = Cross(from, to) / (2 * mag_prod * m_w);
    m_valid = from.isValid() && to.isValid();
    m_age = 1;
  }

return *this;
}

void Quaternion::normalize()
{
  // Assume that we're not too far off, and compute the norm
  // only to linear order in the difference from 1.
  // If q.sqrMag() = 1 + x, q.mag() = 1 + x/2 = (q.SqrMag() + 1)/2
  // to linear order.
  CoordType norm = (m_w * m_w + m_vec.sqrMag() + 1)/2;
  m_w /= norm;
  m_vec /= norm;
  m_age = 1;
}

}
07070100000046000081A40000000200000002000000015D8693EF00001BA2000000000000000000000000000000000000002E00000000wfmath-1569100783.d0f8a54/wfmath/quaternion.h// quaternion.h (based on the Quaternion class from eris)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_QUATERNION_H
#define WFMATH_QUATERNION_H

#include <wfmath/vector.h>
#include <wfmath/rotmatrix.h>

namespace WFMath {

/// A normalized quaternion
class Quaternion
{
 public:

/**
   * Gets a static identity quaternion.
   *
   * @return A static identity quaternion.
   */
  static const Quaternion& IDENTITY();

class Identity {};
  ///
  Quaternion(const Identity &) : m_w(1), m_vec(), m_valid(true), m_age(0) {
    m_vec.zero();
  }
  /// Construct a Quaternion
  Quaternion () : m_w(0), m_vec(), m_valid(false), m_age(0) {}
  /// Construct a Quaternion from (w, x, y, z) components
  /**
   * This normalizes the components so the sum of their squares is one.
   **/
  Quaternion (CoordType w_in, CoordType x_in, CoordType y_in, CoordType z_in);
  /// Construct a Quaternion giving a rotation around axis by angle
  Quaternion (int axis, CoordType angle) : m_w(0), m_vec(), m_valid(false),
                                           m_age(0)
    {rotation(axis, angle);}
  /// Construct a Quaternion giving a rotation around the Vector axis by angle
  Quaternion (const Vector<3>& axis, CoordType angle) : m_w(0), m_vec(),
                                                        m_valid(false),
                                                        m_age(0)
    {rotation(axis, angle);}
  /// Construct a Quaternion giving a rotation around the Vector axis
  /**
   * The angle of rotating is equal to the magnitude of the Vector
   **/
  explicit Quaternion (const Vector<3>& axis) : m_w(0), m_vec(),
                                                m_valid(false), m_age(0)
    {rotation(axis);} // angle == axis.mag()
  /// Construct a copy of a Quaternion
  Quaternion (const Quaternion& p) = default;
  /// Construct a Quaternion from an Atlas::Message::Object
  explicit Quaternion (const AtlasInType& a) : m_w(0), m_vec(),
                                               m_valid(false), m_age(0)
    {fromAtlas(a);}

~Quaternion() = default;

friend std::ostream& operator<<(std::ostream& os, const Quaternion& p);
  friend std::istream& operator>>(std::istream& is, Quaternion& p);

/// Create an Atlas object from the Quaternion
  AtlasOutType toAtlas() const;
  /// Set the Quaternion's value to that given by an Atlas object
  void fromAtlas(const AtlasInType& a);

Quaternion& operator= (const Quaternion& rhs)	= default;

// This regards q and -1*q as equal, since they give the
  // same RotMatrix<3>
  bool isEqualTo(const Quaternion &q, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const;

bool operator== (const Quaternion& rhs) const	{return isEqualTo(rhs);}
  bool operator!= (const Quaternion& rhs) const	{return !isEqualTo(rhs);}

bool isValid() const {return m_valid;}

/// Set the Quaternion to the identity rotation
  Quaternion& identity() {m_w = 1; m_vec.zero(); m_valid = true; m_age = 0; return *this;} // Set to null rotation

// Operators

///
  Quaternion& operator*= (const Quaternion& rhs);
  ///
  Quaternion& operator/= (const Quaternion& rhs);
  ///
  Quaternion operator* (const Quaternion& rhs) const {
    Quaternion out(*this);
    out *= rhs;
    return out;
  }
  ///
  Quaternion operator/ (const Quaternion& rhs) const {
    Quaternion out(*this);
    out /= rhs;
    return out;
  }

// Functions

// Returns "not_flip", similar to RotMatrix<>.toEuler()
  /// set a Quaternion's value from a RotMatrix
  /**
   * Since a Quaternion can only represent an even-parity
   * RotMatrix, this function returns false if the parity of
   * m is odd. In this case, the quaternion is set to the value
   * of m multiplied by a fixed parity-odd RotMatrix, so
   * the full RotMatrix can be recovered by passing
   * the Quaternion and the value of 'not_flip' returned
   * by this function to RotMatrix::fromQuaternion().
   **/
  bool fromRotMatrix(const RotMatrix<3>& m);

/// returns the inverse of the Quaternion
  Quaternion inverse() const;

/// Rotate quaternion using the matrix.
  Quaternion& rotate(const RotMatrix<3>&);

/// rotate the quaternion using another quaternion
  Quaternion& rotate(const Quaternion& q) {return operator*=(q);}

/// sets the Quaternion to a rotation by angle around axis
  Quaternion& rotation(int axis, CoordType angle);
  /// sets the Quaternion to a rotation by angle around the Vector axis
  Quaternion& rotation(const Vector<3>& axis, CoordType angle);
  /// sets the Quaternion to a rotation around the Vector axis
  /**
   * The rotation angle is given by the magnitude of the Vector
   **/
  Quaternion& rotation(const Vector<3>& axis); // angle == axis.mag()

/**
   * @brief Sets the Quaternion to rotate 'from' to be parallel to 'to'.
   *
   * @param from The vector to rotate from.
   * @param to The vector to rotate to.
   *
   * If the vectors are colinear a ColinearVectors exception is thrown.
   * If this is undesirable see rotation(const Vector<3>&, const Vector<3>&, const Vector<3>&)
   * instead
   */
  Quaternion& rotation(const Vector<3>& from, const Vector<3>& to);

/**
   * @brief Sets the Quaternion to rotate 'from' to be parallel to 'to'.
   *
   * @param from The vector to rotate from.
   * @param to The vector to rotate to.
   * @param fallbackAxis If the vectors are colinear, rotate around this axis instead.
   *
   */
  Quaternion& rotation(const Vector<3>& from, const Vector<3>& to, const Vector<3>& fallbackAxis);

/// returns the scalar (w) part of the Quaternion
  CoordType scalar() const		{return m_w;}
  /// returns the Vector (x, y, z) part of the quaternion
  const Vector<3>& vector() const	{return m_vec;}

/// normalize to remove accumulated round-off error
  void normalize();
  /// current round-off age
  unsigned age() const {return m_age;}

private:
  Quaternion(bool valid) : m_w(0), m_vec(), m_valid(valid), m_age(1) {}
  void checkNormalization() {if(m_age >= WFMATH_MAX_NORM_AGE && m_valid) normalize();}
  CoordType m_w;
  Vector<3> m_vec;
  bool m_valid;
  unsigned m_age;
};

} // namespace WFMath

#endif  // WFMATH_QUATERNION_H
07070100000047000081A40000000200000002000000015D8693EF00000E3A000000000000000000000000000000000000003500000000wfmath-1569100783.d0f8a54/wfmath/quaternion_test.cpp// quaternion_test.cpp (Quaternion test functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-1-20

#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include "const.h"
#include "vector.h"
#include "rotmatrix_funcs.h"
#include "quaternion.h"
#include "stream.h"
#include <vector>

#include "general_test.h"

#include <cmath>

using namespace WFMath;

void test_quaternion(const Quaternion& q)
{
  std::cout << "Testing " << q << std::endl;

test_general(q);

Quaternion q2;

q2.identity();

std::cout << "q = " << q << std::endl;
  std::cout << "q2 = " << q2 << std::endl;
  std::cout << "q  * q2= " << q * q2 << std::endl;
  std::cout << "q2 * q = " << q2 * q << std::endl;

assert(q == q * q2);
  assert(q == q2 * q);
  assert(q == q / q2);

q2 /= q;

std::cout << "q = " << q << std::endl;
  std::cout << "q2 = " << q2 << std::endl;

assert(q * q2 == Quaternion().identity());

q2 *= q;

std::cout << "q2 = " << q2 << std::endl;

assert(q2 == Quaternion().identity());

Quaternion qi((Quaternion::Identity()));

std::cout << "qi = " << qi << std::endl;

assert(qi == Quaternion().identity());

Quaternion q3(0, 5.0f/12);

RotMatrix<3> m(q);

// Check orthogonality of created matrix

for(int i = 0; i < 3; ++i) {
    for(int j = i; j < 3; ++j) {
      CoordType dot_sum = 0;
      for(int k = 0; k < 3; ++k)
        dot_sum += m.elem(i, k) * m.elem(j, k);
//      std::cout << '(' << i << ',' << j << ") dot_sum == " << dot_sum << std::endl;
      assert(Equal(dot_sum, (i == j) ? 1 : 0));
    }
  }

Quaternion q4;

assert(q4.fromRotMatrix(m));

//  std::cout << m << std::endl << q4 << std::endl;

assert(q4 == q); //FIXME 2->1 Quaternion->RotMatrix<3> mapping

Vector<3> v(1, 2, 3), v2(v);

v.rotate(q);
  v.rotate(q2 / q);

assert(v2 == v);

//  std::cout << v << std::endl << v2 << std::endl;

v.rotate(q);
  v2 = ProdInv(v2, m);

//  std::cout << v << std::endl << v2 << std::endl;

assert(v == v2);

CoordType s(q.scalar());

assert(Equal(s * s + q.vector().sqrMag(), 1));

Quaternion q_other(1, 2, 3, 4);

v.rotate(q).rotate(q_other);
  v2.rotate(q * q_other);

assert(v == v2);

//Check that an invalid quaternion isn't equal to a valid quaternion
  Quaternion invalid_1;
  Quaternion invalid_2;
  assert(invalid_1 != Quaternion::Identity());

//Two invalid points are never equal
  assert(invalid_1 != invalid_2);

const Quaternion& identity = Quaternion::IDENTITY();
  assert(identity.isValid());
  assert(identity.scalar() == 1.0f);
  assert(identity.vector() == WFMath::Vector<3>::ZERO());
}

int main()
{
  Quaternion q(Vector<3>(1, 3, -std::sqrt(0.7f)), .3f);

test_quaternion(q);

return 0;
}
07070100000048000081A40000000200000002000000015D8693EF000019F6000000000000000000000000000000000000002D00000000wfmath-1569100783.d0f8a54/wfmath/randgen.cpp// randgen.cpp (time and random number implementation)
//
//  The WorldForge Project
//  Copyright (C) 2002, 2013  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//
//  Portions of the code in this file were copied and modified from
//  http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/MT2002/CODES/mt19937ar.c
//
//  Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
//  All rights reserved.
//
//  Redistribution and use in source and binary forms, with or without
//  modification, are permitted provided that the following conditions
//  are met:
//
//    1. Redistributions of source code must retain the above copyright
//       notice, this list of conditions and the following disclaimer.
//
//    2. Redistributions in binary form must reproduce the above copyright
//       notice, this list of conditions and the following disclaimer in the
//       documentation and/or other materials provided with the distribution.
//
//    3. The names of its contributors may not be used to endorse or promote
//       products derived from this software without specific prior written
//       permission.
//
//  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
//  "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
//  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
//  A PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR
//  CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
//  EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
//  PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
//  PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
//  LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
//  NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
//  SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//

// Original Author: Ron Steinke
// Created: 2002-5-23

#include "randgen.h"
#include "timestamp.h"
#include <ctime>
#include <cstdio>
#include <istream>
#include <ostream>

#ifdef HAVE_CONFIG_H
  #include "config.h"
#endif

namespace WFMath {

const MTRand::uint32 MTRand::state_size;

MTRand MTRand::instance;

static const MTRand::uint32 period = 397;
static const MTRand::uint32 MATRIX_A = 0x9908b0df;
static const MTRand::uint32 UPPER_MASK = 0x80000000;
static const MTRand::uint32 LOWER_MASK = 0x7fffffff;

static MTRand::uint32 hash( time_t t, clock_t c )
{
  // Get a uint32 from t and c
  // Better than uint32(x) in case x is floating point in [0,1]
  // Based on code by Lawrence Kirby (fred@genesis.demon.co.uk)

typedef MTRand::uint32 uint32;

// guarantee time-based seeds will change
  static uint32 differ = 0;

uint32 h1 = 0;
  unsigned char *p = (unsigned char *) &t;
  for( size_t i = 0; i < sizeof(t); ++i )
  {
    h1 *= UCHAR_MAX + 2U;
    h1 += p[i];
  }
  uint32 h2 = 0;
  p = (unsigned char *) &c;
  for( size_t j = 0; j < sizeof(c); ++j )
  {
    h2 *= UCHAR_MAX + 2U;
    h2 += p[j];
  }
  return ( h1 + differ++ ) ^ h2;
}

void MTRand::seed()
{
  // First try getting an array from /dev/urandom
  FILE* urandom = fopen( "/dev/urandom", "rb" );
  if( urandom )
  {
    uint32 init_vector[state_size];
    register uint32 *s = init_vector;
    register int i = state_size;
    register bool success = true;
    while( success && i-- )
      success = fread( s++, sizeof(uint32), 1, urandom );
    fclose(urandom);
    if( success ) { seed( init_vector, state_size );  return; }
  }

// Was not successful, so use time() and clock() instead
  seed( hash( time(NULL), clock() ) );
}

void MTRand::seed(uint32 s)
{
  state[0] = s;
  for (index = 1; index < state_size; ++index)
  {
    state[index] = (1812433253UL * (state[index-1] ^ (state[index-1] >> 30)) + index);
  }
}

void MTRand::seed(uint32* const init_vector, const uint32 init_vector_length)
{
  seed(19650218UL);
  uint32 i = 1;
  uint32 j = 0;
  uint32 k = (state_size > init_vector_length ? state_size : init_vector_length);
  for( ; k; --k )
  {
    state[i] ^= ((state[i-1] ^ (state[i-1] >> 30)) * 1664525UL);
    state[i] += (init_vector[j] & 0xffffffffUL) + j;
    ++i;  ++j;
    if (i >= state_size) { state[0] = state[state_size-1];  i = 1; }
    if (j >= init_vector_length) j = 0;
  }
  for (k = state_size - 1; k; --k)
  {
    state[i] ^= ((state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL);
    state[i] -= i;
    ++i;
    if (i >= state_size) { state[0] = state[state_size-1];  i = 1; }
  }
  state[0] = 0x80000000UL;  // MSB is 1, assuring non-zero initial array
}

MTRand::uint32 MTRand::randInt()
{
  uint32 y;
  static unsigned long mag01[2]={0x0UL, MATRIX_A};

/* generate state_size words at one time */
  if (index >= state_size)
  {
    uint32 kk;
    for (kk=0; kk < state_size - period; kk++)
    {
      y = (state[kk]&UPPER_MASK) | (state[kk+1]&LOWER_MASK);
      state[kk] = state[kk + period] ^ (y >> 1) ^ mag01[y & 0x01];
    }
    for (; kk < state_size-1; kk++)
    {
        y = (state[kk]&UPPER_MASK) | (state[kk+1]&LOWER_MASK);
        state[kk] = state[kk+(period - state_size)] ^ (y >> 1) ^ mag01[y & 0x01];
    }
    y = (state[state_size-1]&UPPER_MASK) | (state[0]&LOWER_MASK);
    state[state_size-1] = state[period-1] ^ (y >> 1) ^ mag01[y & 0x1UL];

index = 0;
  }

y = state[index++];

/* Tempering */
  y ^= (y >> 11);
  y ^= (y << 7) & 0x9d2c5680UL;
  y ^= (y << 15) & 0xefc60000UL;
  y ^= (y >> 18);

return y;
}

std::ostream& MTRand::save(std::ostream& ostr) const
{
  for (uint32 i = 0; i < state_size; ++i)
  {
    ostr << state[i] << '\t';
  }
  return ostr << index;
}

std::istream& MTRand::load(std::istream& istr)
{
  for (uint32 i = 0; i < state_size; ++i)
    istr >> state[i];
  istr >> index;
  return istr;
}

}
07070100000049000081A40000000200000002000000015D8693EF00000699000000000000000000000000000000000000002B00000000wfmath-1569100783.d0f8a54/wfmath/randgen.h// randgen.h (random number functions)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-5-23

#ifndef WFMATH_RANDGEN_H
#define WFMATH_RANDGEN_H

#include <wfmath/MersenneTwister.h>

namespace WFMath {

// backwards compatibility functions

#ifdef WFMATH_USE_OLD_RAND

/// Seed WFMath's random number generators.
/**
 * The random number generators use a static instance of MTRand.
 **/
inline void SeedRand(unsigned int val) {MTRand::instance.seed(val);}
/// Get a random number between 0 and 1
inline double DRand() {return MTRand::instance.rand();}
/// Get a random integer ranging from 0 to (val passed) - 1
inline unsigned int IRand(unsigned int val) {return MTRand::instance.randInt(val - 1);}

#endif

} // namespace WFMath

#endif  // WFMATH_RANDGEN_H
0707010000004A000081A40000000200000002000000015D8693EF0000095F000000000000000000000000000000000000003200000000wfmath-1569100783.d0f8a54/wfmath/randgen_test.cpp// randgen.cpp (time and random number implementation)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Alistair Riddoch
// Created: 2011-2-14

#include <assert.h>
#include "randgen.h"
#include <cstdio>
#include <iostream>

#ifdef HAVE_CONFIG_H
	#include "config.h"
#endif

using WFMath::MTRand;

bool test_known_sequence()
{
    static WFMath::MTRand::uint32 expected_results[] = {
      2221777491u,
      2873750246u,
      4067173416u,
      794519497u,
      3287624630u,
      3357287912u,
      1212880927u,
      2464917741u,
      949382604u,
      1898004827u
    };
    WFMath::MTRand rng;
    bool result = true;

rng.seed(23);

for (int i = 0; i < 10; ++i)
    {
        WFMath::MTRand::uint32 rnd = rng.randInt();
        if (rnd != expected_results[i])
        {
            std::cerr << "Mismatch between MTRand and known result sequuence\n"
                      << rnd << " != " << expected_results[i] << std::endl;
            result = false;
        }
        assert(rnd == expected_results[i]);
    }
    return result;
}

bool test_generator_instances()
{
    MTRand one(23);

printf("%.16f %.16f\n", one.rand(), one.rand());
    float oneres = static_cast<float>(one.rand());

MTRand two(23);

printf("%.16f %.16f\n", two.rand<float>(), two.rand<float>());
    float twores = two.rand<float>();

printf("%.16f %.16f\n", oneres, twores);
    return oneres == twores;
}

int main()
{
    return !(test_known_sequence() && test_generator_instances());
}
0707010000004B000081A40000000200000002000000015D8693EF00000A3A000000000000000000000000000000000000002C00000000wfmath-1569100783.d0f8a54/wfmath/rotbox.cpp// rotbox.cpp (RotBox<> implementation)
//
//  The WorldForge Project
//  Copyright (C) 2011  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Alistair Riddoch
// Created: 2011-1-27

// Extensive amounts of this material come from the Vector2D
// and Vector3D classes from stage/math, written by Bryce W.
// Harrington, Kosh, and Jari Sundell (Rakshasa).

#include "rotbox_funcs.h"

#include "quaternion.h"

#include <cmath>

namespace WFMath {

template<> RotBox<3>& RotBox<3>::rotatePoint(const Quaternion& q, const Point<3>& p)
{
  m_orient = m_orient.rotate(q); m_corner0.rotate(q, p); return *this;
}

template<> RotBox<3>& RotBox<3>::rotateCorner(const Quaternion& q, size_t corner)
{
  rotatePoint(q, getCorner(corner)); return *this;
}

template<> RotBox<3>& RotBox<3>::rotateCenter(const Quaternion& q)
{
  rotatePoint(q, getCenter()); return *this;
}

template<> RotBox<3> RotBox<3>::toParentCoords(const Point<3>& origin,
                                               const Quaternion& rotation) const
{
  RotMatrix<3> orient = m_orient;
  return RotBox<3>(m_corner0.toParentCoords(origin, rotation), m_size, orient.rotate(rotation));
}

template<> RotBox<3> RotBox<3>::toLocalCoords(const Point<3>& origin,
                                              const Quaternion& rotation) const
{
  RotMatrix<3> orient = m_orient;
  return RotBox<3>(m_corner0.toLocalCoords(origin, rotation), m_size, orient.rotate(rotation.inverse()));
}

template class RotBox<2>;
template class RotBox<3>;

template Point<2> Point<2>::toLocalCoords(RotBox<2> const&) const;
template Point<3> Point<3>::toLocalCoords(RotBox<3> const&) const;
template Point<2> Point<2>::toParentCoords(RotBox<2> const&) const;
template Point<3> Point<3>::toParentCoords(RotBox<3> const&) const;

}
0707010000004C000081A40000000200000002000000015D8693EF00001F72000000000000000000000000000000000000002A00000000wfmath-1569100783.d0f8a54/wfmath/rotbox.h// rotbox.h (A box with arbitrary orientation)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_ROT_BOX_H
#define WFMATH_ROT_BOX_H

#include <wfmath/point.h>
#include <wfmath/rotmatrix.h>
#include <wfmath/intersect_decls.h>

namespace WFMath {

template<int dim>
std::ostream& operator<<(std::ostream& os, const RotBox<dim>& r);
template<int dim>
std::istream& operator>>(std::istream& is, RotBox<dim>& r);

/// A dim dimensional box, lying at an arbitrary angle
/**
 * This class implements the full shape interface, as described in
 * the fake class Shape.
 **/
template<int dim = 3>
class RotBox
{
 public:
  /// construct an uninitialized box
  RotBox() : m_corner0(), m_size(), m_orient() {}
  /// construct a box from the given parameters
  /**
   * p gives corner 0 of the box, size gives the offset from corner
   * 0 to the opposite corner (corner 2^dim - 1), orientation gives
   * the rotation of the box relative to the coordinate axes
   **/
  RotBox(const Point<dim>& p, const Vector<dim>& size,
  const RotMatrix<dim>& orientation) : m_corner0(p), m_size(size),
    m_orient(orientation) {}
  /// construct a copy of the box
  RotBox(const RotBox& b) : m_corner0(b.m_corner0), m_size(b.m_size),
    m_orient(b.m_orient) {}
  /// Construct a rotbox from an object passed by Atlas
  explicit RotBox(const AtlasInType& a);

~RotBox() = default;

/// Create an Atlas object from the box
  AtlasOutType toAtlas() const;
  /// Set the box's value to that given by an Atlas object
  void fromAtlas(const AtlasInType& a);

friend std::ostream& operator<< <dim>(std::ostream& os, const RotBox& r);
  friend std::istream& operator>> <dim>(std::istream& is, RotBox& r);

RotBox& operator=(const RotBox& s);

bool isEqualTo(const RotBox& b, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const;

bool operator==(const RotBox& b) const	{return isEqualTo(b);}
  bool operator!=(const RotBox& b) const	{return !isEqualTo(b);}

bool isValid() const {return m_corner0.isValid() && m_size.isValid()
  && m_orient.isValid();}

// Descriptive characteristics

size_t numCorners() const {return 1 << dim;}
  Point<dim> getCorner(size_t i) const;
  Point<dim> getCenter() const {return m_corner0 + Prod(m_size / 2, m_orient);}

/// returns the base corner of the box
  const Point<dim>& corner0() const		{return m_corner0;}
  /// returns the base corner of the box
  Point<dim>& corner0()				{return m_corner0;}
  /// returns the size of the box
  const Vector<dim>& size() const		{return m_size;}
  /// returns the size of the box
  Vector<dim>& size()				{return m_size;}
  /// returns the orientation of the box
  const RotMatrix<dim>& orientation() const	{return m_orient;}
  /// returns the orientation of the box
  RotMatrix<dim>& orientation()			{return m_orient;}

// Movement functions

RotBox& shift(const Vector<dim>& v)
  {m_corner0 += v; return *this;}
  RotBox& moveCornerTo(const Point<dim>& p, size_t corner)
  {return shift(p - getCorner(corner));}
  RotBox& moveCenterTo(const Point<dim>& p)
  {return shift(p - getCenter());}

RotBox& rotateCorner(const RotMatrix<dim>& m, size_t corner)
  {rotatePoint(m, getCorner(corner)); return *this;}
  RotBox& rotateCenter(const RotMatrix<dim>& m)
  {rotatePoint(m, getCenter()); return *this;}
  RotBox& rotatePoint(const RotMatrix<dim>& m, const Point<dim>& p)
  {m_orient = Prod(m_orient, m); m_corner0.rotate(m, p); return *this;}

// 3D rotation functions
  RotBox& rotateCorner(const Quaternion& q, size_t corner);
  RotBox& rotateCenter(const Quaternion& q);
  RotBox& rotatePoint(const Quaternion& q, const Point<dim>& p);

// Intersection functions

AxisBox<dim> boundingBox() const;
  Ball<dim> boundingSphere() const
  {return Ball<dim>(getCenter(), m_size.mag() / 2);}
  Ball<dim> boundingSphereSloppy() const
  {return Ball<dim>(getCenter(), m_size.sqrMag() / 2);}

RotBox toParentCoords(const Point<dim>& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
        {return RotBox(m_corner0.toParentCoords(origin, rotation), m_size,
    m_orient * rotation);}
  RotBox toParentCoords(const AxisBox<dim>& coords) const
        {return RotBox(m_corner0.toParentCoords(coords), m_size, m_orient);}
  RotBox toParentCoords(const RotBox<dim>& coords) const
        {return RotBox(m_corner0.toParentCoords(coords), m_size,
    m_orient * coords.m_orient);}

// toLocal is just like toParent, expect we reverse the order of
  // translation and rotation and use the opposite sense of the rotation
  // matrix

RotBox toLocalCoords(const Point<dim>& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
        {return RotBox(m_corner0.toLocalCoords(origin, rotation), m_size,
    rotation * m_orient);}
  RotBox toLocalCoords(const AxisBox<dim>& coords) const
        {return RotBox(m_corner0.toLocalCoords(coords), m_size, m_orient);}
  RotBox toLocalCoords(const RotBox<dim>& coords) const
        {return RotBox(m_corner0.toLocalCoords(coords), m_size,
    coords.m_orient * m_orient);}

// 3D only
  RotBox toParentCoords(const Point<dim>& origin, const Quaternion& rotation) const;
  RotBox toLocalCoords(const Point<dim>& origin, const Quaternion& rotation) const;

friend bool Intersect<dim>(const RotBox& r, const Point<dim>& p, bool proper);
  friend bool Contains<dim>(const Point<dim>& p, const RotBox& r, bool proper);

friend bool Intersect<dim>(const RotBox& r, const AxisBox<dim>& b, bool proper);
  friend bool Contains<dim>(const RotBox& r, const AxisBox<dim>& b, bool proper);
  friend bool Contains<dim>(const AxisBox<dim>& b, const RotBox& r, bool proper);

friend bool Intersect<dim>(const RotBox& r, const Ball<dim>& b, bool proper);
  friend bool Contains<dim>(const RotBox& r, const Ball<dim>& b, bool proper);
  friend bool Contains<dim>(const Ball<dim>& b, const RotBox& r, bool proper);

friend bool Intersect<dim>(const RotBox& r, const Segment<dim>& s, bool proper);
  friend bool Contains<dim>(const RotBox& r, const Segment<dim>& s, bool proper);
  friend bool Contains<dim>(const Segment<dim>& s, const RotBox& r, bool proper);

friend bool Intersect<dim>(const RotBox& r1, const RotBox& r2, bool proper);
  friend bool Contains<dim>(const RotBox& outer, const RotBox& inner, bool proper);

friend bool Intersect<dim>(const Polygon<dim>& p, const RotBox& r, bool proper);
  friend bool Contains<dim>(const Polygon<dim>& p, const RotBox& r, bool proper);
  friend bool Contains<dim>(const RotBox& r, const Polygon<dim>& p, bool proper);

private:

Point<dim> m_corner0;
  Vector<dim> m_size;
  RotMatrix<dim> m_orient;
};

template<int dim>
inline RotBox<dim>& RotBox<dim>::operator=(const RotBox<dim>& s)
{
  m_corner0 = s.m_corner0;
  m_size = s.m_size;
  m_orient = s.m_orient;

return *this;
}

template<int dim>
inline bool RotBox<dim>::isEqualTo(const RotBox<dim>& b, CoordType epsilon) const
{
  return Equal(m_corner0, b.m_corner0, epsilon)
      && Equal(m_size, b.m_size, epsilon)
      && Equal(m_orient, b.m_orient, epsilon);
}

} // namespace WFMath

#endif  // WFMATH_ROT_BOX_H
0707010000004D000081A40000000200000002000000015D8693EF00000BBC000000000000000000000000000000000000003000000000wfmath-1569100783.d0f8a54/wfmath/rotbox_funcs.h// rotbox_funcs.h (line rotbox implementation)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_ROT_BOX_FUNCS_H
#define WFMATH_ROT_BOX_FUNCS_H

#include <wfmath/rotbox.h>

#include <wfmath/vector.h>
#include <wfmath/point.h>
#include <wfmath/axisbox.h>
#include <wfmath/ball.h>

#include <cassert>

namespace WFMath {

template<int dim>
inline Point<dim> RotBox<dim>::getCorner(size_t i) const
{
  assert(i < (1 << dim));

Vector<dim> dist;

if(i == 0)
    return m_corner0;

for(int j = 0; j < dim; ++j)
    dist[j] = (i & (1 << j)) ? m_size[j] : 0;

dist.setValid(m_size.isValid());

return m_corner0 + Prod(dist, m_orient);
}

template<int dim>
AxisBox<dim> RotBox<dim>::boundingBox() const
{
  Point<dim> min = m_corner0, max = m_corner0;

//  for(int i = 0; i < dim; ++i) {
//    Vector<dim> edge;
//    edge.zero();
//    edge[i] = m_size[i];
//    edge = Prod(edge, m_orient);
//    // Edge now represents the i'th edge
//    // pointing away from m_corner0
//    for(int j = 0; j < dim; ++j) {
//      if(edge[j] < 0)
//        min[j] += edge[j];
//      else
//        max[j] += edge[j];
//    }
//  }

// The following is equivalent to the above. The above is easier to understand,
// so leave it in as a comment.

for(int i = 0; i < dim; ++i) {
    for(int j = 0; j < dim; ++j) {
      CoordType value = m_orient.elem(j, i) * m_size[j];
      if(value < 0)
        min[i] += value;
      else
        max[i] += value;
    }
  }

bool valid = isValid();

min.setValid(valid);
  max.setValid(valid);

return AxisBox<dim>(min, max, true);
}

// This is here, instead of defined in the class, to
// avoid include order problems

template<int dim>
Point<dim> Point<dim>::toParentCoords(const RotBox<dim>& coords) const
{
  return coords.corner0() + (*this - Point().setToOrigin()) * coords.orientation();
}

template<int dim>
Point<dim> Point<dim>::toLocalCoords(const RotBox<dim>& coords) const
{
  return Point().setToOrigin() + coords.orientation() * (*this - coords.corner0());
}

} // namespace WFMath

#endif  // WFMATH_ROT_BOX_FUNCS_H
0707010000004E000081A40000000200000002000000015D8693EF00002CF6000000000000000000000000000000000000002F00000000wfmath-1569100783.d0f8a54/wfmath/rotmatrix.cpp// rotmatrix.cpp (RotMatrix<> implementation)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include "rotmatrix_funcs.h"
#include "quaternion.h"

#include <limits>

namespace WFMath {

static CoordType _MatrixDeterminantImpl(int size, CoordType* m);

template<> RotMatrix<3>& RotMatrix<3>::fromQuaternion(const Quaternion& q,
						      const bool not_flip)
{
  CoordType xx, yy, zz, xy, xz, yz;
  const Vector<3> &vref = q.vector();

xx = vref[0] * vref[0];
  xy = vref[0] * vref[1];
  xz = vref[0] * vref[2];
  yy = vref[1] * vref[1];
  yz = vref[1] * vref[2];
  zz = vref[2] * vref[2];

Vector<3> wvec = vref * q.scalar();

m_elem[0][0] = 1 - 2 * (yy + zz);
  m_elem[1][1] = 1 - 2 * (xx + zz);
  m_elem[2][2] = 1 - 2 * (xx + yy);

m_elem[0][1] = 2 * (xy - wvec[2]);
  m_elem[0][2] = 2 * (xz + wvec[1]);

m_elem[1][0] = 2 * (xy + wvec[2]);
  m_elem[1][2] = 2 * (yz - wvec[0]);

m_elem[2][0] = 2 * (xz - wvec[1]);
  m_elem[2][1] = 2 * (yz + wvec[0]);

m_flip = !not_flip;
  m_age = q.age();
  if(!not_flip)
    *this = Prod(*this, RotMatrix<3>().mirror(0));

m_valid = true;
  return *this;
}

template<> RotMatrix<3>& RotMatrix<3>::rotate(const Quaternion& q)
{
  Vector<3> vec;
  vec.setValid();
  m_valid = m_valid && q.isValid();
  m_age += q.age();

// rotate both sides by q

for(auto & vec_num : m_elem) {
    for(int elem_num = 0; elem_num < 3; ++elem_num)
      vec[elem_num] = vec_num[elem_num];
    vec.rotate(q);
    for(int elem_num = 0; elem_num < 3; ++elem_num)
      vec_num[elem_num] = vec[elem_num];
  }

checkNormalization();

return *this;
}

template<>
RotMatrix<3>& RotMatrix<3>::rotation (const Vector<3>& axis,
					      CoordType theta)
{
  CoordType max = 0;
  int main_comp = -1;

for(int i = 0; i < 3; ++i) {
    CoordType val = std::fabs(axis[i]);
    if(val > max) {
      max = val;
      main_comp = i;
    }
  }

assert("Must pass a nonzero length vector as axis to avoid this" && main_comp != -1);

Vector<3> tmp, v1, v2;

int new_comp = main_comp ? main_comp - 1 : 2; // Not parallel to axis
  for(int i = 0; i < 3; ++i)
    tmp[i] = ((i == new_comp) ? 1.f : 0.f);

v1 = Cross(axis, tmp); // 3D specific part
  v2 = Cross(axis, v1);

return rotation(v1, v2, theta);
}

template<>
RotMatrix<3>& RotMatrix<3>::rotation (const Vector<3>& axis)
{
  CoordType max = 0;
  int main_comp = -1;
  CoordType angle = axis.mag();

if(angle == 0) {
    return identity();
  }

for(int i = 0; i < 3; ++i) {
    CoordType val = std::fabs(axis[i]);
    if(val > max) {
      max = val;
      main_comp = i;
    }
  }

assert("Can't happen with nonzero angle" && main_comp != -1);

Vector<3> tmp, v1, v2;

int new_comp = main_comp ? main_comp - 1 : 2; // Not parallel to axis
  for(int i = 0; i < 3; ++i)
    tmp[i] = ((i == new_comp) ? 1.f : 0.f);

v1 = Cross(axis, tmp); // 3D specific part
  v2 = Cross(axis, v1);

return rotation(v1, v2, angle);
}

bool _MatrixSetValsImpl(const int size, CoordType* vals, bool& flip,
			CoordType* buf1, CoordType* buf2, CoordType precision)
{
  precision = std::fabs(precision);

if(precision >= .9) // Can get an infinite loop for precision == 1
    return false;

// Check that vals form an orthogonal matrix, also increase their
  // precision to WFMATH_EPSILON

while(true) {
    CoordType try_prec = 0;

for(int i = 0; i < size; ++i) {
      for(int j = 0; j < size; ++j) {
        CoordType ans = 0;
        for(int k = 0; k < size; ++k) {
          ans += vals[i*size+k] * vals[j*size+k];
        }

if(i == j) // Subtract identity matrix
          --ans;
        ans = std::fabs(ans);
        if(ans >= try_prec)
          try_prec = ans;
      }
    }

if(try_prec > precision)
      return false;

if(try_prec <= numeric_constants<CoordType>::epsilon())
      break;

// Precision needs improvement, use linear approximation scheme.

// This scheme takes the original matrix (call it A)
    // and subtracts another matrix (delta), where
    //
    // delta = (A - (A^T)^-1) / 2
    //
    // This is correct, up to errors of order delta^2,
    // if you assume you can choose a delta such that
    // A^T * delta is symmetric (delta is underdetermined
    // by the linear approximation scheme)

// This procedure will not increase the precision of
    // the parameters which determine the matrix (i.e. the
    // Euler angles), but it will increase the precision
    // to which the matrix satisfies the condition
    // A^T * A == (identity matrix).

// The symmetry condition on A^T * delta represents an
    // arbitrary condition which will determine the higher
    // precision components of the Euler angles. This
    // makes the problem of increasing the precision of
    // the matrix well determined, and solvable by this
    // perturbative method.

for(int i = 0; i < size; ++i) {
      for(int j = 0; j < size; ++j) {
        buf1[i*size+j] = vals[j*size+i];
        buf2[i*size+j] = ((i == j) ? 1.f : 0.f);
      }
    }

bool ans = _MatrixInverseImpl(size, buf1, buf2);

if(!ans) { // Degenerate matrix, something badly wrong
		return false;
	}

for(int i = 0; i < size; ++i) {
      for(int j = 0; j < size; ++j) {
        CoordType& elem = vals[i*size+j];
        elem += buf2[i*size+j];
        elem /= 2;
      }
    }

// The above scheme should approx. square the precision.
    // That is, try_prec -> try_prec * try_prec * (fudge factor)
    // in the next iteration.
  }

// The determinant is either 1 or -1, depending on the parity.
  // Use that to calculate flip.

for(int i = 0; i < size; ++i)
    for(int j = 0; j < size; ++j)
      buf1[i*size+j] = vals[i*size+j];

flip = _MatrixDeterminantImpl(size, buf1) < 0;

return true;
}

static CoordType _MatrixDeterminantImpl(const int size, CoordType* m)
{
  // First, construct an upper triangular matrix with the
  // same determinant as the original matrix. Then just
  // multiply the diagonal terms to get the determinant.

for(int i = 0; i < size - 1; ++i) {
    CoordType minval = 0;
    for(int j = 0; j < size; ++j)
      minval += m[j*size+i] * m[j*size+i];
    minval /= std::numeric_limits<CoordType>::max();
    if(minval < std::numeric_limits<CoordType>::min())
      minval = std::numeric_limits<CoordType>::min();
    if(m[i*size+i] * m[i*size+i] < minval) { // Find a row with nonzero element
      int j;
      for(j = i + 1; j < size; ++j)
        if(m[j*size+i] * m[j*size+i] >= minval)
          break;
      if(j == size) // No nonzero element found, degenerate matrix, det == 0
        return 0;
      m[i*size+i] = m[j*size+i];
      for(int k = i + 1; k < size; ++k) // For k < i, m[j*size+k] == 0
        m[i*size+k] += m[j*size+k];
    }
    for(int j = i + 1; j < size; ++j) {
      CoordType factor = m[j*size+i] / m[i*size+i];
      // We know factor isn't bigger than about sqrt(WFMATH_MAX), due to
      // the comparison with minval done above.
      m[j*size+i] = 0;
      if(factor != 0) {
        for(int k = i + 1; k < size; ++k) // For k < i, m[k*size+j] == 0
	  m[j*size+k] -= m[i*size+k] * factor;
      }
    }
  }

CoordType out = 1;

for(int i = 0; i < size; ++i)
    out *= m[i*size+i];

return out;
}

bool _MatrixInverseImpl(const int size, CoordType* in, CoordType* out)
{
  // Invert using row operations. First, make m upper triangular,
  // with 1's on the diagonal

for(int i = 0; i < size; ++i) {

// Make sure in[i*size+i] is nonzero
    CoordType minval = 0;
    for(int j = 0; j < size; ++j)
      minval += in[j*size+i] * in[j*size+i];
    minval /= std::numeric_limits<CoordType>::max();
    if(minval < std::numeric_limits<CoordType>::min())
      minval = std::numeric_limits<CoordType>::min();
    if(in[i*size+i] * in[i*size+i] < minval) { // Find a nonzero element
      int j;
      for(j = i + 1;  j < size; ++j)
        if(in[j*size+i] * in[j*size+i] >= minval)
          break;
      if(j == size) // degenerate matrix
        return false;
      for(int k = 0; k < size; ++k) {
        out[i*size+k] += out[j*size+k];
        in[i*size+k] += in[j*size+k];
      }
    }
    // We now know in[i*size+i] / in[j*size+i] >= sqrt(WFMATH_MIN) for any j

// Normalize the row, so in[i*size+i] == 1
    CoordType tmp = in[i*size+i];
    in[i*size+i] = 1;
    for(int j = 0; j < size; ++j) {
      out[i*size+j] /= tmp;
      if(j > i) // in[i*size+j] == 0 for j < i
        in[i*size+j] /= tmp;
    }

// Do row subtraction to make in[j*size+i] zero for j > i
    for(int j = i + 1; j < size; ++j) {
      CoordType tmp2 = in[j*size+i];
      in[j*size+i] = 0;
      if(tmp2 != 0) {
        for(int k = 0; k < size; ++k) {
          out[j*size+k] -= out[i*size+k] * tmp2;
          in[j*size+k] -= in[i*size+k] * tmp2;
        }
      }
    }
  }

// Now perform row operations on "out" which would make "m"
  // into the identity matrix

for(int i = size - 1; i >= 1; --i) {
    for(int j = i - 1; j >= 0; --j) {
      CoordType tmp = in[j*size+i];
      if(tmp != 0)
        for(int k = 0; k < size; ++k)
          out[j*size+k] -= out[i*size+k] * tmp;
          // Don't bother modifying in[j*size+k], we never use it again.
    }
  }

return true;
}

template <>
RotMatrix<3>::RotMatrix(const Quaternion& q,
                        const bool not_flip) : m_flip(false), m_valid(false),
                                               m_age(0)
{
  fromQuaternion(q, not_flip);
}

template class RotMatrix<2>;
template class RotMatrix<3>;

template RotMatrix<2> operator*<2>(RotMatrix<2> const&, RotMatrix<2> const&);
template RotMatrix<3> operator*<3>(RotMatrix<3> const&, RotMatrix<3> const&);

template RotMatrix<2> ProdInv<2>(RotMatrix<2> const&, RotMatrix<2> const&);
template RotMatrix<3> ProdInv<3>(RotMatrix<3> const&, RotMatrix<3> const&);

template Vector<2> operator*<2>(Vector<2> const&, RotMatrix<2> const&);
template Vector<3> operator*<3>(Vector<3> const&, RotMatrix<3> const&);

template Vector<2> operator*<2>(RotMatrix<2> const&, Vector<2> const&);
template Vector<3> operator*<3>(RotMatrix<3> const&, Vector<3> const&);

template Vector<2> ProdInv<2>(Vector<2> const&, RotMatrix<2> const&);
template Vector<3> ProdInv<3>(Vector<3> const&, RotMatrix<3> const&);

template Vector<3> Prod<3>(Vector<3> const&, RotMatrix<3> const&);
template Vector<2> Prod<2>(Vector<2> const&, RotMatrix<2> const&);

template RotMatrix<3> Prod<3>(RotMatrix<3> const&, RotMatrix<3> const&);
template RotMatrix<2> Prod<2>(RotMatrix<2> const&, RotMatrix<2> const&);

}
0707010000004F000081A40000000200000002000000015D8693EF00002886000000000000000000000000000000000000002D00000000wfmath-1569100783.d0f8a54/wfmath/rotmatrix.h// rotmatrix.h (RotMatrix<> class definition)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#ifndef WFMATH_ROTMATRIX_H
#define WFMATH_ROTMATRIX_H

#include <wfmath/const.h>

#include <iosfwd>

namespace WFMath {

/// returns m1 * m2
template<int dim> // m1 * m2
RotMatrix<dim> Prod(const RotMatrix<dim>& m1, const RotMatrix<dim>& m2);
/// returns m1 * m2^-1
template<int dim> // m1 * m2^-1
RotMatrix<dim> ProdInv(const RotMatrix<dim>& m1, const RotMatrix<dim>& m2);
/// returns m1^-1 * m2
template<int dim> // m1^-1 * m2
RotMatrix<dim> InvProd(const RotMatrix<dim>& m1, const RotMatrix<dim>& m2);
/// returns m1^-1 * m2^-1
template<int dim> // m1^-1 * m2^-1
RotMatrix<dim> InvProdInv(const RotMatrix<dim>& m1, const RotMatrix<dim>& m2);

template<int dim> // m * v
Vector<dim> Prod(const RotMatrix<dim>& m, const Vector<dim>& v);
template<int dim> // m^-1 * v
Vector<dim> InvProd(const RotMatrix<dim>& m, const Vector<dim>& v);
template<int dim> // v * m
Vector<dim> Prod(const Vector<dim>& v, const RotMatrix<dim>& m);
template<int dim> // v * m^-1
Vector<dim> ProdInv(const Vector<dim>& v, const RotMatrix<dim>& m);

/// returns m1 * m2
template<int dim>
RotMatrix<dim> operator*(const RotMatrix<dim>& m1, const RotMatrix<dim>& m2);
template<int dim>
Vector<dim> operator*(const RotMatrix<dim>& m, const Vector<dim>& v);
template<int dim>
Vector<dim> operator*(const Vector<dim>& v, const RotMatrix<dim>& m);

template<int dim>
std::ostream& operator<<(std::ostream& os, const RotMatrix<dim>& m);
template<int dim>
std::istream& operator>>(std::istream& is, RotMatrix<dim>& m);

/// A dim dimensional rotation matrix. Technically, a member of the group O(dim).
/**
 * Elements of this class represent rotation matrices. The NxN dimensional
 * rotation matrices form a group called O(N), the orthogonal
 * matrices. They satisfy the following condition:
 *
 *  They are orthogonal. That is, their transpose is equal to their inverse.
 *  Hence, this class does not implement a transpose() method, only an
 *  inverse().
 *
 * A general N dimensional matrix of this type has N(N-1)/2 degrees of freedom.
 * This gives one rotation angle in 2D, the three Euler angles in 3D, etc.
 *
 * This class implements the 'generic' subset of the interface in
 * the fake class Shape.
 **/
template<int dim = 3>
class RotMatrix {
 public:
  ///
  RotMatrix() : m_flip(false), m_valid(false), m_age(0) {}
  ///
  RotMatrix(const RotMatrix& m);

friend std::ostream& operator<< <dim>(std::ostream& os, const RotMatrix& m);
  friend std::istream& operator>> <dim>(std::istream& is, RotMatrix& m);

RotMatrix& operator=(const RotMatrix& m);
  // No operator=(CoordType d[dim][dim]), since it can fail.
  // Use setVals() instead.

bool isEqualTo(const RotMatrix& m, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const;

bool operator==(const RotMatrix& m) const {return isEqualTo(m);}
  bool operator!=(const RotMatrix& m) const {return !isEqualTo(m);}

bool isValid() const {return m_valid;}

/// set the matrix to the identity matrix
  RotMatrix& identity();

/// get the (i, j) element of the matrix
  CoordType elem(const int i, const int j) const {return m_elem[i][j];}

/// Set the values of the elements of the matrix
  /**
   * Can't set one element at a time and keep it an O(N) matrix,
   * but can try to set all values at once, and see if they match.
   * This fails if the passed matrix is not orthogonal within the
   * passed precision, and orthogonalizes the matrix to within
   * precision WFMATH_EPSILON.
   **/
  bool setVals(const CoordType vals[dim][dim], CoordType precision = numeric_constants<CoordType>::epsilon());
  /// Set the values of the elements of the matrix
  /**
   * Can't set one element at a time and keep it an O(N) matrix,
   * but can try to set all values at once, and see if they match.
   * This fails if the passed matrix is not orthogonal within the
   * passed precision, and orthogonalizes the matrix to within
   * precision WFMATH_EPSILON.
   **/
  bool setVals(const CoordType vals[dim*dim], CoordType precision = numeric_constants<CoordType>::epsilon());

/// Get a copy of the i'th row as a Vector
  Vector<dim> row(int i) const;
  /// Get a copy of the i'th column as a Vector
  Vector<dim> column(int i) const;

/// Get the trace of the matrix
  CoordType trace() const;
  /// Get the determinant of the matrix
  /**
   * Since the matrix is orthogonal, the determinant is always either 1 or -1.
   **/
  CoordType determinant() const {return (m_flip ? -1.f : 1.f);}
  /// Get the inverse of the matrix
  /**
   * Since the matrix is orthogonal, the inverse is equal to the transpose.
   **/
  RotMatrix inverse() const;
  /// Get the parity of the matrix
  /**
   * Returns true for odd parity, false for even.
   **/
  bool parity() const {return m_flip;}

// documented outside the class

friend RotMatrix Prod<dim>	   (const RotMatrix& m1, const RotMatrix& m2);
  friend RotMatrix ProdInv<dim>	   (const RotMatrix& m1, const RotMatrix& m2);
  friend RotMatrix InvProd<dim>	   (const RotMatrix& m1, const RotMatrix& m2);
  friend RotMatrix InvProdInv<dim> (const RotMatrix& m1, const RotMatrix& m2);
  friend Vector<dim> Prod<dim>	   (const RotMatrix& m, const Vector<dim>& v);
  friend Vector<dim> InvProd<dim>  (const RotMatrix& m, const Vector<dim>& v);

// Set the value to a given rotation

/// set the matrix to a rotation by the angle theta in the (i, j) plane
  RotMatrix& rotation	(int i, int j, CoordType theta);
  /// set the matrix to a rotation by the angle theta in the v1, v2 plane
  /**
   * Throws CollinearVectors if v1 and v2 are parallel
   **/
  RotMatrix& rotation	(const Vector<dim>& v1, const Vector<dim>& v2,
			 CoordType theta);
  /// set the matrix to a rotation which will move "from" to lie parallel to "to"
  /**
   * Throws CollinearVectors if v1 and v2 are antiparallel (parallel but
   * pointing in opposite directions). If v1 and v2 point in the
   * same direction, the matrix is set to the identity.
   **/
  RotMatrix& rotation	(const Vector<dim>& from, const Vector<dim>& to);

// Set the value to mirror image about a certain axis

/// set the matrix to a mirror perpendicular to the i'th axis
  RotMatrix& mirror(int i);
  /// set the matrix to a mirror perpendicular to the Vector v
  RotMatrix& mirror(const Vector<dim>& v);
  /// set the matrix to mirror all axes
  /**
   * This is a good parity operator if dim is odd.
   **/
  RotMatrix& mirror();

/// rotate the matrix using another matrix
  RotMatrix& rotate(const RotMatrix& m) {return *this = Prod(*this, m);}

/// normalize to remove accumulated round-off error
  void normalize();
  /// current round-off age
  unsigned age() const {return m_age;}

// 2D/3D stuff

/// 3D only: Construct a RotMatrix from a Quaternion
  /**
   * since Quaternions can only specify parity-even
   * rotations, you can pass the return value of
   * Quaternion::fromRotMatrix() as not_flip to
   * recover the full RotMatrix
   **/
  RotMatrix(const Quaternion& q, bool not_flip = true);

/// 2D only: Construct a RotMatrix from an angle theta
  RotMatrix& rotation(CoordType theta)
	{return rotation(0, 1, theta);}

/// 3D only: set a RotMatrix to a rotation about the x axis by angle theta
  RotMatrix& rotationX(CoordType theta) {return rotation(1, 2, theta);}
  /// 3D only: set a RotMatrix to a rotation about the y axis by angle theta
  RotMatrix& rotationY(CoordType theta) {return rotation(2, 0, theta);}
  /// 3D only: set a RotMatrix to a rotation about the z axis by angle theta
  RotMatrix& rotationZ(CoordType theta) {return rotation(0, 1, theta);}
  /// 3D only: set a RotMatrix to a rotation about the axis given by the Vector
  RotMatrix& rotation(const Vector<dim>& axis, CoordType theta);
  /// 3D only: set a RotMatrix to a rotation about the axis given by the Vector
  /**
   * the rotation angle is taken from the Vector's magnitude
   **/
  RotMatrix& rotation(const Vector<dim>& axis); // angle taken from magnitude of axis

/// 3D only: set a RotMatrix from a Quaternion
  /**
   * since Quaternions can only specify parity-even
   * rotations, you can pass the return value of
   * Quaternion::fromRotMatrix() as not_flip to
   * recover the full RotMatrix
   **/
  RotMatrix& fromQuaternion(const Quaternion& q, bool not_flip = true);

/// rotate the matrix using the quaternion
  RotMatrix& rotate(const Quaternion&);

/// set a RotMatrix to a mirror perpendicular to the x axis
  RotMatrix& mirrorX()	{return mirror(0);}
  /// set a RotMatrix to a mirror perpendicular to the y axis
  RotMatrix& mirrorY()	{return mirror(1);}
  /// set a RotMatrix to a mirror perpendicular to the z axis
  RotMatrix& mirrorZ();

private:
  CoordType m_elem[dim][dim];
  bool m_flip; // True if the matrix is parity odd
  bool m_valid;
  unsigned m_age;

// Backend to setVals() above, also used in fromStream()
  bool _setVals(CoordType *vals, CoordType precision = numeric_constants<CoordType>::epsilon());
  void checkNormalization() {if(m_age >= WFMATH_MAX_NORM_AGE && m_valid) normalize();}
};

template<>
inline RotMatrix<3>& RotMatrix<3>::mirrorZ()
{
  return mirror(2);
}

template<int dim>
inline RotMatrix<dim>& RotMatrix<dim>::mirror(const int i)
{
  identity();
  m_elem[i][i] = -1;
  m_flip = true;
  // m_valid and m_age already set correctly

return *this;
}

} // namespace WFMath

#endif // WFMATH_ROTMATRIX_H
07070100000050000081A40000000200000002000000015D8693EF00003A44000000000000000000000000000000000000003300000000wfmath-1569100783.d0f8a54/wfmath/rotmatrix_funcs.h// rotmatrix_funcs.h (RotMatrix<> template functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#ifndef WFMATH_ROTMATRIX_FUNCS_H
#define WFMATH_ROTMATRIX_FUNCS_H

#include <wfmath/rotmatrix.h>

#include <wfmath/vector.h>
#include <wfmath/error.h>
#include <wfmath/const.h>

#include <cmath>

#include <cassert>

namespace WFMath {

template<int dim>
inline RotMatrix<dim>::RotMatrix(const RotMatrix<dim>& m)
	: m_flip(m.m_flip), m_valid(m.m_valid), m_age(1)
{
  for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      m_elem[i][j] = m.m_elem[i][j];
}

template<int dim>
inline RotMatrix<dim>& RotMatrix<dim>::operator=(const RotMatrix<dim>& m)
{
  for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      m_elem[i][j] = m.m_elem[i][j];

m_flip = m.m_flip;
  m_valid = m.m_valid;
  m_age = m.m_age;

return *this;
}

template<int dim>
inline bool RotMatrix<dim>::isEqualTo(const RotMatrix<dim>& m, CoordType epsilon) const
{
  // Since the sum of the squares of the elements in any row or column add
  // up to 1, all the elements lie between -1 and 1, and each row has
  // at least one element whose magnitude is at least 1/sqrt(dim).
  // Therefore, we don't need to scale epsilon, as we did for
  // Vector<> and Point<>.

assert(epsilon > 0);

//If anyone is invalid they are never equal
  if (!m.m_valid || !m_valid) {
    return false;
  }

for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      if(std::fabs(m_elem[i][j] - m.m_elem[i][j]) > epsilon)
        return false;

// Don't need to test m_flip, it's determined by the values of m_elem.

assert("Generated values, must be equal if all components are equal" &&
         m_flip == m.m_flip);

return true;
}

template<int dim> // m1 * m2
inline RotMatrix<dim> Prod(const RotMatrix<dim>& m1, const RotMatrix<dim>& m2)
{
  RotMatrix<dim> out;

for(int i = 0; i < dim; ++i) {
    for(int j = 0; j < dim; ++j) {
      out.m_elem[i][j] = 0;
      for(int k = 0; k < dim; ++k) {
        out.m_elem[i][j] += m1.m_elem[i][k] * m2.m_elem[k][j];
      }
    }
  }

out.m_flip = (m1.m_flip != m2.m_flip); // XOR
  out.m_valid = m1.m_valid && m2.m_valid;
  out.m_age = m1.m_age + m2.m_age;
  out.checkNormalization();

return out;
}

template<int dim> // m1 * m2^-1
inline RotMatrix<dim> ProdInv(const RotMatrix<dim>& m1, const RotMatrix<dim>& m2)
{
  RotMatrix<dim> out;

for(int i = 0; i < dim; ++i) {
    for(int j = 0; j < dim; ++j) {
      out.m_elem[i][j] = 0;
      for(int k = 0; k < dim; ++k) {
        out.m_elem[i][j] += m1.m_elem[i][k] * m2.m_elem[j][k];
      }
    }
  }

out.m_flip = (m1.m_flip != m2.m_flip); // XOR
  out.m_valid = m1.m_valid && m2.m_valid;
  out.m_age = m1.m_age + m2.m_age;
  out.checkNormalization();

return out;
}

template<int dim> // m1^-1 * m2
inline RotMatrix<dim> InvProd(const RotMatrix<dim>& m1, const RotMatrix<dim>& m2)
{
  RotMatrix<dim> out;

for(int i = 0; i < dim; ++i) {
    for(int j = 0; j < dim; ++j) {
      out.m_elem[i][j] = 0;
      for(int k = 0; k < dim; ++k) {
        out.m_elem[i][j] += m1.m_elem[k][i] * m2.m_elem[k][j];
      }
    }
  }

out.m_flip = (m1.m_flip != m2.m_flip); // XOR
  out.m_valid = m1.m_valid && m2.m_valid;
  out.m_age = m1.m_age + m2.m_age;
  out.checkNormalization();

return out;
}

template<int dim> // m1^-1 * m2^-1
inline RotMatrix<dim> InvProdInv(const RotMatrix<dim>& m1, const RotMatrix<dim>& m2)
{
  RotMatrix<dim> out;

for(int i = 0; i < dim; ++i) {
    for(int j = 0; j < dim; ++j) {
      out.m_elem[i][j] = 0;
      for(int k = 0; k < dim; ++k) {
        out.m_elem[i][j] += m1.m_elem[k][i] * m2.m_elem[j][k];
      }
    }
  }

out.m_flip = (m1.m_flip != m2.m_flip); // XOR
  out.m_valid = m1.m_valid && m2.m_valid;
  out.m_age = m1.m_age + m2.m_age;
  out.checkNormalization();

return out;
}

template<int dim> // m * v
inline Vector<dim> Prod(const RotMatrix<dim>& m, const Vector<dim>& v)
{
  Vector<dim> out;

for(int i = 0; i < dim; ++i) {
    out.m_elem[i] = 0;
    for(int j = 0; j < dim; ++j) {
      out.m_elem[i] += m.m_elem[i][j] * v.m_elem[j];
    }
  }

out.m_valid = m.m_valid && v.m_valid;

return out;
}

template<int dim> // m^-1 * v
inline Vector<dim> InvProd(const RotMatrix<dim>& m, const Vector<dim>& v)
{
  Vector<dim> out;

for(int i = 0; i < dim; ++i) {
    out.m_elem[i] = 0;
    for(int j = 0; j < dim; ++j) {
      out.m_elem[i] += m.m_elem[j][i] * v.m_elem[j];
    }
  }

out.m_valid = m.m_valid && v.m_valid;

return out;
}

template<int dim> // v * m
inline Vector<dim> Prod(const Vector<dim>& v, const RotMatrix<dim>& m)
{
  return InvProd(m, v); // Since transpose() and inverse() are the same
}

template<int dim> // v * m^-1
inline Vector<dim> ProdInv(const Vector<dim>& v, const RotMatrix<dim>& m)
{
  return Prod(m, v); // Since transpose() and inverse() are the same
}

template<int dim>
inline RotMatrix<dim> operator*(const RotMatrix<dim>& m1, const RotMatrix<dim>& m2)
{
  return Prod(m1, m2);
}

template<int dim>
inline Vector<dim> operator*(const RotMatrix<dim>& m, const Vector<dim>& v)
{
  return Prod(m, v);
}

template<int dim>
inline Vector<dim> operator*(const Vector<dim>& v, const RotMatrix<dim>& m)
{
  return InvProd(m, v); // Since transpose() and inverse() are the same
}

template<int dim>
inline bool RotMatrix<dim>::setVals(const CoordType vals[dim][dim], CoordType precision)
{
  // Scratch space for the backend
  CoordType scratch_vals[dim*dim];

for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      scratch_vals[i*dim+j] = vals[i][j];

return _setVals(scratch_vals, precision);
}

template<int dim>
inline bool RotMatrix<dim>::setVals(const CoordType vals[dim*dim], CoordType precision)
{
  // Scratch space for the backend
  CoordType scratch_vals[dim*dim];

for(int i = 0; i < dim*dim; ++i)
      scratch_vals[i] = vals[i];

return _setVals(scratch_vals, precision);
}

bool _MatrixSetValsImpl(int size, CoordType* vals, bool& flip,
			CoordType* buf1, CoordType* buf2, CoordType precision);

template<int dim>
inline bool RotMatrix<dim>::_setVals(CoordType *vals, CoordType precision)
{
  // Cheaper to allocate space on the stack here than with
  // new in _MatrixSetValsImpl()
  CoordType buf1[dim*dim], buf2[dim*dim];
  bool flip;

if(!_MatrixSetValsImpl(dim, vals, flip, buf1, buf2, precision))
    return false;

// Do the assignment

for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      m_elem[i][j] = vals[i*dim+j];

m_flip = flip;
  m_valid = true;
  m_age = 1;

return true;
}

template<int dim>
inline Vector<dim> RotMatrix<dim>::row(const int i) const
{
  Vector<dim> out;

for(int j = 0; j < dim; ++j)
    out[j] = m_elem[i][j];

out.setValid(m_valid);

return out;
}

template<int dim>
inline Vector<dim> RotMatrix<dim>::column(const int i) const
{
  Vector<dim> out;

for(int j = 0; j < dim; ++j)
    out[j] = m_elem[j][i];

out.setValid(m_valid);

return out;
}

template<int dim>
inline RotMatrix<dim> RotMatrix<dim>::inverse() const
{
  RotMatrix<dim> m;

for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      m.m_elem[j][i] = m_elem[i][j];

m.m_flip = m_flip;
  m.m_valid = m_valid;
  m.m_age = m_age + 1;

return m;
}

template<int dim>
inline RotMatrix<dim>& RotMatrix<dim>::identity()
{
  for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      m_elem[i][j] = ((i == j) ? 1.0f : 0.0f);

m_flip = false;
  m_valid = true;
  m_age = 0; // 1 and 0 are exact, no roundoff error

return *this;
}

template<int dim>
inline CoordType RotMatrix<dim>::trace() const
{
  CoordType out = 0;

for(int i = 0; i < dim; ++i)
    out += m_elem[i][i];

return out;
}

template<int dim>
RotMatrix<dim>& RotMatrix<dim>::rotation (const int i, const int j,
					  CoordType theta)
{
  assert(i >= 0 && i < dim && j >= 0 && j < dim && i != j);

CoordType ctheta = std::cos(theta), stheta = std::sin(theta);

for(int k = 0; k < dim; ++k) {
    for(int l = 0; l < dim; ++l) {
      if(k == l) {
        if(k == i || k == j)
          m_elem[k][l] = ctheta;
        else
          m_elem[k][l] = 1;
      }
      else {
        if(k == i && l == j)
          m_elem[k][l] = stheta;
        else if(k == j && l == i)
          m_elem[k][l] = -stheta;
        else
          m_elem[k][l] = 0;
      }
    }
  }

m_flip = false;
  m_valid = true;
  m_age = 1;

return *this;
}

template<int dim>
RotMatrix<dim>& RotMatrix<dim>::rotation (const Vector<dim>& v1,
					  const Vector<dim>& v2,
					  CoordType theta)
{
  CoordType v1_sqr_mag = v1.sqrMag();

assert("need nonzero length vector" && v1_sqr_mag > 0);

// Get an in-plane vector which is perpendicular to v1

Vector<dim> vperp = v2 - v1 * Dot(v1, v2) / v1_sqr_mag;
  CoordType vperp_sqr_mag = vperp.sqrMag();

if((vperp_sqr_mag / v1_sqr_mag) < (dim * numeric_constants<CoordType>::epsilon() * numeric_constants<CoordType>::epsilon())) {
    assert("need nonzero length vector" && v2.sqrMag() > 0);
    // The original vectors were parallel
    throw ColinearVectors<dim>(v1, v2);
  }

// If we were rotating a vector vin, the answer would be
  // vin + Dot(v1, vin) * (v1 (cos(theta) - 1)/ v1_sqr_mag
  // + vperp * sin(theta) / sqrt(v1_sqr_mag * vperp_sqr_mag))
  // + Dot(vperp, vin) * (a similar term). From this, we find
  // the matrix components.

CoordType mag_prod = std::sqrt(v1_sqr_mag * vperp_sqr_mag);
  CoordType ctheta = std::cos(theta),
            stheta = std::sin(theta);

identity(); // Initialize to identity matrix

for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      m_elem[i][j] += ((ctheta - 1) * (v1[i] * v1[j] / v1_sqr_mag
		      + vperp[i] * vperp[j] / vperp_sqr_mag)
		      - stheta * (vperp[i] * v1[j] - v1[i] * vperp[j]) / mag_prod);

m_flip = false;
  m_valid = true;
  m_age = 1;

return *this;
}

template<int dim>
RotMatrix<dim>& RotMatrix<dim>::rotation(const Vector<dim>& from,
					 const Vector<dim>& to)
{
  // This is sort of similar to the above, with the rotation angle determined
  // by the angle between the vectors

CoordType fromSqrMag = from.sqrMag();
  assert("need nonzero length vector" && fromSqrMag > 0);
  CoordType toSqrMag = to.sqrMag();
  assert("need nonzero length vector" && toSqrMag > 0);
  CoordType dot = Dot(from, to);
  CoordType sqrmagprod = fromSqrMag * toSqrMag;
  CoordType magprod = std::sqrt(sqrmagprod);
  CoordType ctheta_plus_1 = dot / magprod + 1;

if(ctheta_plus_1 < numeric_constants<CoordType>::epsilon()) {
    // 180 degree rotation, rotation plane indeterminate
    if(dim == 2) { // special case, only one rotation plane possible
      m_elem[0][0] = m_elem[1][1] = ctheta_plus_1 - 1;
      CoordType sin_theta = std::sqrt(2 * ctheta_plus_1); // to leading order
      bool direction = ((to[0] * from[1] - to[1] * from[0]) >= 0);
      m_elem[0][1] = direction ?  sin_theta : -sin_theta;
      m_elem[1][0] = -m_elem[0][1];
      m_flip = false;
      m_valid = true;
      m_age = 1;
      return *this;
    }
    throw ColinearVectors<dim>(from, to);
  }

for(int i = 0; i < dim; ++i) {
    for(int j = i; j < dim; ++j) {
      CoordType projfrom = from[i] * from[j] / fromSqrMag;
      CoordType projto = to[i] * to[j] / toSqrMag;

CoordType ijprod = from[i] * to[j], jiprod = to[i] * from[j];

CoordType termthree = (ijprod + jiprod) * dot / sqrmagprod;

CoordType combined = (projfrom + projto - termthree) / ctheta_plus_1;

if(i == j) {
        m_elem[i][i] = 1 - combined;
      }
      else {
        CoordType diffterm = (jiprod - ijprod) / magprod;

m_elem[i][j] = -diffterm - combined;
        m_elem[j][i] = diffterm - combined;
      }
    }
  }

m_flip = false;
  m_valid = true;
  m_age = 1;

return *this;
}

template<> RotMatrix<3>& RotMatrix<3>::rotation (const Vector<3>& axis,
						 CoordType theta);
template<> RotMatrix<3>& RotMatrix<3>::rotation (const Vector<3>& axis);
template<> RotMatrix<3>& RotMatrix<3>::fromQuaternion(const Quaternion& q,
						      const bool not_flip);

template<> RotMatrix<3>& RotMatrix<3>::rotate(const Quaternion&);

template<int dim>
inline RotMatrix<dim>& RotMatrix<dim>::mirror	(const Vector<dim>& v)
{
  // Get a flip by subtracting twice the projection operator in the
  // direction of the vector. A projection operator is idempotent (P*P == P),
  // and symmetric, so I - 2P is an orthogonal matrix.
  //
  // (I - 2P) * (I - 2P)^T == (I - 2P)^2 == I - 4P + 4P^2 == I

CoordType sqr_mag = v.sqrMag();

assert("need nonzero length vector" && sqr_mag > 0);

// off diagonal
  for(int i = 0; i < dim - 1; ++i)
    for(int j = i + 1; j < dim; ++j)
      m_elem[i][j] = m_elem[j][i] = -2 * v[i] * v[j] / sqr_mag;

// diagonal
  for(int i = 0; i < dim; ++i)
    m_elem[i][i] = 1 - 2 * v[i] * v[i] / sqr_mag;

m_flip = true;
  m_valid = true;
  m_age = 1;

return *this;
}

template<int dim>
inline RotMatrix<dim>& RotMatrix<dim>::mirror()
{
  for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      m_elem[i][j] = (i == j) ? -1 : 0;

m_flip = dim%2;
  m_valid = true;
  m_age = 0; // -1 and 0 are exact, no roundoff error

return *this;
}

bool _MatrixInverseImpl(int size, CoordType* in, CoordType* out);

template<int dim>
inline void RotMatrix<dim>::normalize()
{
  // average the matrix with it's inverse transpose,
  // that will clean up the error to linear order

CoordType buf1[dim*dim], buf2[dim*dim];

for(int i = 0; i < dim; ++i) {
    for(int j = 0; j < dim; ++j) {
      buf1[j*dim + i] = m_elem[i][j];
      buf2[j*dim + i] = ((i == j) ? 1.f : 0.f);
    }
  }

bool success = _MatrixInverseImpl(dim, buf1, buf2);
  assert(success); // matrix can't be degenerate
  if (!success) {
    return;
  }

for(int i = 0; i < dim; ++i) {
    for(int j = 0; j < dim; ++j) {
      CoordType& elem = m_elem[i][j];
      elem += buf2[i*dim + j];
      elem /= 2;
    }
  }

m_age = 1;
}

} // namespace WFMath

#endif // WFMATH_ROTMATRIX_FUNCS_H
07070100000051000081A40000000200000002000000015D8693EF00000C91000000000000000000000000000000000000003400000000wfmath-1569100783.d0f8a54/wfmath/rotmatrix_test.cpp// rotmatrix_test.cpp (RotMatrix<> test functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include "const.h"
#include "vector.h"
#include "rotmatrix.h"
#include "stream.h"

#include "general_test.h"

#include <cmath>

using namespace WFMath;

template<int dim>
void test_rotmatrix(const RotMatrix<dim>& m)
{
  std::cout << "Testing RotMatrix: " << m << std::endl;

test_general(m);

RotMatrix<dim> minv = m.inverse();

//  cout << "Inverse is: " << minv << std::endl;

RotMatrix<dim> ident;

ident.identity();

RotMatrix<dim> try_ident;

try_ident = ProdInv(m, m);

//  cout << "This should be the identity: " << try_ident << std::endl;

for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      assert(Equal(ident.elem(i, j), try_ident.elem(i, j)));

try_ident = Prod(m, minv);

//  cout << "This should be the identity: " << try_ident << std::endl;

for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      assert(Equal(ident.elem(i, j), try_ident.elem(i, j)));

std::string s_mat = ToString(m);

RotMatrix<dim> str_m;

FromString(str_m, s_mat);

//  cout << "After conversion through a string, the matrix is " << str_m << std::endl;

//  cout << "Element differences after conversion are: ";
  for(int i = 0; i < dim; ++i) {
    for(int j = 0; j < dim; ++j) {
      CoordType diff = m.elem(i, j) - str_m.elem(i, j);
//      cout << diff;
      assert(std::fabs(diff) < FloatMax(numeric_constants<CoordType>::epsilon(), 1e-6f));
//      if(i < dim - 1 || j < dim - 1)
//        cout << ", ";
    }
  }
//  cout << std::endl;

RotMatrix<dim> conv_ident = Prod(str_m, str_m.inverse());

//  cout << "Converted M * M^T identity check: " << conv_ident;
//  cout << std::endl;

for(int i = 0; i < dim; ++i)
    for(int j = 0; j < dim; ++j)
      assert(Equal(conv_ident.elem(i, j), (i == j) ? 1 : 0));

// FIXME much more
}

int main()
{
  RotMatrix<2> m2;
  RotMatrix<3> m3;

m2.rotation(numeric_constants<CoordType>::pi() / 6);
  m3.rotation(Vector<3>(1, 0, numeric_constants<CoordType>::sqrt2()),
              numeric_constants<CoordType>::pi() / 5);

test_rotmatrix(m2);
  test_rotmatrix(m3);

// FIXME toEuler(), fromEuler()

return 0;
}
07070100000052000081A40000000200000002000000015D8693EF000008C9000000000000000000000000000000000000002D00000000wfmath-1569100783.d0f8a54/wfmath/segment.cpp// vector.cpp (Vector<> implementation)
//
//  The WorldForge Project
//  Copyright (C) 2011  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Alistair Riddoch
// Created: 2011-1-29

// Extensive amounts of this material come from the Vector2D
// and Vector3D classes from stage/math, written by Bryce W.
// Harrington, Kosh, and Jari Sundell (Rakshasa).

#include "segment_funcs.h"

#include "axisbox.h"
#include "ball.h"
#include "vector.h"

#include <cmath>

namespace WFMath {

template<> Segment<3>& Segment<3>::rotatePoint(const Quaternion& q,
                                               const Point<3>& p)
{
  m_p1.rotate(q, p);
  m_p2.rotate(q, p);
  return *this;
}

template<> Segment<3>& Segment<3>::rotateCenter(const Quaternion& q)
{
  rotatePoint(q, getCenter());
  return *this;
}

template<> Segment<3> Segment<3>::toParentCoords(const Point<3>& origin,
                                                 const Quaternion& rotation) const
{
  return Segment(m_p1.toParentCoords(origin, rotation),
                 m_p2.toParentCoords(origin, rotation));
}

template<> Segment<3> Segment<3>::toLocalCoords(const Point<3>& origin,
                                                const Quaternion& rotation) const
{
  return Segment(m_p1.toLocalCoords(origin, rotation),
                 m_p2.toLocalCoords(origin, rotation));
}

template class Segment<2>;
template class Segment<3>;

}
07070100000053000081A40000000200000002000000015D8693EF00001A0E000000000000000000000000000000000000002B00000000wfmath-1569100783.d0f8a54/wfmath/segment.h// segment.h (A line segment)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_SEGMENT_H
#define WFMATH_SEGMENT_H

#include <wfmath/point.h>
#include <wfmath/intersect_decls.h>

namespace WFMath {

template<int dim>
std::ostream& operator<<(std::ostream& os, const Segment<dim>& s);
template<int dim>
std::istream& operator>>(std::istream& is, Segment<dim>& s);

/// A line segment embedded in dim dimensions
/**
 * This class implements the full shape interface, as described in
 * the fake class Shape.
 **/
template<int dim = 3>
class Segment
{
 public:
  /// construct an uninitialized segment
  Segment() :m_p1(), m_p2() {}
  /// construct a segment with endpoints p1 and p2
  Segment(const Point<dim>& p1, const Point<dim>& p2) : m_p1(p1), m_p2(p2) {}
  /// construct a copy of a segment
  Segment(const Segment& s) : m_p1(s.m_p1), m_p2(s.m_p2) {}

~Segment() {}

friend std::ostream& operator<< <dim>(std::ostream& os, const Segment& s);
  friend std::istream& operator>> <dim>(std::istream& is, Segment& s);

Segment& operator=(const Segment& s)
	{m_p1 = s.m_p1; m_p2 = s.m_p2; return *this;}

bool isEqualTo(const Segment& s, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const;

bool operator==(const Segment& b) const	{return isEqualTo(b);}
  bool operator!=(const Segment& b) const	{return !isEqualTo(b);}

bool isValid() const {return m_p1.isValid() && m_p2.isValid();}

// Descriptive characteristics

size_t numCorners() const {return 2;}
  Point<dim> getCorner(size_t i) const {return i ? m_p2 : m_p1;}
  Point<dim> getCenter() const {return Midpoint(m_p1, m_p2);}

/// get one end of the segment
  const Point<dim>& endpoint(const int i) const	{return i ? m_p2 : m_p1;}
  /// get one end of the segment
  Point<dim>& endpoint(const int i)		{return i ? m_p2 : m_p1;}

// Movement functions

Segment& shift(const Vector<dim>& v)
	{m_p1 += v; m_p2 += v; return *this;}
  Segment& moveCornerTo(const Point<dim>& p, size_t corner);
  Segment& moveCenterTo(const Point<dim>& p)
	{return shift(p - getCenter());}

Segment& rotateCorner(const RotMatrix<dim>& m, size_t corner);
  Segment& rotateCenter(const RotMatrix<dim>& m)
	{rotatePoint(m, getCenter()); return *this;}
  Segment<dim>& rotatePoint(const RotMatrix<dim>& m, const Point<dim>& p)
	{m_p1.rotate(m, p); m_p2.rotate(m, p); return *this;}

// 3D rotation functions
  Segment& rotateCorner(const Quaternion& q, size_t corner);
  Segment& rotateCenter(const Quaternion& q);
  Segment& rotatePoint(const Quaternion& q, const Point<dim>& p);

// Intersection functions

AxisBox<dim> boundingBox() const {return AxisBox<dim>(m_p1, m_p2);}
  Ball<dim> boundingSphere() const
	{return Ball<dim>(getCenter(), Distance(m_p1, m_p2) / 2);}
  Ball<dim> boundingSphereSloppy() const
	{return Ball<dim>(getCenter(), SloppyDistance(m_p1, m_p2) / 2);}

Segment toParentCoords(const Point<dim>& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
        {return Segment(m_p1.toParentCoords(origin, rotation),
		m_p2.toParentCoords(origin, rotation));}
  Segment toParentCoords(const AxisBox<dim>& coords) const
        {return Segment(m_p1.toParentCoords(coords), m_p2.toParentCoords(coords));}
  Segment toParentCoords(const RotBox<dim>& coords) const
        {return Segment(m_p1.toParentCoords(coords), m_p2.toParentCoords(coords));}

// toLocal is just like toParent, expect we reverse the order of
  // translation and rotation and use the opposite sense of the rotation
  // matrix

Segment toLocalCoords(const Point<dim>& origin,
      const RotMatrix<dim>& rotation = RotMatrix<dim>().identity()) const
        {return Segment(m_p1.toLocalCoords(origin, rotation),
		m_p2.toLocalCoords(origin, rotation));}
  Segment toLocalCoords(const AxisBox<dim>& coords) const
        {return Segment(m_p1.toLocalCoords(coords), m_p2.toLocalCoords(coords));}
  Segment toLocalCoords(const RotBox<dim>& coords) const
        {return Segment(m_p1.toLocalCoords(coords), m_p2.toLocalCoords(coords));}

// 3D only
  Segment toParentCoords(const Point<dim>& origin,
                         const Quaternion& rotation) const;
  Segment toLocalCoords(const Point<dim>& origin,
                        const Quaternion& rotation) const;

friend bool Intersect<dim>(const Segment& s, const Point<dim>& p, bool proper);
  friend bool Contains<dim>(const Point<dim>& p, const Segment& s, bool proper);

friend bool Intersect<dim>(const Segment& s, const AxisBox<dim>& b, bool proper);
  friend bool Contains<dim>(const AxisBox<dim>& b, const Segment& s, bool proper);

friend bool Intersect<dim>(const Segment& s, const Ball<dim>& b, bool proper);
  friend bool Contains<dim>(const Ball<dim>& b, const Segment& s, bool proper);

friend bool Intersect<dim>(const Segment& s1, const Segment& s2, bool proper);
  friend bool Contains<dim>(const Segment& s1, const Segment& s2, bool proper);

friend bool Intersect<dim>(const RotBox<dim>& r, const Segment& s, bool proper);
  friend bool Contains<dim>(const RotBox<dim>& r, const Segment& s, bool proper);
  friend bool Contains<dim>(const Segment& s, const RotBox<dim>& r, bool proper);

friend bool Intersect<dim>(const Polygon<dim>& r, const Segment& s, bool proper);
  friend bool Contains<dim>(const Polygon<dim>& p, const Segment& s, bool proper);
  friend bool Contains<dim>(const Segment& s, const Polygon<dim>& p, bool proper);

private:

Point<dim> m_p1, m_p2;
};

template<int dim>
inline bool Segment<dim>::isEqualTo(const Segment<dim>& s,
                                    CoordType epsilon) const
{
  return Equal(m_p1, s.m_p1, epsilon)
      && Equal(m_p2, s.m_p2, epsilon);
}

} // namespace WFMath

#endif  // WFMATH_SEGMENT_H
07070100000054000081A40000000200000002000000015D8693EF000007B6000000000000000000000000000000000000003100000000wfmath-1569100783.d0f8a54/wfmath/segment_funcs.h// segment_funcs.h (line segment implementation)
//
//  The WorldForge Project
//  Copyright (C) 2000, 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.
//

// Author: Ron Steinke

#ifndef WFMATH_SEGMENT_FUNCS_H
#define WFMATH_SEGMENT_FUNCS_H

#include <wfmath/segment.h>

#include <cassert>

namespace WFMath {

template<int dim>
inline Segment<dim>& Segment<dim>::moveCornerTo(const Point<dim>& p, size_t corner)
{
  assert(corner == 0 || corner == 1);

Vector<dim> diff = m_p2 - m_p1;

if(!corner) {
    m_p1 = p;
    m_p2 = p + diff;
  }
  else {
    m_p2 = p;
    m_p1 = p - diff;
  }

return *this;
}

template<int dim>
inline Segment<dim>& Segment<dim>::rotateCorner(const RotMatrix<dim>& m, size_t corner)
{
  assert(corner == 0 || corner == 1);

if(corner)
    m_p1.rotate(m, m_p2);
  else
    m_p2.rotate(m, m_p1);

return *this;
}

template<>
inline Segment<3>& Segment<3>::rotateCorner(const Quaternion& q, size_t corner)
{
  assert(corner == 0 || corner == 1);

if(corner)
    m_p1.rotate(q, m_p2);
  else
    m_p2.rotate(q, m_p1);

return *this;
}

} // namespace WFMath

#endif  // WFMATH_SEGMENT_FUNCS_H
07070100000055000081A40000000200000002000000015D8693EF000013CC000000000000000000000000000000000000003000000000wfmath-1569100783.d0f8a54/wfmath/shape_test.cpp// shape_test.cpp (basic shape test functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-12

#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include "const.h"
#include "vector.h"
#include "rotmatrix.h"
#include "point.h"
#include "axisbox.h"
#include "ball.h"
#include "segment.h"
#include "rotbox.h"
#include "intersect.h"
#include "stream.h"
#include <vector>

#include "general_test.h"
#include "shape_test.h"

#include <cmath>

using namespace WFMath;

template<int dim>
void test_shape(const Point<dim>& p1, const Point<dim>& p2)
{
  CoordType sqr_dist = SquaredDistance(p1, p2);

AxisBox<dim> box(p1, p2), tmp;

std::cout << "Testing " << box << std::endl;

test_general(box);
  test_shape_no_rotate(box);

tmp = Union(box, box);
  assert(tmp == box);
  assert(Intersection(box, box, tmp));
  assert(tmp == box);
  std::vector<AxisBox<dim> > boxvec;
  boxvec.push_back(box);
  assert(box == BoundingBox(boxvec));

assert(Intersect(box, p1, false));
  assert(!Intersect(box, p1, true));

assert(Intersect(box, box, false));
  assert(Intersect(box, box, true));
  assert(Contains(box, box, false));
  assert(!Contains(box, box, true));

Ball<dim> ball(p1, 1);

std::cout << "Testing " << ball << std::endl;

test_general(ball);
  test_shape(ball);

assert(Intersect(ball, p1, false));
  assert(Intersect(ball, p1, true));

assert(Intersect(ball, box, false));
  assert(Intersect(ball, box, true));
  assert(Contains(ball, box, false) == (sqr_dist <= 1));
  assert(Contains(ball, box, true) == (sqr_dist < 1));
  assert(!Contains(box, ball, false));
  assert(!Contains(box, ball, true));

assert(Intersect(ball, ball, false));
  assert(Intersect(ball, ball, true));
  assert(Contains(ball, ball, false));
  assert(!Contains(ball, ball, true));

Segment<dim> seg(p1, p2);

std::cout << "Testing " << seg << std::endl;

test_general(seg);
  test_shape(seg);

assert(Intersect(seg, p1, false));
  assert(!Intersect(seg, p1, true));

assert(Intersect(seg, box, false));
  assert(Intersect(seg, box, true));
  assert(!Contains(seg, box, false));
  assert(!Contains(seg, box, true));
  assert(Contains(box, seg, false));
  assert(!Contains(box, seg, true));

assert(Intersect(seg, ball, false));
  assert(Intersect(seg, ball, true));
  assert(!Contains(seg, ball, false));
  assert(!Contains(seg, ball, true));
  assert(Contains(ball, seg, false) == (sqr_dist <= 1));
  assert(Contains(ball, seg, true) == (sqr_dist < 1));

assert(Intersect(seg, seg, false));
  assert(Intersect(seg, seg, true));
  assert(Contains(seg, seg, false));
  assert(!Contains(seg, seg, true));

RotBox<dim> rbox(
      p1,
      p2 - p1,
      RotMatrix<dim>().rotation(0, 1, numeric_constants<CoordType>::pi() / 6));

std::cout << "Testing " << rbox << std::endl;

test_general(rbox);
  test_shape(rbox);

assert(Intersect(rbox, p1, false));
  assert(!Intersect(rbox, p1, true));

assert(Intersect(rbox, box, false));
  assert(Intersect(rbox, box, true));
  assert(!Contains(rbox, box, false));
  assert(!Contains(rbox, box, true));
  assert(!Contains(box, rbox, false));
  assert(!Contains(box, rbox, true));

assert(Intersect(rbox, ball, false));
  assert(Intersect(rbox, ball, true));
  assert(!Contains(rbox, ball, false));
  assert(!Contains(rbox, ball, true));
  assert(Contains(ball, rbox, false) == (sqr_dist <= 1));
  assert(Contains(ball, rbox, true) == (sqr_dist < 1));

assert(Intersect(rbox, seg, false));
  // The next function may either succeed or fail, depending on the points passed.
  Intersect(rbox, seg, true);
  assert(!Contains(rbox, seg, false));
  assert(!Contains(rbox, seg, true));
  assert(!Contains(seg, rbox, false));
  assert(!Contains(seg, rbox, true));

assert(Intersect(rbox, rbox, false));
  assert(Intersect(rbox, rbox, true));
  assert(Contains(rbox, rbox, false));
  assert(!Contains(rbox, rbox, true));

// FIXME more tests
}

int main()
{
  test_shape(Point<2>(1, -1),
             Point<2>().setToOrigin());
  test_shape(Point<3>(1, -1, numeric_constants<CoordType>::sqrt2()),
             Point<3>().setToOrigin());

return 0;
}
07070100000056000081A40000000200000002000000015D8693EF00000998000000000000000000000000000000000000002E00000000wfmath-1569100783.d0f8a54/wfmath/shape_test.h// shape_test.h (generic shape interface test functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-1-6

#ifndef WFMATH_SHAPE_TEST_H
#define WFMATH_SHAPE_TEST_H

#include "const.h"
#include "vector.h"
#include "rotmatrix.h"
#include "point.h"
#include "axisbox.h"
#include "ball.h"
#include "intersect.h"
#include "stream.h"

namespace WFMath {

template<int dim, template<int> class Shape>
void test_shape_no_rotate(const Shape<dim>& s)
{
  Shape<dim> s2 = s;

size_t corners = s2.numCorners();

Point<dim> p = s2.getCenter();
  Vector<dim> v;

v.zero();
  v[0] = 1;
  s2.shift(v);

for(size_t i = 0; i < corners; ++i) {
    s2.moveCornerTo(p, i);
    p = s2.getCorner(i);
  }

s2.moveCenterTo(p);

assert(s2 == s);

AxisBox<dim> box = s.boundingBox();
  assert(Contains(box, s, false));
  Ball<dim> ball1 = s.boundingSphere(), ball2 = s.boundingSphereSloppy();
//  cout << ball1 << std::endl << ball2 << std::endl;
  assert(Contains(ball1, s, false));
  assert(Contains(ball2, ball1, false));
}

template<int dim, template<int> class Shape>
void test_shape(const Shape<dim>& s)
{
  test_shape_no_rotate(s);

Shape<dim> s2 = s;
  RotMatrix<dim> m;
  Point<dim> p;
  size_t corners = s2.numCorners();

if(dim >= 2)
    m.rotation(0, 1, numeric_constants<CoordType>::pi() / 6);
  else
    m.identity();

for(size_t i = 0; i < corners; ++i) {
    s2.rotateCorner(m, i);
    p = s2.getCorner(i);
  }

s2.rotatePoint(m, p);
  s2.rotateCenter(m);
}

} // namespace WFMath

#endif // WFMATH_SHAPE_TEST_H
07070100000057000081A40000000200000002000000015D8693EF00000816000000000000000000000000000000000000002B00000000wfmath-1569100783.d0f8a54/wfmath/shuffle.h// randgen.h (random number functions)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-5-23

#ifndef WFMATH_SHUFFLE_H
#define WFMATH_SHUFFLE_H

#include <wfmath/MersenneTwister.h>

#include <vector>

namespace WFMath {

/// Randomly reorder the contents of a std::vector
/**
 * For things like shuffling a deck of cards, etc.
 **/
template<class C>
void Shuffle(std::vector<C>& v) // need vector for random access
{
  typedef typename std::vector<C>::size_type size_type;
  size_type pos = v.size();

if(!pos) // handle size() == 0 nicely
    return;

// This swaps each element with one of the ones before
  // it, starting with the last element. Essentially,
  // this generates an operation from the permutation
  // group of size() elements, and applies it to the
  // vector. Note that the loop only executes size() - 1
  // times, as element 0 has nothing to swap with.
  while(--pos) {
    size_type new_pos = MTRand::instance.randInt(pos); // 0 <= new_pos <= pos
    if(new_pos == pos)
      continue;
    C tmp = v[pos];
    v[pos] = v[new_pos];
    v[new_pos] = tmp;
  }
}

} // namespace WFMath

#endif  // WFMATH_SHUFFLE_H
07070100000058000081A40000000200000002000000015D8693EF00001883000000000000000000000000000000000000002C00000000wfmath-1569100783.d0f8a54/wfmath/stream.cpp// stream.cpp (Stream conversion backend in the WFMath library)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-13

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include "stream.h"
#include "quaternion.h"
#include "MersenneTwister.h"

#include <sstream>

namespace WFMath {

std::string _IOWrapper::ToStringImpl(const _IOWrapper::BaseWrite& b,
					     std::streamsize precision)
{
  std::ostringstream ost;

ost.precision(precision);
 b.write(ost);

return ost.str();
}

void _IOWrapper::FromStringImpl(_IOWrapper::BaseRead& b,
					const std::string& s, std::streamsize precision)
{
  std::istringstream ist(s);

ist.precision(precision);
 b.read(ist);
}

// force a bunch of instantiations

template std::ostream& operator<< <3>(std::ostream& os, const Vector<3>& r);
template std::istream& operator>> <3>(std::istream& is, Vector<3>& r);
template std::ostream& operator<< <2>(std::ostream& os, const Vector<2>& r);
template std::istream& operator>> <2>(std::istream& is, Vector<2>& r);
template std::ostream& operator<< <3>(std::ostream& os, const Point<3>& r);
template std::istream& operator>> <3>(std::istream& is, Point<3>& r);
template std::ostream& operator<< <2>(std::ostream& os, const Point<2>& r);
template std::istream& operator>> <2>(std::istream& is, Point<2>& r);
template std::ostream& operator<< <3>(std::ostream& os, const RotMatrix<3>& r);
template std::istream& operator>> <3>(std::istream& is, RotMatrix<3>& r);
template std::ostream& operator<< <2>(std::ostream& os, const RotMatrix<2>& r);
template std::istream& operator>> <2>(std::istream& is, RotMatrix<2>& r);
template std::ostream& operator<< <3>(std::ostream& os, const AxisBox<3>& r);
template std::istream& operator>> <3>(std::istream& is, AxisBox<3>& r);
template std::ostream& operator<< <2>(std::ostream& os, const AxisBox<2>& r);
template std::istream& operator>> <2>(std::istream& is, AxisBox<2>& r);
template std::ostream& operator<< <3>(std::ostream& os, const Ball<3>& r);
template std::istream& operator>> <3>(std::istream& is, Ball<3>& r);
template std::ostream& operator<< <2>(std::ostream& os, const Ball<2>& r);
template std::istream& operator>> <2>(std::istream& is, Ball<2>& r);
template std::ostream& operator<< <3>(std::ostream& os, const Segment<3>& r);
template std::istream& operator>> <3>(std::istream& is, Segment<3>& r);
template std::ostream& operator<< <2>(std::ostream& os, const Segment<2>& r);
template std::istream& operator>> <2>(std::istream& is, Segment<2>& r);
template std::ostream& operator<< <3>(std::ostream& os, const RotBox<3>& r);
template std::istream& operator>> <3>(std::istream& is, RotBox<3>& r);
template std::ostream& operator<< <2>(std::ostream& os, const RotBox<2>& r);
template std::istream& operator>> <2>(std::istream& is, RotBox<2>& r);
// don't need 2d for Polygon, since it's a specialization
template std::ostream& operator<< <3>(std::ostream& os, const Polygon<3>& r);
template std::istream& operator>> <3>(std::istream& is, Polygon<3>& r);

void _WriteCoordList(std::ostream& os, const CoordType* d, const int num)
{
  os << '(';

for(int i = 0; i < num; ++i)
    os << d[i] << (i < (num - 1) ? ',' : ')');
}

void _ReadCoordList(std::istream& is, CoordType* d, const int num)
{
  char next;

is >> next;

if(next != '(')
    throw ParseError();

for(int i = 0; i < num; ++i) {
    is >> d[i] >> next;
    char want = (i == num - 1) ? ')' : ',';
    if(next != want)
      throw ParseError();
  }
}

CoordType _GetEpsilon(std::istream& is)
{
  std::streamsize str_prec = is.precision();
  CoordType str_eps = 1;
  while(--str_prec > 0) // Precision of 6 gives epsilon = 1e-5
    str_eps /= 10;

return str_eps;
}

// This is the only way I could get the operator<<() and operator>>()
// templates to recognize the declarations in the headers

template<>
std::ostream& operator<<(std::ostream& os, const Polygon<2>& r)
{
  size_t size = r.m_points.size();

if(size == 0) {
    os << "<empty>";
    return os;
  }

os << "Polygon: (";

for(size_t i = 0; i < size; ++i) {
    os << r.m_points[i] << (i < (size - 1) ? ',' : ')');
  }

return os;
}

template<>
std::istream& operator>>(std::istream& is, Polygon<2>& r)
{
  char next;
  Point<2> p;

r.m_points.clear();

do {
    is >> next;
    if(next == '<') { // empty polygon
       do {
         is >> next;
       } while(next != '>');
       return is;
    }
  } while(next != '(');

while(true) {
    is >> p;
    r.m_points.push_back(p);
    is >> next;
    if(next == ')')
      return is;
    if(next != ',')
      throw ParseError();
  }
}

std::ostream& operator<<(std::ostream& os, const Quaternion& q)
{
  return os << "Quaternion: (" << q.m_w << ',' << q.m_vec << ')';
}

std::istream& operator>>(std::istream& is, Quaternion& q)
{
  char next;

do {
    is >> next;
  } while(next != '(');

is >> q.m_w;

is >> next;
  if(next != ',')
    throw ParseError();

is >> q.m_vec;

CoordType norm = q.m_w * q.m_w + q.m_vec.sqrMag();

norm =  std::sqrt(norm);
  q.m_w /= norm;
  q.m_vec /= norm;
  q.m_valid = true;

is >> next;
  if(next != ')')
    throw ParseError();

return is;
}

std::ostream& operator<<(std::ostream& os, MTRand const& mtrand)
{
  return mtrand.save(os);
}

std::istream& operator>>(std::istream& is, MTRand& mtrand)
{
  return mtrand.load(is);
}

} // namespace WFMath
07070100000059000081A40000000200000002000000015D8693EF0000285A000000000000000000000000000000000000002A00000000wfmath-1569100783.d0f8a54/wfmath/stream.h// stream.h (Functions in the WFMath library that use streams)
//
//  The WorldForge Project
//  Copyright (C) 2001,2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#ifndef WFMATH_STREAM_H
#define WFMATH_STREAM_H

#include <wfmath/vector.h>
#include <wfmath/rotmatrix.h>
#include <wfmath/point.h>
#include <wfmath/axisbox.h>
#include <wfmath/ball.h>
#include <wfmath/segment.h>
#include <wfmath/rotbox.h>
#include <wfmath/polygon.h>
#include <wfmath/line.h>
#include <wfmath/error.h>
#include <string>
#include <iostream>
#include <list> // For Polygon<>::operator>>()

#include <cassert>

namespace WFMath {

// sstream vs. strstream compatibility wrapper

namespace _IOWrapper {

// Need separate read/write classes, since one is const C& and the other is C&

class BaseRead {
   public:
    virtual ~BaseRead() {}

virtual void read(std::istream& is) = 0;
  };

class BaseWrite {
   public:
    virtual ~BaseWrite() {}

virtual void write(std::ostream& os) const = 0;
  };

template<class C>
  class ImplRead : public BaseRead {
   public:
    ImplRead(C& c) : m_data(c) {}
    virtual ~ImplRead() {}

virtual void read(std::istream& is) {is >> m_data;}

private:
    C &m_data;
  };

template<class C>
  class ImplWrite : public BaseWrite {
   public:
    ImplWrite(const C& c) : m_data(c) {}
    virtual ~ImplWrite() {}

virtual void write(std::ostream& os) const {os << m_data;}

private:
    const C &m_data;
  };

std::string ToStringImpl(const BaseWrite& b, std::streamsize precision);
  void FromStringImpl(BaseRead& b, const std::string& s, std::streamsize precision);
}

/// Output a WFMath type as a string
/**
 * This uses operator<<() in its backend.
 **/
template<class C>
inline std::string ToString(const C& c, std::streamsize precision = 6)
{
  return _IOWrapper::ToStringImpl(_IOWrapper::ImplWrite<C>(c), precision);
}

/// Parse a WFMath type from a string
/**
 * This uses operator>>() in its backend.
 **/
template<class C>
inline void FromString(C& c, const std::string& s, std::streamsize = 6)
{
  _IOWrapper::ImplRead<C> i(c);
  _IOWrapper::FromStringImpl(i, s, 6);
}

void _ReadCoordList(std::istream& is, CoordType* d, const int num);
void _WriteCoordList(std::ostream& os, const CoordType* d, const int num);
CoordType _GetEpsilon(std::istream& is);

template<int dim>
inline std::ostream& operator<<(std::ostream& os, const Vector<dim>& v)
{
  _WriteCoordList(os, v.m_elem, dim);
  return os;
}

template<int dim>
inline std::istream& operator>>(std::istream& is, Vector<dim>& v)
{
  _ReadCoordList(is, v.m_elem, dim);
  v.m_valid = true;
  return is;
}

template<int dim>
inline std::ostream& operator<<(std::ostream& os, const RotMatrix<dim>& m)
{
  os << '(';

for(int i = 0; i < dim; ++i) {
    _WriteCoordList(os, m.m_elem[i], dim);
    os << (i < (dim - 1) ? ',' : ')');
  }

return os;
}

template<int dim>
inline std::istream& operator>>(std::istream& is, RotMatrix<dim>& m)
{
  CoordType d[dim*dim];
  char next;

is >> next;
  if(next != '(')
    throw ParseError();

for(int i = 0; i < dim; ++i) {
    _ReadCoordList(is, d + i * dim, dim);
    is >> next;
    char want = (i == dim - 1) ? ')' : ',';
    if(next != want)
      throw ParseError();
  }

if(!m._setVals(d, FloatMax(numeric_constants<CoordType>::epsilon(), _GetEpsilon(is))))
    throw ParseError();

return is;
}

template<int dim>
inline std::ostream& operator<<(std::ostream& os, const Point<dim>& p)
{
  _WriteCoordList(os, p.m_elem, dim);
  return os;
}

template<int dim>
inline std::istream& operator>>(std::istream& is, Point<dim>& p)
{
  _ReadCoordList(is, p.m_elem, dim);
  p.m_valid = true;
  return is;
}

template<int dim>
inline std::ostream& operator<<(std::ostream& os, const AxisBox<dim>& a)
{
  return os << "AxisBox: m_low = " << a.m_low << ", m_high = " << a.m_high;
}

template<int dim>
inline std::istream& operator>>(std::istream& is, AxisBox<dim>& a)
{
  char next;

do {
    is >> next;
  } while(next != '=');

is >> a.m_low;

do {
    is >> next;
  } while(next != '=');

is >> a.m_high;

return is;
}

template<int dim>
inline std::ostream& operator<<(std::ostream& os, const Ball<dim>& b)
{
  return os << "Ball: m_center = " << b.m_center <<
	  + ", m_radius = " << b.m_radius;
}

template<int dim>
inline std::istream& operator>>(std::istream& is, Ball<dim>& b)
{
  char next;

do {
    is >> next;
  } while(next != '=');

is >> b.m_center;

do {
    is >> next;
  } while(next != '=');

is >> b.m_radius;

return is;
}

template<int dim>
inline std::ostream& operator<<(std::ostream& os, const Segment<dim>& s)
{
  return os << "Segment: m_p1 = " << s.m_p1 << ", m_p2 = " << s.m_p2;
}

template<int dim>
inline std::istream& operator>>(std::istream& is, Segment<dim>& s)
{
  char next;

do {
    is >> next;
  } while(next != '=');

is >> s.m_p1;

do {
    is >> next;
  } while(next != '=');

is >> s.m_p2;

return is;
}

template<int dim>
inline std::ostream& operator<<(std::ostream& os, const RotBox<dim>& r)
{
  return os << "RotBox: m_corner0 = " << r.m_corner0
	 << ", m_size = " << r.m_size
	 << ", m_orient = " << r.m_orient;
}

template<int dim>
inline std::istream& operator>>(std::istream& is, RotBox<dim>& r)
{
  char next;

do {
    is >> next;
  } while(next != '=');

is >> r.m_corner0;

do {
    is >> next;
  } while(next != '=');

is >> r.m_size;

do {
    is >> next;
  } while(next != '=');

is >> r.m_orient;

return is;
}

template<> std::ostream& operator<<(std::ostream& os, const Polygon<2>& r);
template<> std::istream& operator>>(std::istream& is, Polygon<2>& r);

template<int dim>
inline std::ostream& operator<<(std::ostream& os, const Polygon<dim>& r)
{
  size_t size = r.m_poly.numCorners();

if(size == 0) {
    os << "<empty>";
    return os;
  }

os << "Polygon: (";

for(size_t i = 0; i < size; ++i)
    os << r.getCorner(i) << (i < (dim - 1) ? ',' : ')');

return os;
}

// Can't stick this in operator>>(std::istream&, Polygon<>&), because
// we use it as a template argument for list<>. Why isn't that allowed?
template<int dim> struct _PolyReader
{
  Point<dim> pd;
  Point<2> p2;
};

template<int dim>
std::istream& operator>>(std::istream& is, Polygon<dim>& r)
{
  char next;
  _PolyReader<dim> read;
  std::list<_PolyReader<dim> > read_list;

// Read in the points

do {
    is >> next;
    if(next == '<') { // empty polygon
       do {
         is >> next;
       } while(next != '>');
       return is;
    }
  } while(next != '(');

while(true) {
    is >> read.pd;
    read_list.push_back(read);
    is >> next;
    if(next == ')')
      break;
    if(next != ',')
      throw ParseError();
  }

// Convert to internal format. Be careful about the order points are
  // added to the orientation. If the first few points are too close together,
  // round off error can skew the plane, and later points that are further
  // away may fail.

typename std::list<_PolyReader<dim> >::iterator i, end = read_list.end();
  bool succ;

std::streamsize str_prec = is.precision();
  float str_eps = 1;
  while(--str_prec > 0) // Precision of 6 gives epsilon = 1e-5
    str_eps /= 10;
  CoordType epsilon = FloatMax(str_eps, numeric_constants<CoordType>::epsilon());

r.m_orient = _Poly2Orient<dim>();

if(read_list.size() < 3) { // This will always work
    for(i = read_list.begin(); i != end; ++i) {
      succ = r.m_orient.expand(i->pd, i->p2, epsilon);
      assert(succ);
    }
  }
  else { // Find the three furthest apart points
    typename std::list<_PolyReader<dim> >::iterator p1 = end, p2 = end, p3 = end, j; // invalid values
    CoordType dist = -1;

for(i = read_list.begin(); i != end; ++i) {
      for(j = i, ++j; j != end; ++j) {
        CoordType new_dist = SloppyDistance(i->pd, j->pd);
        if(new_dist > dist) {
          p1 = i;
          p2 = j;
          dist = new_dist;
        }
      }
    }

assert(p1 != end);
    assert(p2 != end);

dist = -1;

for(i = read_list.begin(); i != end; ++i) {
      // Don't want to be near either p1 or p2
      if(i == p1 || i == p2)
        continue;
      CoordType new_dist = FloatMin(SloppyDistance(i->pd, p1->pd),
				    SloppyDistance(i->pd, p2->pd));
      if(new_dist > dist) {
        p3 = i;
        dist = new_dist;
      }
    }

assert(p3 != end);

// Add p1, p2, p3 first

succ = r.m_orient.expand(p1->pd, p1->p2, epsilon);
    assert(succ);
    succ = r.m_orient.expand(p2->pd, p2->p2, epsilon);
    assert(succ);
    succ = r.m_orient.expand(p3->pd, p3->p2, epsilon);
    assert(succ);

// Try to add the rest

for(i = read_list.begin(); i != end; ++i) {
      if(i == p1 || i == p2 || i == p3) // Did these already
        continue;
      succ = r.m_orient.expand(i->pd, i->p2, epsilon);
      if(!succ) {
        r.clear();
        throw ParseError();
      }
    }
  }

// Got valid points, add them to m_poly

r.m_poly.resize(read_list.size());

int pnum;
  for(i = read_list.begin(), pnum = 0; i != end; ++i, ++pnum)
    r.m_poly[pnum] = i->p2;

return is;
}

template<int dim>
inline std::ostream& operator<<(std::ostream& os, const Line<dim>& r)
{
  size_t size = r.numCorners();

if(size == 0) {
    os << "<empty>";
    return os;
  }

os << "Line: (";

for(size_t i = 0; i < size; ++i)
    os << r.getCorner(i) << (i < (dim - 1) ? ',' : ')');

return os;
}

} // namespace WFMath

#endif // WFMATH_STREAM_H
0707010000005A000081A40000000200000002000000015D8693EF0000151C000000000000000000000000000000000000002F00000000wfmath-1569100783.d0f8a54/wfmath/timestamp.cpp// timestamp.cpp (time and random number implementation)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-5-23

#if defined _WIN32
#include <sys/timeb.h>
#else
#include <unistd.h>	
#include <sys/time.h>
#endif

#include "timestamp.h"

#ifdef _WIN32
#include <winsock2.h> 
#endif

#ifdef HAVE_CONFIG_H
	#include "config.h"
#endif

static const long Million = 1000000;

// apparently, some architectures use int instead of long
// in struct timeval
template<class T1, class T2>
static void regularize(T1 &sec, T2 &usec)
{
  if(usec >= Million) {
    usec -= Million;
    ++sec;
  }
  else if(usec < 0) {
    usec += Million;
    --sec;
  }
}

namespace WFMath {

TimeDiff::TimeDiff(long sec, long usec, bool is_valid) : m_isvalid(is_valid),
  m_sec(sec), m_usec(usec)
{
    if (m_isvalid)
        regularize(m_sec, m_usec);
}

TimeDiff::TimeDiff(long msec) : 
    m_isvalid(true),
    m_sec(msec / 1000),
    m_usec(msec % 1000)
{
  if(msec < 0) {
    --m_sec;
    if(m_usec < 0) // behavior of % is machine dependent
      m_usec += Million;
  }
}

long TimeDiff::milliseconds() const
{
  return m_sec * 1000 + m_usec / 1000;
}

TimeDiff& operator+=(TimeDiff &val, const TimeDiff &d)
{
  val.m_sec += d.m_sec;
  val.m_usec += d.m_usec;
  val.m_isvalid = val.m_isvalid && d.m_isvalid;

if (val.m_isvalid)
        regularize(val.m_sec, val.m_usec);

return val;
}

TimeDiff& operator-=(TimeDiff &val, const TimeDiff &d)
{
  val.m_sec -= d.m_sec;
  val.m_usec -= d.m_usec;
  val.m_isvalid = val.m_isvalid && d.m_isvalid;
    
    if (val.m_isvalid)
        regularize(val.m_sec, val.m_usec);

return val;
}

TimeDiff operator+(const TimeDiff &a, const TimeDiff &b)
{
  return TimeDiff(a.m_sec + b.m_sec, a.m_usec + b.m_usec, a.m_isvalid && b.m_isvalid);
}

TimeDiff operator-(const TimeDiff &a, const TimeDiff &b)
{
  return TimeDiff(a.m_sec - b.m_sec, a.m_usec - b.m_usec, a.m_isvalid && b.m_isvalid);
}

bool operator<(const TimeDiff &a, const TimeDiff &b)
{
  return (a.m_sec < b.m_sec) || ((a.m_sec == b.m_sec) && (a.m_usec < b.m_usec));
}

bool operator==(const TimeDiff &a, const TimeDiff &b)
{
  return (a.m_sec == b.m_sec) && (a.m_usec == b.m_usec);
}

TimeStamp TimeStamp::now()
{
    TimeStamp ret;
#ifndef _WIN32
    gettimeofday(&ret._val, NULL);
#else
  SYSTEMTIME sysTime;
  FILETIME fileTime = {0};  /* 100ns == 1 */
  LARGE_INTEGER i;

GetSystemTime(&sysTime);
  SystemTimeToFileTime(&sysTime, &fileTime);
  /* Documented as the way to get a 64 bit from a
   * FILETIME. */
  memcpy(&i, &fileTime, sizeof(LARGE_INTEGER));

ret._val.tv_sec = i.QuadPart / 10000000; /*10e7*/
    ret._val.tv_usec = (i.QuadPart / 10) % 1000000;  /*10e6*/
                                  
#endif
    ret._isvalid = true;
    return ret;
}

TimeStamp TimeStamp::epochStart()
{
  TimeStamp ret;

ret._val.tv_sec = 0;
  ret._val.tv_usec = 0;
  ret._isvalid = true;

return ret;
}

// FIXME C++0x supports initialising _val this way
// _val({sec, usec}),
TimeStamp::TimeStamp(long sec, long usec, bool isvalid) : _isvalid(isvalid)
{
  _val.tv_sec = sec;
  _val.tv_usec = usec;
  
  if (_isvalid)
    regularize(_val.tv_sec, _val.tv_usec);
}

bool operator<(const TimeStamp &a, const TimeStamp &b)
{
	if (a._val.tv_sec == b._val.tv_sec)
		return (a._val.tv_usec < b._val.tv_usec);
	else
		return a._val.tv_sec < b._val.tv_sec;
}

bool operator==(const TimeStamp &a, const TimeStamp &b)
{
	return (a._val.tv_sec == b._val.tv_sec)
		&& (a._val.tv_usec == b._val.tv_usec);
}

TimeStamp& operator+=(TimeStamp &a, const TimeDiff &d)
{
  a._val.tv_sec += d.m_sec;
  a._val.tv_usec += d.m_usec;
  a._isvalid = a._isvalid && d.m_isvalid;

if (a._isvalid)
        regularize(a._val.tv_sec, a._val.tv_usec);
  return a;
}

TimeStamp& operator-=(TimeStamp &a, const TimeDiff &d)
{
  a._val.tv_sec -= d.m_sec;
  a._val.tv_usec -= d.m_usec;
  a._isvalid = a._isvalid && d.m_isvalid;

if (a._isvalid)
        regularize(a._val.tv_sec, a._val.tv_usec);
  return a;
}

TimeStamp operator+(const TimeStamp &a, const TimeDiff &d)
{
  return TimeStamp(a._val.tv_sec + d.m_sec, a._val.tv_usec + d.m_usec,
	a._isvalid && d.m_isvalid);
}

TimeStamp operator-(const TimeStamp &a, const TimeDiff &d)
{
  return TimeStamp(a._val.tv_sec - d.m_sec, a._val.tv_usec - d.m_usec,
	a._isvalid && d.m_isvalid);
}

TimeDiff operator-(const TimeStamp &a, const TimeStamp &b)
{
  return TimeDiff(a._val.tv_sec - b._val.tv_sec,
    a._val.tv_usec - b._val.tv_usec, a._isvalid && b._isvalid);
}

}
0707010000005B000081A40000000200000002000000015D8693EF000016EB000000000000000000000000000000000000002D00000000wfmath-1569100783.d0f8a54/wfmath/timestamp.h// timestamp.h (time functions, taken from Eris)
//
//  The WorldForge Project
//  Copyright (C) 2002  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2002-5-23

#ifndef WFMATH_TIMESTAMP_H
#define WFMATH_TIMESTAMP_H

#include <wfmath/const.h>
#include <algorithm> // For std::pair
#include <iosfwd>

/** Timing related primitives in a portable fashion - note this is for interval / elapsed
time measurement, not displaying a human readable time. */

#ifdef _MSC_VER
#include <sys/timeb.h>
#else
#include <sys/time.h>
#endif

namespace WFMath {

class TimeStamp;

/// The difference between two timestamps
/**
 * This class implements the 'generic' subset of the interface in
 * the fake class Shape, with the exception of the stream operators.
 * It also has the full set of comparison * operators (<, <=, >, >=, ==, !=).
 **/
class TimeDiff
{
  TimeDiff(long sec, long usec, bool is_valid);
 public:
  /// construct an uninitialized TimeDiff
  TimeDiff() : m_isvalid(false) {}
  /// construct a TimeDiff of a given number of milliseconds
  TimeDiff(long msec);
  // default copy constructor is fine

/// Get the value of a TimeDiff in milliseconds
  /**
   * WARNING! This function does not check for overflow, if the
   * number of milliseconds is large
   **/
  long milliseconds() const;
  /// Get the value of a TimeDiff in (seconds, microseconds)
  std::pair<long,long> full_time() const {return std::make_pair(m_sec,m_usec);}

bool isValid() const {return m_isvalid;}

/// increment a TimeDiff
  friend TimeDiff& operator+=(TimeDiff&, const TimeDiff&);
  /// decrement a TimeDiff
  friend TimeDiff& operator-=(TimeDiff&, const TimeDiff&);
  /// negate a TimeDiff
  TimeDiff operator-() const {return TimeDiff(-m_sec, -m_usec, m_isvalid);}

/// add two TimeDiff instances
  friend TimeDiff operator+(const TimeDiff &a, const TimeDiff &b);
  /// subtract two TimeDiff instances
  friend TimeDiff operator-(const TimeDiff &a, const TimeDiff &b);

/// advance a TimeStamp by a TimeDiff
  friend TimeStamp& operator+=(TimeStamp&, const TimeDiff&);
  /// regress a TimeStamp by a TimeDiff
  friend TimeStamp& operator-=(TimeStamp&, const TimeDiff&);

/// find the result of advancing a TimeStamp
  friend TimeStamp operator+(const TimeStamp &a, const TimeDiff &msec);
  /// find the result of regressing a TimeStamp
  friend TimeStamp operator-(const TimeStamp &a, const TimeDiff &msec);

/// find the time difference between two time stamps
  friend TimeDiff operator-(const TimeStamp &a, const TimeStamp &b);

friend bool operator<(const TimeDiff&, const TimeDiff&);
  friend bool operator==(const TimeDiff&, const TimeDiff&);

private:
  bool m_isvalid;
  long m_sec, m_usec;
};

inline bool operator>(const TimeDiff &a, const TimeDiff &b) {return b < a;}
inline bool operator<=(const TimeDiff &a, const TimeDiff &b) {return !(b < a);}
inline bool operator>=(const TimeDiff &a, const TimeDiff &b) {return !(a < b);}
inline bool operator!=(const TimeDiff &a, const TimeDiff &b) {return !(b == a);}

/// A time stamp
/**
 * This class implements the 'generic' subset of the interface in
 * the fake class Shape, with the exception of the stream operators.
 * It also has the full set of comparison operators (<, <=, >, >=, ==, !=).
 **/
class TimeStamp {
 private:
#ifdef _WIN32 
  // We roll our own timeval... may only need to be done for mingw32.
  struct {
    long tv_sec;	/* seconds */
    long tv_usec;	/* microseconds */
  } _val;
#else
  // POSIX, BeOS, ....
  struct timeval _val;
#endif
  bool _isvalid;
  TimeStamp(long sec, long usec, bool isvalid);
 public:
  /// Construct an uninitialized TimeStamp
  TimeStamp() : _isvalid(false) {}
  // default copy constructor is fine

friend bool operator<(const TimeStamp &a, const TimeStamp &b);
  friend bool operator==(const TimeStamp &a, const TimeStamp &b);

friend std::ostream& operator<<(std::ostream& os, const TimeStamp&);
  friend std::istream& operator>>(std::istream& is, TimeStamp&);

bool isValid() const {return _isvalid;}
  ///
  friend TimeStamp& operator+=(TimeStamp&, const TimeDiff&);
  ///
  friend TimeStamp& operator-=(TimeStamp&, const TimeDiff&);

///
  friend TimeStamp operator+(const TimeStamp &a, const TimeDiff &msec);
  ///
  friend TimeStamp operator-(const TimeStamp &a, const TimeDiff &msec);

///
  friend TimeDiff operator-(const TimeStamp &a, const TimeStamp &b);

/// set a TimeStamp to the current time
  static TimeStamp now();
  /// set a TimeStamp to Jan 1, 1970
  static TimeStamp epochStart();
};

///
inline TimeStamp operator+(TimeDiff msec, const TimeStamp &a) {return a + msec;}

inline bool operator>(const TimeStamp &a, const TimeStamp &b) {return b < a;}
inline bool operator<=(const TimeStamp &a, const TimeStamp &b) {return !(b < a);}
inline bool operator>=(const TimeStamp &a, const TimeStamp &b) {return !(a < b);}
inline bool operator!=(const TimeStamp &a, const TimeStamp &b) {return !(b == a);}

} // namespace WFMath

#endif  // WFMATH_TIMESTAMP_H
0707010000005C000081A40000000200000002000000015D8693EF000004CA000000000000000000000000000000000000003400000000wfmath-1569100783.d0f8a54/wfmath/timestamp_test.cpp#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include <wfmath/timestamp.h>
#include <stdlib.h>
#include <iostream>

using namespace WFMath;
using std::cout;
using std::endl;

int main()
{

TimeStamp tsa;
    if (tsa.isValid()) {
        cout << "default constructor returned valid" << endl;
        return EXIT_FAILURE;
    }
    
    tsa += TimeDiff(50);
    if (tsa.isValid()) {
        cout << "invalid stamp += valid time diff returned valid" << endl;
        return EXIT_FAILURE;
    }
    
    tsa = TimeStamp::now();
    if (!tsa.isValid()) return EXIT_FAILURE;
    
    tsa += TimeDiff();
    if (tsa.isValid()) {
        cout << "valid time += invalid diff returned valid" << endl;
        return EXIT_FAILURE;
    }
    
    TimeDiff tda(1000);
    if (!tda.isValid()) {
        cout << "construct diff from literal msecs is broken" << endl;
        return EXIT_FAILURE;
    }
    
    tsa = TimeStamp::now();
    TimeStamp tsb = tsa;
    if (tsa != tsb) {
        cout << "equality of stamps is broken" << endl;
        return EXIT_FAILURE; // equality is broken
    }
    
    tsb += tda;
    if (tsa >= tsb) return EXIT_FAILURE; // compare is broken
    
    return EXIT_SUCCESS;
}
0707010000005D000041ED0000000200000002000000025D8693EF00000000000000000000000000000000000000000000002800000000wfmath-1569100783.d0f8a54/wfmath/unused0707010000005E000081A40000000200000002000000015D8693EF000005AE000000000000000000000000000000000000003600000000wfmath-1569100783.d0f8a54/wfmath/unused/oldmatrix.cpp// -*-C++-*-
// matrix.cpp (Matrix<> implementation)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#include "matrix_funcs.h"
#include "const.h"
#include <float.h>

namespace WF { namespace Math {

Matrix<3> SkewSymmetric(const Vector<3>& v)
{
  Matrix<3> out;

out.elem(0, 0) = out.elem(1, 1) = out.elem(2, 2) = 0;

out.elem(0, 1) = v[2];
  out.elem(1, 0) = -v[2];
  out.elem(1, 2) = v[0];
  out.elem(2, 1) = -v[0];
  out.elem(2, 0) = v[1];
  out.elem(0, 2) = -v[1];

return out;
}

}} // namespace WF::Math
0707010000005F000081A40000000200000002000000015D8693EF00001357000000000000000000000000000000000000003400000000wfmath-1569100783.d0f8a54/wfmath/unused/oldmatrix.h// -*-C++-*-
// matrix.h (Matrix<> class definition)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#ifndef WFMATH_MATRIX_H
#define WFMATH_MATRIX_H

#include <wfmath/vector.h>

namespace WF { namespace Math {

template<const int rows, const int columns> class RowVector;

template<const int rows, const int columns>
Matrix<rows,columns> operator*(const double& d, const Matrix<rows,columns>& m);
template<const int rows, const int columns>
Matrix<rows,columns> OuterProduct(const Vector<rows>& v1, const Vector<columns>& v2);

template<const int size>
Matrix<size,size> DiagonalMatrix(const Vector<size>& v);
template<const int size>
double Trace(const Matrix<size,size>& m);
template<const int size>
double Determinant(const Matrix<size,size>& m);
template<const int size>
Matrix<size,size> Inverse(const Matrix<size,size>& m);

template<const int rows, const int columns = rows>
class Matrix {
 public:
  Matrix() {}
  Matrix(const Matrix<rows,columns>& m);

bool operator==(const Matrix<rows,columns>& m) const;
  bool operator!=(const Matrix<rows,columns>& m) const {return !(*this == m);}

// WARNING! This operator is for sorting only. It does not
  // reflect any property of the matrix.
  bool operator< (const Matrix<rows,columns>& m) const;

// Division only makes sense for square matrices, make people use
  // inverse() explicitly

Matrix<rows,columns> operator+(const Matrix<rows,columns>& m) const;
  Matrix<rows,columns> operator-(const Matrix<rows,columns>& m) const;
  template<const int i>
    Matrix<rows,i> operator*(const Matrix<columns,i>& m) const;
  Matrix<rows,columns> operator*(const double& d) const;
  Matrix<rows,columns> operator/(const double& d) const;

Matrix<rows,columns> operator-() const; // Unary minus

Matrix<rows,columns>& operator+=(const Matrix<rows,columns>& m);
  Matrix<rows,columns>& operator-=(const Matrix<rows,columns>& m);
  // Since we need to construct a matrix to hold the temporary values
  // anyway, just use operator* to implement this one
  Matrix<rows,columns>& operator*=(const Matrix<columns,columns>& m)
	{*this = *this * m; return *this;}
  Matrix<rows,columns>& operator*=(const double& d);
  Matrix<rows,columns>& operator/=(const double& d);

Vector<rows> operator*(const Vector<columns>& v) const;

// FIXME it doesn't like this
//  friend Matrix<rows,columns> operator*<rows,columns>(const double& d,
//					const Matrix<rows,columns>& m);

friend Matrix<rows,columns> OuterProduct<rows,columns>(const Vector<rows>& v1,
							 const Vector<columns>& v2);

const double& elem(const int i, const int j) const 	{return m_elem[i][j];}
  double& elem(const int i, const int j)		{return m_elem[i][j];}

Vector<columns> row(const int i) const;
  void setRow(const int i, const Vector<columns>& v);
  Vector<rows> column(const int i) const;
  void setColumn(const int i, const Vector<rows>& v);

Matrix<rows,columns>& zero();

Matrix<columns,rows> transpose() const;

// The following are only defined for square matrices. Trying
  // to use them with non-square matrices will result in various
  // compiler/linker errors.

// FIXME is there some way to do this with partial specialization,
  // without having to rewrite all the operator functions?

Matrix<rows,columns>& identity();
  Matrix<rows,columns>& diagonal(const Vector<rows>& v)
	{return *this = DiagonalMatrix(v);}

double trace() const			{return Trace(*this);}
  double determinant() const		{return Determinant(*this);}
  Matrix<columns,rows> inverse() const	{return Inverse(*this);}

friend Matrix<rows> DiagonalMatrix<rows>(const Vector<rows>& v);

friend double Trace<rows>(const Matrix<rows>& m);
  friend double Determinant<rows>(const Matrix<rows>& m);
  friend Matrix<rows> Inverse<rows>(const Matrix<rows>& m);

//TODO rotate() and string functions, Atlas and Tcross functions from stage/math

private:
  double m_elem[rows][columns];
};

Matrix<3> SkewSymmetric(const Vector<3>& v);

}} // namespace WF::Math

#endif // WFMATH_MATRIX_H
07070100000060000081A40000000200000002000000015D8693EF000021AB000000000000000000000000000000000000003A00000000wfmath-1569100783.d0f8a54/wfmath/unused/oldmatrix_funcs.h// -*-C++-*-
// matrix_funcs.h (Matrix<> template functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#ifndef WFMATH_MATRIX_FUNCS_H
#define WFMATH_MATRIX_FUNCS_H

#include <wfmath/matrix.h>
#include <wfmath/error.h>

namespace WF { namespace Math {

template<const int rows, const int columns>
inline Matrix<rows,columns>::Matrix(const Matrix<rows,columns>& m)
{
  for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      m_elem[i][j] = m.m_elem[i][j];
}

template<const int rows, const int columns>
inline bool Matrix<rows,columns>::operator==(const Matrix<rows,columns>& m) const
{
  for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      if(m_elem[i][j] != m.m_elem[i][j])
        return false;

return true;
}

template<const int rows, const int columns>
bool Matrix<rows,columns>::operator< (const Matrix<rows,columns>& m) const
{
  for(int i = 0; i < rows; ++i) {
    for(int j = 0; j < columns; ++j) {
      if(m_elem[i][j] < m.m_elem[i][j])
        return true;
      if(m_elem[i][j] > m.m_elem[i][j])
        return false;
    }
  }

return false;
}

template<const int rows, const int columns>
inline Matrix<rows,columns> Matrix<rows,columns>::operator+(const Matrix<rows,columns>& m) const
{
  Matrix<rows,columns> out;

for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      out.m_elem[i][j] = this->m_elem[i][j] + m.m_elem[i][j];

return out;
}

template<const int rows, const int columns>
inline Matrix<rows,columns> Matrix<rows,columns>::operator-(const Matrix<rows,columns>& m) const
{
  Matrix<rows,columns> out;

for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      out.m_elem[i][j] = m_elem[i][j] - m.m_elem[i][j];

return out;
}

template<const int rows, const int columns> template<const int i>
inline Matrix<rows,i> Matrix<rows,columns>::operator*(const Matrix<columns, i>& m) const
{
  Matrix<columns, i> out;

for(int j = 0; j < rows; ++j) {
    for(int k = 0; k < i; ++k) {
      out.m_elem[j][k] = 0;
      for(int l = 0; l < columns; ++l)
        out.m_elem[j][k] += m_elem[j][l] * m.m_elem[l][k];
    }
  }

return out;
}

template<const int rows, const int columns>
Matrix<rows,columns> Matrix<rows,columns>::operator*(const double& d) const
{
  Matrix<rows,columns> out;

for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      out.m_elem[i][j] = m_elem[i][j] * d;

return out;
}

template<const int rows, const int columns>
Matrix<rows,columns> operator*(const double& d, const Matrix<rows,columns>& m)
{
  Matrix<rows,columns> out;

for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      out.m_elem[i][j] = m.m_elem[i][j] * d;

return out;
}

template<const int rows, const int columns>
Matrix<rows,columns> Matrix<rows,columns>::operator/(const double& d) const
{
  Matrix<rows,columns> out;

for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      out.m_elem[i][j] = m_elem[i][j] / d;

return out;
}

template<const int rows, const int columns>
inline Matrix<rows,columns> Matrix<rows,columns>::operator-() const // Unary minus
{
  Matrix<rows,columns> out;

for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      out.m_elem[i][j] = -m_elem[i][j];

return out;
}

template<const int rows, const int columns>
inline Matrix<rows,columns>& Matrix<rows,columns>::operator+=(const Matrix<rows,columns>& m)
{
  for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      m_elem[i][j] += m.m_elem[i][j];

return *this;
}

template<const int rows, const int columns>
inline Matrix<rows,columns>& Matrix<rows,columns>::operator-=(const Matrix<rows,columns>& m)
{
  for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      m_elem[i][j] -= m.m_elem[i][j];

return *this;
}

template<const int rows, const int columns>
Matrix<rows,columns>& Matrix<rows,columns>::operator*=(const double& d)
{
  for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      m_elem[i][j] *= d;

return *this;
}

template<const int rows, const int columns>
Matrix<rows,columns>& Matrix<rows,columns>::operator/=(const double& d)
{
  for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      m_elem[i][j] /= d;

return *this;
}

template<const int rows, const int columns>
inline Vector<rows> Matrix<rows,columns>::operator*(const Vector<columns>& v) const
{
  Vector<rows> out;

for(int i = 0; i < rows; ++i) {
    out[i] = 0;
    for(int j = 0; j < columns; ++j)
      out[i] += m_elem[i][j] * v[j];
  }

return out;
}

template<const int rows, const int columns>
inline Matrix<rows,columns> OuterProduct(const Vector<rows>& v1, const Vector<columns>& v2)
{
  Matrix<rows,columns> out;

for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      out.m_elem[i][j] = v1[i] * v2[j];
}

template<const int rows, const int columns>
inline Vector<columns> Matrix<rows,columns>::row(const int i) const
{
  Vector<columns> out;

for(int j = 0; j < columns; ++j)
    out[j] = m_elem[i][j];

return out;
}

template<const int rows, const int columns>
void Matrix<rows,columns>::setRow(const int i, const Vector<columns>& v)
{
  for(int j = 0; j < columns; ++j)
    m_elem[i][j] = v[j];
}

template<const int rows, const int columns>
inline Vector<rows> Matrix<rows,columns>::column(const int i) const
{
  Vector<columns> out;

for(int j = 0; j < rows; ++j)
    out[j] = m_elem[j][i];

return out;
}

template<const int rows, const int columns>
void Matrix<rows,columns>::setColumn(const int i, const Vector<rows>& v)
{
  for(int j = 0; j < rows; ++j)
    m_elem[j][i] = v[j];
}

template<const int rows, const int columns>
inline Matrix<rows,columns>& Matrix<rows,columns>::zero()
{
  for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      m_elem[i][j] = 0;

return *this;
}

template<const int rows, const int columns>
inline Matrix<columns,rows> Matrix<rows,columns>::transpose() const
{
  Matrix<columns,rows> m;

for(int i = 0; i < rows; ++i)
    for(int j = 0; j < columns; ++j)
      m.m_elem[j][i] = m_elem[i][j];

return m;
}

template<const int rows, const int columns>
inline Matrix<rows,columns>& Matrix<rows,columns>::identity()
{
  Vector<rows> v;

for(int i = 0; i < rows; ++i)
    v[i] = 1;

this->diagonal(v);

return *this;
}

template<const int size>
inline Matrix<size> DiagonalMatrix(const Vector<size>& v)
{
  Matrix<size> out;

out.zero();

for(int i = 0; i < size; ++i)
    out.m_elem[i][i] = v[i];

return out;
}

template<const int size>
inline double Trace(const Matrix<size>& m)
{
  double out = 0;

for(int i = 0; i < size; ++i)
    out += m.m_elem[i][i];

return out;
}

double _MatrixDeterminantImpl(const int size, double* m);

template<const int size>
inline double Determinant(const Matrix<size>& m)
{
  double mtmp[size*size]; // Scratch space

for(int i = 0; i < size; ++i)
    for(int j = 0; j < size; ++j)
      mtmp[i*size+j] = m.elem(i, j);

return _MatrixDeterminantImpl(size, mtmp);
}

int _MatrixInverseImpl(const int size, double* in, double* out);

template<const int size>
inline Matrix<size> Inverse(const Matrix<size>& m)
{
  double in[size*size], out[size*size]; // Scratch space

for(int i = 0; i < size; ++i) {
    for(int j = 0; j < size; ++j) {
      in[i*size+j] = m.elem(i, j);
      out[i*size+j] = (i == j) ? 1 : 0;
    }
  }

if(_MatrixInverseImpl(size, in, out) != 0)
    throw DegenerateMatrix<size>(m);

Matrix<size> mout;

for(int i = 0; i < size; ++i)
    for(int j = 0; j < size; ++j)
      mout.elem(i, j) = out[i*size+j];

return mout;
}

}} // namespace WF::Math

#endif // WFMATH_MATRIX_FUNCS_H
07070100000061000081A40000000200000002000000015D8693EF0000087F000000000000000000000000000000000000003B00000000wfmath-1569100783.d0f8a54/wfmath/unused/oldmatrix_test.cpp// -*-C++-*-
// matrix_test.cpp (Matrix<> test functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#include "vector.h"
#include "vector_funcs.h"
#include "matrix.h"
#include "matrix_funcs.h"
#include "const.h"
#include <assert.h>
#include "stream_funcs.h"
#include <iostream>

using namespace WF::Math;

//TODO tests for non-square matrices

template<const int size>
void test_matrix(const Matrix<size>& m)
{
  cout << "Testing matrix: " << m << std::endl;

cout << "Transpose is: " << m.transpose() << std::endl;

Matrix<size> minv = m.inverse();

double mdet = m.determinant(), minvdet = minv.determinant();

cout << "Inverse is: " << minv << std::endl;

assert(fabs(mdet * minvdet - 1) < WFMATH_EPSILON);

Matrix<size> nothing;

nothing.identity();

nothing -= m * minv;

cout << "This should be zero: " << nothing << std::endl;

for(int i = 0; i < size; ++i)
    for(int j = 0; j < size; ++j)
      assert(fabs(nothing.elem(i, j)) < WFMATH_EPSILON);
}

int main()
{
  Matrix<2> m2;
  Matrix<3> m3;

m2.identity();
  m2.elem(1, 0) = 1;

test_matrix(m2);

m3.identity();
  m3.elem(1, 0) = 1;
  m3.elem(0, 2) = WFMATH_CONST_SQRT2;
  m3.elem(2, 0) = WFMATH_CONST_SQRT3;

test_matrix(m3);

return 0;
}
07070100000062000081A40000000200000002000000015D8693EF00001801000000000000000000000000000000000000002C00000000wfmath-1569100783.d0f8a54/wfmath/vector.cpp// vector.cpp (Vector<> implementation)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

// Extensive amounts of this material come from the Vector2D
// and Vector3D classes from stage/math, written by Bryce W.
// Harrington, Kosh, and Jari Sundell (Rakshasa).

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include "vector_funcs.h"
#include "basis.h"
#include "point.h"
#include "quaternion.h"

namespace WFMath {

template<> CoordType Vector<2>::sloppyMag() const
{
  CoordType ax = std::fabs(m_elem[0]),
            ay = std::fabs(m_elem[1]);
  const CoordType p = numeric_constants<CoordType>::sqrt2() - 1;

// Don't need float add, all terms > 0

if(ax > ay)
    return ax + p * ay;
  else if (ay > 0)
    return ay + p * ax;
  else
    return 0;
}

template<> CoordType Vector<3>::sloppyMag() const
{
  CoordType ax = std::fabs(m_elem[0]),
            ay = std::fabs(m_elem[1]),
            az = std::fabs(m_elem[2]);
  const CoordType p = numeric_constants<CoordType>::sqrt2() - 1;
  const CoordType q = numeric_constants<CoordType>::sqrt3() + 1 - 2 * numeric_constants<CoordType>::sqrt2();

// Don't need FloatAdd, only term < 0 is q, it's very small,
  // and amin1 * amin2 / amax < amax.

if(ax > ay && ax > az)
    return ax + p * (ay + az) + q * ay * az / ax;
  else if (ay > az)
    return ay + p * (ax + az) + q * ax * az / ay;
  else if (az > 0)
    return az + p * (ax + ay) + q * ax * ay / az;
  else
    return 0;
}

template<> Vector<3>& Vector<3>::rotate(const Vector<3>& axis, CoordType theta)
{
  CoordType axis_sqr_mag = axis.sqrMag();

assert(axis_sqr_mag != 0);

Vector<3> perp_part = *this - axis * Dot(*this, axis) / axis_sqr_mag;
  Vector<3> rot90 = Cross(axis, perp_part) / std::sqrt(axis_sqr_mag);

*this += perp_part * (std::cos(theta) - 1) + rot90 * std::sin(theta);

return *this;
}

template<> Vector<3>& Vector<3>::rotate(const Quaternion& q)
{
  *this = (2 * q.scalar() * q.scalar() - 1) * *this +
          2 * q.vector() * Dot(q.vector(), *this) +
          2 * q.scalar() * Cross(q.vector(), *this);

return *this;
}

CoordType Cross(const Vector<2>& v1, const Vector<2>& v2)
{
  CoordType ans = v1[0] * v2[1] - v2[0] * v1[1];

return (ans >= v1._scaleEpsilon(v2)) ? ans : 0;
}

Vector<3> Cross(const Vector<3>& v1, const Vector<3>& v2)
{
  Vector<3> ans;

ans.setValid(v1.isValid() && v2.isValid());

ans[0] = v1[1] * v2[2] - v2[1] * v1[2];
  ans[1] = v1[2] * v2[0] - v2[2] * v1[0];
  ans[2] = v1[0] * v2[1] - v2[0] * v1[1];

double delta = v1._scaleEpsilon(v2);

for(int i = 0; i < 3; ++i)
    if(std::fabs(ans[i]) < delta)
      ans[i] = 0;

return ans;
}

template<>
Vector<2>& Vector<2>::polar(CoordType r, CoordType theta)
{
  CoordType d[2] = {r, theta};
  _PolarToCart(d, m_elem);
  m_valid = true;
  return *this;
}

template<>
void Vector<2>::asPolar(CoordType& r, CoordType& theta) const
{
  CoordType d[2];
  _CartToPolar(m_elem, d);
  r = d[0];
  theta = d[1];
}

template<>
Vector<3>& Vector<3>::polar(CoordType r, CoordType theta, CoordType z)
{
  CoordType d[2] = {r, theta};
  _PolarToCart(d, m_elem);
  m_elem[2] = z;
  m_valid = true;
  return *this;
}

template<>
void Vector<3>::asPolar(CoordType& r, CoordType& theta, CoordType& z) const
{
  CoordType d[2];
  _CartToPolar(m_elem, d);
  r = d[0];
  theta = d[1];
  z = m_elem[2];
}

template<>
Vector<3>& Vector<3>::spherical(CoordType r, CoordType theta, CoordType phi)
{
  CoordType d[3] = {r, theta, phi};
  _SphericalToCart(d, m_elem);
  m_valid = true;
  return *this;
}

template<>
void Vector<3>::asSpherical(CoordType& r, CoordType& theta,
				      CoordType& phi) const
{
  CoordType d[3];
  _CartToSpherical(m_elem, d);
  r = d[0];
  theta = d[1];
  phi = d[2];
}

template class Vector<3>;
template class Vector<2>;

template Vector<3>& operator-=(Vector<3>& v1, const Vector<3>& v2);
template Vector<2>& operator-=(Vector<2>& v1, const Vector<2>& v2);

template Vector<3>& operator+=(Vector<3>& v1, const Vector<3>& v2);
template Vector<2>& operator+=(Vector<2>& v1, const Vector<2>& v2);

template Vector<3>& operator*=(Vector<3>& v1, CoordType d);
template Vector<2>& operator*=(Vector<2>& v1, CoordType d);

template Vector<3>& operator/=(Vector<3>& v1, CoordType d);
template Vector<2>& operator/=(Vector<2>& v1, CoordType d);

template CoordType Dot<3>(const Vector<3> &, const Vector<3> &);
template CoordType Dot<2>(const Vector<2> &, const Vector<2> &);
template CoordType Angle<3>(const Vector<3> &, const Vector<3> &);

template Vector<3> operator-<3>(const Vector<3> &);

template Vector<3> operator*<3>(CoordType, const Vector<3> &);
template Vector<2> operator*<2>(CoordType, const Vector<2> &);
template Vector<3> operator*<3>(const Vector<3> &, CoordType);
template Vector<2> operator*<2>(const Vector<2> &, CoordType);
template Vector<3> operator/<3>(const Vector<3> &, CoordType);
template Vector<2> operator/<2>(const Vector<2> &, CoordType);

template Vector<3> operator+<3>(const Vector<3> &, const Vector<3> &);
template Vector<2> operator+<2>(const Vector<2> &, const Vector<2> &);

template Vector<3> operator-<3>(const Vector<3> &, const Vector<3> &);
template Vector<2> operator-<2>(const Vector<2> &, const Vector<2> &);

}
07070100000063000081A40000000200000002000000015D8693EF00003EDF000000000000000000000000000000000000002A00000000wfmath-1569100783.d0f8a54/wfmath/vector.h// vector.h (Vector<> class definition)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

// Extensive amounts of this material come from the Vector2D
// and Vector3D classes from stage/math, written by Bryce W.
// Harrington, Kosh, and Jari Sundell (Rakshasa).

#ifndef WFMATH_VECTOR_H
#define WFMATH_VECTOR_H

#include <wfmath/const.h>

#include <iosfwd>

#include <cmath>

namespace WFMath {

template<int dim>
Vector<dim>& operator+=(Vector<dim>& v1, const Vector<dim>& v2);
template<int dim>
Vector<dim>& operator-=(Vector<dim>& v1, const Vector<dim>& v2);
template<int dim>
Vector<dim>& operator*=(Vector<dim>& v, CoordType d);
template<int dim>
Vector<dim>& operator/=(Vector<dim>& v, CoordType d);

template<int dim>
Vector<dim> operator+(const Vector<dim>& v1, const Vector<dim>& v2);
template<int dim>
Vector<dim> operator-(const Vector<dim>& v1, const Vector<dim>& v2);
template<int dim>
Vector<dim> operator-(const Vector<dim>& v); // Unary minus
template<int dim>
Vector<dim> operator*(CoordType d, const Vector<dim>& v);
template<int dim>
Vector<dim> operator*(const Vector<dim>& v, CoordType d);
template<int dim>
Vector<dim> operator/(const Vector<dim>& v, CoordType d);

template<int dim>
CoordType Dot(const Vector<dim>& v1, const Vector<dim>& v2);

template<int dim>
CoordType Angle(const Vector<dim>& v, const Vector<dim>& u);

// The following are defined in rotmatrix_funcs.h
/// returns m * v
template<int dim> // m * v
Vector<dim> Prod(const RotMatrix<dim>& m, const Vector<dim>& v);
/// returns m^-1 * v
template<int dim> // m^-1 * v
Vector<dim> InvProd(const RotMatrix<dim>& m, const Vector<dim>& v);
/// returns v * m
/**
 * This is the function to use to rotate a Vector v using a Matrix m
 **/
template<int dim> // v * m
Vector<dim> Prod(const Vector<dim>& v, const RotMatrix<dim>& m);
/// return v * m^-1
template<int dim> // v * m^-1
Vector<dim> ProdInv(const Vector<dim>& v, const RotMatrix<dim>& m);

///
template<int dim>
Vector<dim> operator*(const RotMatrix<dim>& m, const Vector<dim>& v);
///
template<int dim>
Vector<dim> operator*(const Vector<dim>& v, const RotMatrix<dim>& m);

template<int dim>
Vector<dim> operator-(const Point<dim>& c1, const Point<dim>& c2);
template<int dim>
Point<dim> operator+(const Point<dim>& c, const Vector<dim>& v);
template<int dim>
Point<dim> operator-(const Point<dim>& c, const Vector<dim>& v);
template<int dim>
Point<dim> operator+(const Vector<dim>& v, const Point<dim>& c);

template<int dim>
Point<dim>& operator+=(Point<dim>& p, const Vector<dim>& v);
template<int dim>
Point<dim>& operator-=(Point<dim>& p, const Vector<dim>& v);

template<int dim>
std::ostream& operator<<(std::ostream& os, const Vector<dim>& v);
template<int dim>
std::istream& operator>>(std::istream& is, Vector<dim>& v);

template<typename Shape>
class ZeroPrimitive;

/// A dim dimensional vector
/**
 * This class implements the 'generic' subset of the interface in
 * the fake class Shape.
 **/
template<int dim = 3>
class Vector {
 friend class ZeroPrimitive<Vector<dim> >;
 public:
  /// Construct an uninitialized vector
  Vector() : m_valid(false) {}
  /// Construct a copy of a vector
  Vector(const Vector& v);
  /// Construct a vector from an object passed by Atlas
  explicit Vector(const AtlasInType& a);
  /// Construct a vector from a point.
  explicit Vector(const Point<dim>& point);

/**
   * @brief Provides a global instance preset to zero.
   */
  static const Vector<dim>& ZERO();
  
  friend std::ostream& operator<< <dim>(std::ostream& os, const Vector& v);
  friend std::istream& operator>> <dim>(std::istream& is, Vector& v);

/// Create an Atlas object from the vector
  AtlasOutType toAtlas() const;
  /// Set the vector's value to that given by an Atlas object
  void fromAtlas(const AtlasInType& a);

Vector& operator=(const Vector& v);

bool isEqualTo(const Vector& v, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const;
  bool operator==(const Vector& v) const {return isEqualTo(v);}
  bool operator!=(const Vector& v) const {return !isEqualTo(v);}

bool isValid() const {return m_valid;}
  /// make isValid() return true if you've initialized the vector by hand
  void setValid(bool valid = true) {m_valid = valid;}

/// Zero the components of a vector
  Vector& zero();

// Math operators

/// Add the second vector to the first
  friend Vector& operator+=<dim>(Vector& v1, const Vector& v2);
  /// Subtract the second vector from the first
  friend Vector& operator-=<dim>(Vector& v1, const Vector& v2);
  /// Multiply the magnitude of v by d
  friend Vector& operator*=<dim>(Vector& v, CoordType d);
  /// Divide the magnitude of v by d
  friend Vector& operator/=<dim>(Vector& v, CoordType d);

/// Take the sum of two vectors
  friend Vector operator+<dim>(const Vector& v1, const Vector& v2);
  /// Take the difference of two vectors
  friend Vector operator-<dim>(const Vector& v1, const Vector& v2);
  /// Reverse the direction of a vector
  friend Vector operator-<dim>(const Vector& v); // Unary minus
  /// Multiply a vector by a scalar
  friend Vector operator*<dim>(CoordType d, const Vector& v);
  /// Multiply a vector by a scalar
  friend Vector operator*<dim>(const Vector& v, CoordType d);
  /// Divide a vector by a scalar
  friend Vector operator/<dim>(const Vector& v, CoordType d);

// documented outside the class definition
  friend Vector Prod<dim>(const RotMatrix<dim>& m, const Vector& v);
  friend Vector InvProd<dim>(const RotMatrix<dim>& m, const Vector& v);

/// Get the i'th element of the vector
  CoordType operator[](const int i) const {return m_elem[i];}
  /// Get the i'th element of the vector
  CoordType& operator[](const int i)      {return m_elem[i];}

/// Find the vector which gives the offset between two points
  friend Vector operator-<dim>(const Point<dim>& c1, const Point<dim>& c2);
  /// Find the point at the offset v from the point c
  friend Point<dim> operator+<dim>(const Point<dim>& c, const Vector& v);
  /// Find the point at the offset -v from the point c
  friend Point<dim> operator-<dim>(const Point<dim>& c, const Vector& v);
  /// Find the point at the offset v from the point c
  friend Point<dim> operator+<dim>(const Vector& v, const Point<dim>& c);

/// Shift a point by a vector
  friend Point<dim>& operator+=<dim>(Point<dim>& p, const Vector& rhs);
  /// Shift a point by a vector, in the opposite direction
  friend Point<dim>& operator-=<dim>(Point<dim>& p, const Vector& rhs);

friend CoordType Cross(const Vector<2>& v1, const Vector<2>& v2);
  friend Vector<3> Cross(const Vector<3>& v1, const Vector<3>& v2);

/// The dot product of two vectors
  friend CoordType Dot<dim>(const Vector& v1, const Vector& v2);
  /// The angle between two vectors
  friend CoordType Angle<dim>(const Vector& v, const Vector& u);

/// The squared magnitude of a vector
  CoordType sqrMag() const;
  /// The magnitude of a vector
  CoordType mag() const		{return std::sqrt(sqrMag());}
  /// Normalize a vector
  Vector& normalize(CoordType norm = 1.0)
  {CoordType themag = mag(); return (*this *= norm / themag);}

/// An approximation to the magnitude of a vector
  /**
   * The sloppyMag() function gives a value between
   * the true magnitude and sloppyMagMax multiplied by the
   * true magnitude. sloppyNorm() uses sloppyMag() to normalize
   * the vector. This is currently only implemented for
   * dim = {1, 2, 3}. For all current implementations,
   * sloppyMagMax is greater than or equal to one.
   * The constant sloppyMagMaxSqrt is provided for those
   * who want to most closely approximate the true magnitude,
   * without caring whether it's too low or too high.
   **/
  CoordType sloppyMag() const;
  /// Approximately normalize a vector
  /**
   * Normalize a vector using sloppyMag() instead of the true magnitude.
   * The new length of the vector will be between norm/sloppyMagMax()
   * and norm.
   **/
  Vector& sloppyNorm(CoordType norm = 1.0);

// Can't seem to implement these as constants, implementing
  // inline lookup functions instead.
  /// The maximum ratio of the return value of sloppyMag() to the true magnitude
  static CoordType sloppyMagMax();
  /// The square root of sloppyMagMax()
  /**
   * This is provided for people who want to obtain maximum accuracy from
   * sloppyMag(), without caring whether the answer is high or low.
   * The result sloppyMag()/sloppyMagMaxSqrt() will be within sloppyMagMaxSqrt()
   * of the true magnitude.
   **/
  static CoordType sloppyMagMaxSqrt();

/// Rotate the vector in the (axis1, axis2) plane by the angle theta
  Vector& rotate(int axis1, int axis2, CoordType theta);

/// Rotate the vector in the (v1, v2) plane by the angle theta
  /**
   * This throws CollinearVectors if v1 and v2 are parallel.
   **/
  Vector& rotate(const Vector& v1, const Vector& v2, CoordType theta);

/// Rotate the vector using a matrix
  Vector& rotate(const RotMatrix<dim>&);

// mirror image functions

/// Reflect a vector in the direction of the i'th axis
  Vector& mirror(const int i) { m_elem[i] *= -1; return *this;}
  /// Reflect a vector in the direction specified by v
  Vector& mirror(const Vector& v)
  {return operator-=(*this, 2 * v * Dot(v, *this) / v.sqrMag());}
  /// Reflect a vector in all directions simultaneously.
  /**
   * This is a nice way to implement the parity operation if dim is odd.
   **/
  Vector& mirror()		{return operator*=(*this, -1);}

// Specialized 2D/3D stuff starts here

// The following functions are defined only for
  // two dimensional (rotate(CoordType), Vector<>(CoordType, CoordType))
  // and three dimensional (the rest of them) vectors.
  // Attempting to call these on any other vector will
  // result in a linker error.

/// 2D only: construct a vector from (x, y) coordinates
  Vector(CoordType x, CoordType y);
  /// 3D only: construct a vector from (x, y, z) coordinates
  Vector(CoordType x, CoordType y, CoordType z);

/// 2D only: rotate a vector by an angle theta
  Vector& rotate(CoordType theta);

/// 3D only: rotate a vector about the x axis by an angle theta
  Vector& rotateX(CoordType theta);
  /// 3D only: rotate a vector about the y axis by an angle theta
  Vector& rotateY(CoordType theta);
  /// 3D only: rotate a vector about the z axis by an angle theta
  Vector& rotateZ(CoordType theta);

/// 3D only: rotate a vector about the i'th axis by an angle theta
  Vector& rotate(const Vector& axis, CoordType theta);
  /// 3D only: rotate a vector using a Quaternion
  Vector& rotate(const Quaternion& q);

// Label the first three components of the vector as (x,y,z) for
  // 2D/3D convienience

/// Access the first component of a vector
  CoordType x() const	{return m_elem[0];}
  /// Access the first component of a vector
  CoordType& x()	{return m_elem[0];}
  /// Access the second component of a vector
  CoordType y() const	{return m_elem[1];}
  /// Access the second component of a vector
  CoordType& y()	{return m_elem[1];}
  /// Access the third component of a vector
  CoordType z() const;
  /// Access the third component of a vector
  CoordType& z();

/// Flip the x component of a vector
  Vector& mirrorX()	{return mirror(0);}
  /// Flip the y component of a vector
  Vector& mirrorY()	{return mirror(1);}
  /// Flip the z component of a vector
  Vector& mirrorZ();

/// 2D only: construct a vector from polar coordinates
  Vector& polar(CoordType r, CoordType theta);
  /// 2D only: convert a vector to polar coordinates
  void asPolar(CoordType& r, CoordType& theta) const;

/// 3D only: construct a vector from polar coordinates
  Vector& polar(CoordType r, CoordType theta, CoordType z);
  /// 3D only: convert a vector to polar coordinates
  void asPolar(CoordType& r, CoordType& theta, CoordType& z) const;
  /// 3D only: construct a vector from shperical coordinates
  Vector& spherical(CoordType r, CoordType theta, CoordType phi);
  /// 3D only: convert a vector to shperical coordinates
  void asSpherical(CoordType& r, CoordType& theta, CoordType& phi) const;

const CoordType* elements() const {return m_elem;}

private:
  double _scaleEpsilon(const Vector& v, CoordType epsilon = numeric_constants<CoordType>::epsilon()) const
  {return _ScaleEpsilon(m_elem, v.m_elem, dim, epsilon);}

CoordType m_elem[dim];
  bool m_valid;
};

template<>
inline CoordType Vector<3>::z() const
{
  return m_elem[2];
}

template<>
inline CoordType& Vector<3>::z()
{
  return m_elem[2];
}

template<>
inline Vector<3>& Vector<3>::mirrorZ()
{
  return mirror(2);
}

/// 2D only: get the z component of the cross product of two vectors
CoordType Cross(const Vector<2>& v1, const Vector<2>& v2);
/// 3D only: get the cross product of two vectors
Vector<3> Cross(const Vector<3>& v1, const Vector<3>& v2);

/// Check if two vectors are parallel
/**
 * Returns true if the vectors are parallel. For parallel
 * vectors, same_dir is set to true if they point the same
 * direction, and false if they point opposite directions
 **/
template<int dim>
bool Parallel(const Vector<dim>& v1, const Vector<dim>& v2, bool& same_dir);

/// Check if two vectors are parallel
/**
 * Convienience wrapper if you don't care about same_dir
 **/
template<int dim>
bool Parallel(const Vector<dim>& v1, const Vector<dim>& v2);

/// Check if two vectors are perpendicular
template<int dim>
bool Perpendicular(const Vector<dim>& v1, const Vector<dim>& v2);

template <int dim>
inline Vector<dim> operator+(const Vector<dim>& v1, const Vector<dim>& v2)
{
  Vector<dim> ans(v1);

ans += v2;

return ans;
}

template <int dim>
inline Vector<dim> operator-(const Vector<dim>& v1, const Vector<dim>& v2)
{
  Vector<dim> ans(v1);

ans -= v2;

return ans;
}

template <int dim>
inline Vector<dim> operator*(const Vector<dim>& v, CoordType d)
{
  Vector<dim> ans(v);

ans *= d;

return ans;
}

template<int dim>
inline Vector<dim> operator*(CoordType d, const Vector<dim>& v)
{
  Vector<dim> ans(v);

ans *= d;

return ans;
}

template <int dim>
inline Vector<dim> operator/(const Vector<dim>& v, CoordType d)
{
  Vector<dim> ans(v);

ans /= d;

return ans;
}

template<int dim>
inline bool Parallel(const Vector<dim>& v1,
                     const Vector<dim>& v2,
                     bool& same_dir)
{
  CoordType dot = Dot(v1, v2);

same_dir = (dot > 0);

return Equal(dot * dot, v1.sqrMag() * v2.sqrMag());
}

template<int dim>
inline bool Parallel(const Vector<dim>& v1, const Vector<dim>& v2)
{
  bool same_dir;

return Parallel(v1, v2, same_dir);
}

template<>
inline CoordType Vector<1>::sloppyMagMax()
{
  return 1.f;
}

template<>
inline CoordType Vector<2>::sloppyMagMax()
{
  return 1.082392200292393968799446410733f;
}

template<>
inline CoordType Vector<3>::sloppyMagMax()
{
  return 1.145934719303161490541433900265f;
}

template<>
inline CoordType Vector<1>::sloppyMagMaxSqrt()
{
  return 1.f;
}

template<>
inline CoordType Vector<2>::sloppyMagMaxSqrt()
{
  return 1.040380795811030899095785063701f;
}

template<>
inline CoordType Vector<3>::sloppyMagMaxSqrt()
{
  return 1.070483404496847625250328653179f;
}

} // namespace WFMath

#endif // WFMATH_VECTOR_H
07070100000064000081A40000000200000002000000015D8693EF00001FAD000000000000000000000000000000000000003000000000wfmath-1569100783.d0f8a54/wfmath/vector_funcs.h// vector_funcs.h (Vector<> template functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

// Extensive amounts of this material come from the Vector2D
// and Vector3D classes from stage/math, written by Bryce W.
// Harrington, Kosh, and Jari Sundell (Rakshasa).

#ifndef WFMATH_VECTOR_FUNCS_H
#define WFMATH_VECTOR_FUNCS_H

#include <wfmath/vector.h>
#include <wfmath/rotmatrix.h>
#include <wfmath/zero.h>

#include <limits>

#include <cmath>

#include <cassert>

namespace WFMath {

template<int dim>
Vector<dim>::Vector(const Vector<dim>& v) : m_valid(v.m_valid)
{
  for(int i = 0; i < dim; ++i) {
    m_elem[i] = v.m_elem[i];
  }
}

template<int dim>
Vector<dim>::Vector(const Point<dim>& p) : m_valid(p.isValid())
{
  for(int i = 0; i < dim; ++i) {
    m_elem[i] = p.elements()[i];
  }
}

template<int dim>
const Vector<dim>& Vector<dim>::ZERO()
{
  static ZeroPrimitive<Vector<dim> > zeroVector(dim);
  return zeroVector.getShape();
}

template<int dim>
Vector<dim>& Vector<dim>::operator=(const Vector<dim>& v)
{
  m_valid = v.m_valid;

for(int i = 0; i < dim; ++i) {
    m_elem[i] = v.m_elem[i];
  }

return *this;
}

template<int dim>
bool Vector<dim>::isEqualTo(const Vector<dim>& v, CoordType epsilon) const
{
  double delta = _ScaleEpsilon(m_elem, v.m_elem, dim, epsilon);

//If anyone is invalid they are never equal
  if (!v.m_valid || !m_valid) {
    return false;
  }

for(int i = 0; i < dim; ++i) {
    if(std::fabs(m_elem[i] - v.m_elem[i]) > delta) {
      return false;
    }
  }

return true;
}

template <int dim>
Vector<dim>& operator+=(Vector<dim>& v1, const Vector<dim>& v2)
{
  v1.m_valid = v1.m_valid && v2.m_valid;

for(int i = 0; i < dim; ++i) {
    v1.m_elem[i] += v2.m_elem[i];
  }

return v1;
}

template <int dim>
Vector<dim>& operator-=(Vector<dim>& v1, const Vector<dim>& v2)
{
  v1.m_valid = v1.m_valid && v2.m_valid;

for(int i = 0; i < dim; ++i) {
    v1.m_elem[i] -= v2.m_elem[i];
  }

return v1;
}

template <int dim>
Vector<dim>& operator*=(Vector<dim>& v, CoordType d)
{
  for(int i = 0; i < dim; ++i) {
    v.m_elem[i] *= d;
  }

return v;
}

template <int dim>
Vector<dim>& operator/=(Vector<dim>& v, CoordType d)
{
  for(int i = 0; i < dim; ++i) {
    v.m_elem[i] /= d;
  }

return v;
}

template <int dim>
Vector<dim> operator-(const Vector<dim>& v)
{
  Vector<dim> ans;

ans.m_valid = v.m_valid;

for(int i = 0; i < dim; ++i) {
    ans.m_elem[i] = -v.m_elem[i];
  }

return ans;
}

template<int dim>
Vector<dim>& Vector<dim>::sloppyNorm(CoordType norm)
{
  CoordType mag = sloppyMag();

assert("need nonzero length vector" && mag > norm / std::numeric_limits<CoordType>::max());

return (*this *= norm / mag);
}

template<int dim>
Vector<dim>& Vector<dim>::zero()
{
  m_valid = true;

for(int i = 0; i < dim; ++i) {
    m_elem[i] = 0;
  }

return *this;
}

template<int dim>
CoordType Angle(const Vector<dim>& v, const Vector<dim>& u)
{
  // Adding numbers with large magnitude differences can cause
  // a loss of precision, but Dot() checks for this now

CoordType dp = FloatClamp(Dot(u, v) / std::sqrt(u.sqrMag() * v.sqrMag()),
			 -1.0, 1.0);

CoordType angle = std::acos(dp);
 
  return angle;
}

template<int dim>
Vector<dim>& Vector<dim>::rotate(int axis1, int axis2, CoordType theta)
{
  assert(axis1 >= 0 && axis2 >= 0 && axis1 < dim && axis2 < dim && axis1 != axis2);

CoordType tmp1 = m_elem[axis1], tmp2 = m_elem[axis2];
  CoordType stheta = std::sin(theta),
            ctheta = std::cos(theta);

m_elem[axis1] = tmp1 * ctheta - tmp2 * stheta;
  m_elem[axis2] = tmp2 * ctheta + tmp1 * stheta;

return *this;
}

template<int dim>
Vector<dim>& Vector<dim>::rotate(const Vector<dim>& v1, const Vector<dim>& v2,
				 CoordType theta)
{
  RotMatrix<dim> m;
  return operator=(Prod(*this, m.rotation(v1, v2, theta)));
}

template<int dim>
Vector<dim>& Vector<dim>::rotate(const RotMatrix<dim>& m)
{
  return *this = Prod(*this, m);
}

template<> Vector<3>& Vector<3>::rotate(const Vector<3>& axis, CoordType theta);
template<> Vector<3>& Vector<3>::rotate(const Quaternion& q);

template<int dim>
CoordType Dot(const Vector<dim>& v1, const Vector<dim>& v2)
{
  double delta = _ScaleEpsilon(v1.m_elem, v2.m_elem, dim);

CoordType ans = 0;

for(int i = 0; i < dim; ++i) {
    ans += v1.m_elem[i] * v2.m_elem[i];
  }

return (std::fabs(ans) >= delta) ? ans : 0;
}

template<int dim>
CoordType Vector<dim>::sqrMag() const
{
  CoordType ans = 0;

for(int i = 0; i < dim; ++i) {
    // all terms > 0, no loss of precision through cancelation
    ans += m_elem[i] * m_elem[i];
  }

return ans;
}

template<int dim>
bool Perpendicular(const Vector<dim>& v1, const Vector<dim>& v2)
{
  CoordType max1 = 0, max2 = 0;

for(int i = 0; i < dim; ++i) {
    CoordType val1 = std::fabs(v1[i]), val2 = std::fabs(v2[i]);
    if(val1 > max1) {
      max1 = val1;
    }
    if(val2 > max2) {
      max2 = val2;
    }
  }

// Need to scale by both, since Dot(v1, v2) goes like the product of the magnitudes
  int exp1, exp2;
  (void) std::frexp(max1, &exp1);
  (void) std::frexp(max2, &exp2);

return std::fabs(Dot(v1, v2)) < std::ldexp(numeric_constants<CoordType>::epsilon(), exp1 + exp2);
}

// Note for people trying to compute the above numbers
// more accurately:

// The worst value for dim == 2 occurs when the ratio of the components
// of the vector is sqrt(2) - 1. The value above is equal to sqrt(4 - 2 * sqrt(2)).

// The worst value for dim == 3 occurs when the two smaller components
// are equal, and their ratio with the large component is the
// (unique, real) solution to the equation q x^3 + (q-1) x + p == 0,
// where p = sqrt(2) - 1, and q = sqrt(3) + 1 - 2 * sqrt(2).
// Running the script bc_sloppy_mag_3 provided with the WFMath source
// will calculate the above number.

template<> Vector<2>& Vector<2>::polar(CoordType r, CoordType theta);
template<> void Vector<2>::asPolar(CoordType& r, CoordType& theta) const;

template<> Vector<3>& Vector<3>::polar(CoordType r, CoordType theta,
				       CoordType z);
template<> void Vector<3>::asPolar(CoordType& r, CoordType& theta,
				   CoordType& z) const;
template<> Vector<3>& Vector<3>::spherical(CoordType r, CoordType theta,
					   CoordType phi);
template<> void Vector<3>::asSpherical(CoordType& r, CoordType& theta,
				       CoordType& phi) const;

template<> CoordType Vector<2>::sloppyMag() const;
template<> CoordType Vector<3>::sloppyMag() const;

template<> CoordType Vector<1>::sloppyMag() const
	{return std::fabs(m_elem[0]);}

template<> Vector<2>::Vector(CoordType x, CoordType y) : m_valid(true)
	{m_elem[0] = x; m_elem[1] = y;}
template<> Vector<3>::Vector(CoordType x, CoordType y, CoordType z) : m_valid(true)
	{m_elem[0] = x; m_elem[1] = y; m_elem[2] = z;}

template<> Vector<2>& Vector<2>::rotate(CoordType theta)
	{return rotate(0, 1, theta);}

template<> Vector<3>& Vector<3>::rotateX(CoordType theta)
	{return rotate(1, 2, theta);}
template<> Vector<3>& Vector<3>::rotateY(CoordType theta)
	{return rotate(2, 0, theta);}
template<> Vector<3>& Vector<3>::rotateZ(CoordType theta)
	{return rotate(0, 1, theta);}

} // namespace WFMath

#endif // WFMATH_VECTOR_FUNCS_H
07070100000065000081A40000000200000002000000015D8693EF00000F8B000000000000000000000000000000000000003100000000wfmath-1569100783.d0f8a54/wfmath/vector_test.cpp// vector_test.cpp (Vector<> test functions)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#ifdef NDEBUG
#undef NDEBUG
#endif
#ifndef DEBUG
#define DEBUG
#endif

#include "const.h"
#include "vector.h"
#include "rotmatrix.h"
#include "stream.h"

#include "general_test.h"

#include <cmath>

using namespace WFMath;

template<int dim>
void test_vector(const Vector<dim>& v)
{
  std::cout << "Testing vector: " << v << std::endl;

test_general(v);

CoordType sqr_mag = v.sqrMag();

assert(Equal(std::sqrt(sqr_mag), v.mag()));

assert(Equal(sqr_mag, Dot(v, v)));

Vector<dim> v1, v2;

v1.zero();
  v1[0] = 1;
  for(int i = 0; i < dim; ++i)
    v2[i] = 1;

const int steps = 8;

Vector<dim> vcopy = v;

for(int j = 0; j < dim; ++j) {
    for(int i = 0; i < steps; ++i) {
      vcopy.rotate(v1, v2, 2 * numeric_constants<CoordType>::pi() / steps);
//      std::cout << vcopy << std::endl;
      assert(Equal(sqr_mag, vcopy.sqrMag()));
    }

for(int i = 0; i < dim; ++i)
      assert(Equal(v[i], vcopy[i]));

v2 -= v1 / 2; // operator-=(), operator/()

int k = (j < dim - 1) ? j + 1 : 0;
    v1.rotate(j, k, numeric_constants<CoordType>::pi() / 2);
  }

v2 *= 2; // operator*=()

for(int i = 0; i < dim; ++i)
    assert(Equal(v2[i], 1.0f));

// operator+(), operator-(), operator*() (pre and post), operator/()
  CoordType check = Dot((v1 + v2) * 5 - v2 / 4, 2 * v2);
  assert(Equal((10.0f + dim * 38.0f / 4.0f), check));

Vector<dim> v3 = v;
  v3 += v;
  v3 *= 2;
  v3 -= 2 * v;
  v3 /= 2;
  assert(v == v3);
  for(int i = 0; i < dim; ++i)
    assert(v[i] == v3[i]); // const and non-const operator[]()

CoordType check_mag = v.sloppyMag() / v.mag();

assert(1 - numeric_constants<CoordType>::epsilon() < check_mag);
  assert(check_mag < Vector<dim>::sloppyMagMax() + numeric_constants<CoordType>::epsilon());

//Check that an invalid vector isn't equal to a valid vector, even if the values are equal
  Vector<dim> invalid_1;
  Vector<dim> invalid_2;
  for (size_t i = 0; i < dim; ++i) {
      invalid_1[i] = 0.0;
      invalid_2[i] = 0.0;
  }
  assert(invalid_1 != Vector<dim>::ZERO());

//Two invalid points are never equal
  assert(invalid_1 != invalid_2);

// Still need Dot(), Angle(), normalize(), mirror()
}

int main()
{
  Vector<2> v2(1, -1);
  Vector<3> v3(1, -1, numeric_constants<CoordType>::sqrt2());

test_vector(v2);
  test_vector(v3);
  
  Vector<2> zero2 = Vector<2>::ZERO();
  assert(zero2.x() == 0 && zero2.y() == 0);
  Vector<3> zero3 = Vector<3>::ZERO();
  assert(zero3.x() == 0 && zero3.y() == 0 && zero3.z() == 0);

assert(v2.sloppyMag() / v2.mag() < Vector<2>::sloppyMagMax());
  assert(v3.sloppyMag() / v3.mag() < Vector<3>::sloppyMagMax());

v2.sloppyNorm(1);
  v3.sloppyNorm(1);

assert((Vector<3>(1, 0, 0).rotate(Cross(Vector<3>(1, 0, 0), Vector<3>(0, 1, 0)),
	 numeric_constants<CoordType>::pi() / 2) - Vector<3>(0, 1, 0)).sqrMag()
	 < numeric_constants<CoordType>::epsilon() * numeric_constants<CoordType>::epsilon());

// Need 2D+3D stuff

return 0;
}
07070100000066000081A40000000200000002000000015D8693EF00000928000000000000000000000000000000000000002A00000000wfmath-1569100783.d0f8a54/wfmath/wfmath.h// -*-C++-*-
// wfmath.h (General include file for the WFMath library)
//
//  The WorldForge Project
//  Copyright (C) 2001  The WorldForge Project
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

// Author: Ron Steinke
// Created: 2001-12-7

#ifndef WFMATH_WFMATH_H
#define WFMATH_WFMATH_H

// Simple stuff
#include <wfmath/error.h>
#include <wfmath/const.h>
// Basic types
#include <wfmath/vector.h>
#include <wfmath/rotmatrix.h>
#include <wfmath/point.h>
#include <wfmath/quaternion.h>
// Shape types
#include <wfmath/axisbox.h>
#include <wfmath/ball.h>
#include <wfmath/segment.h>
#include <wfmath/rotbox.h>
#include <wfmath/polygon.h>
// Shape intersection functions
#include <wfmath/intersect.h>
// Probability and statistics
#include <wfmath/probability.h>
#include <wfmath/timestamp.h>
#include <wfmath/randgen.h>
#include <wfmath/shuffle.h>
// iostreams and strings
#include <wfmath/stream.h>
#include <wfmath/int_to_string.h>

// Don't include atlasconv.h, which includes <Atlas/Message/Object.h>
// There is, however, no linker dependency on atlas in the library,
// so it is quite safe to use WFMath without atlas, as long as you
// don't include this header

// This file doesn't include basis.h, which only contains declarations
// for some functions which are used in vector.cpp and point.cpp

// Any header file "foo_funcs.h" is automatically included in "foo.h",
// so those files are not listed here. Similarly, "intersect_decls.h"
// is included in "intersect.h" (among other places).

#endif // WFMATH_WFMATH_H
07070100000067000081A40000000200000002000000015D8693EF000009B9000000000000000000000000000000000000003100000000wfmath-1569100783.d0f8a54/wfmath/wrapped_array.h

#ifndef WFMATH_WRAPPED_ARRAY_H
#define WFMATH_WRAPPED_ARRAY_H

namespace WFMath { namespace _miniball {
   
   template <int d>
   class Wrapped_array {
       private:
           double coord [d];
   
       public:
           // default
           Wrapped_array()
           {}
   
           // copy from Wrapped_array
           Wrapped_array (const Wrapped_array& p)
           {
               for (int i=0; i<d; ++i)
                   coord[i] = p.coord[i];
           }
   
           // copy from double*
           Wrapped_array (const double* p)
           {
               for (int i=0; i<d; ++i)
                   coord[i] = p[i];
           }
   
           // assignment
           Wrapped_array& operator = (const Wrapped_array& p)
           {
               for (int i=0; i<d; ++i)
                   coord[i] = p.coord[i];
               return *this;
           }
   
           // coordinate access
           double& operator [] (int i)
           {
               return coord[i];
           }
           const double& operator [] (int i) const
           {
               return coord[i];
           }
           const double* begin() const
           {
               return coord;
           }
           const double* end() const
           {
               return coord+d;
           }
   };
   
}} // namespace WFMath::_miniball

#endif // WFMATH_WRAPPED_ARRAY_H
07070100000068000081A40000000200000002000000015D8693EF0000077D000000000000000000000000000000000000002800000000wfmath-1569100783.d0f8a54/wfmath/zero.h//  The WorldForge Project
//  Copyright (C) 2009  The WorldForge Project
//
//  Author: Erik Hjortsberg <erik@worlforge.org, (C) 2009
//
//  This program is free software; you can redistribute it and/or modify
//  it under the terms of the GNU General Public License as published by
//  the Free Software Foundation; either version 2 of the License, or
//  (at your option) any later version.
//
//  This program is distributed in the hope that it will be useful,
//  but WITHOUT ANY WARRANTY; without even the implied warranty of
//  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
//  GNU General Public License for more details.
//
//  You should have received a copy of the GNU General Public License
//  along with this program; if not, write to the Free Software
//  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
//
//  For information about WorldForge and its authors, please contact
//  the Worldforge Web Site at http://www.worldforge.org.

#ifndef WFMATH_ZERO_H
#define WFMATH_ZERO_H

namespace WFMath {

/**
@brief Utility class for providing zero primitives. This class will only work with simple structures such as Vector or Point which provide a m_elem structure.
In order for it to access the m_elem structure it must be declared as a friend class of the class it will provide an instance of.
@author Erik Hjortsberg <erik@worldforge.org>
*/
template<typename Shape>
class ZeroPrimitive
{
public:
/**
@brief Ctor.
An instance of Shape with zero values will be created at construction time.
@param dim The dimensions of the shape.
*/
explicit ZeroPrimitive(int dim) : m_shape()
{
  for (int i = 0; i < dim; ++i) {
    m_shape.m_elem[i] = 0;
  }
  m_shape.m_valid = true;
}

/**
@brief Gets the zeroed shape.
*/
const Shape& getShape() const
{
	return m_shape;
}

private:
/**
@brief The interal zeroed shape.
*/
Shape m_shape;
};
}

#endif //WFMATH_ZERO_H
07070100000000000000000000000000000000000000010000000000000000000000000000000000000000000000000000000B00000000TRAILER!!!1467 blocks

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