Detailed Description

The Expanding-Polytope Algorithm.

#include <EPA.h>

Classes
class	EPA_Edge
	Class storing Information about an Edge of the EPA-Polytope. More...

class	EPA_Triangle
	Class storing Information about a triangular facette (Triangle) of the EPA-Polytope. More...

class	EPA_TriangleComp
	Compare Triangles by their closest points to sort the triangle heap. More...

Public Member Functions
Query functions
bool	doEPAcontactThreshold (Support &geom1, Support &geom2, const GJK &gjk, Vec3 &normal, Vec3 &contactPoint, real_t &penetrationDepth)
	Does an EPA computation with contactthreshold added. More...

bool	doEPAcontactThreshold (Support &geom1, Support &geom2, const GJK &gjk, Vec3 &normal, Vec3 &contactPoint, real_t &penetrationDepth, real_t eps_rel)
	Does an EPA computation with contactThreshold added. More...

bool	doEPAmargin (Support &geom1, Support &geom2, const GJK &gjk, Vec3 &normal, Vec3 &contactPoint, real_t &penetrationDepth, real_t margin)
	Does an EPA computation with margin added. More...

bool	doEPA (Support &geom1, Support &geom2, const GJK &gjk, Vec3 &normal, Vec3 &contactPoint, real_t &penetrationDepth, real_t margin, real_t eps_rel)
	Does an epa computation with contact margin added and specified relative error. More...

Getter and Setter functions
void	setMaxSupportPoints (size_t maxSupportPoints)

size_t	getMaxSupportPoints ()

void	setMaxTriangles (size_t maxTriangles)

size_t	getMaxTriangles ()

int	getNumIterations () const

bool	useSphereOptimization () const

void	useSphereOptimization (const bool useIt)

Static Public Attributes
static constexpr real_t	contactThreshold = real_t(1e-8)

Private Types
using	EPA_EntryBuffer = std::vector< EPA_Triangle >

using	EPA_EntryHeap = std::vector< EPA_Triangle * >

using	EPA_EdgeBuffer = std::vector< EPA_Edge >

Utility functions
size_t	maxSupportPoints_ = 100

size_t	maxTriangles_ = 200

int	numIterations_ = 0

bool	bUseSphereOptimization_ = false

void	pushSupportMargin (const Support &geom1, const Support &geom2, const Vec3 &dir, const real_t margin, std::vector< Vec3 > &epaVolume, std::vector< Vec3 > &supportA, std::vector< Vec3 > &supportB)
	Calculates a support point of a body extended by threshold. More...

void	replaceSupportMargin (const Support &geom1, const Support &geom2, const Vec3 &dir, const real_t margin, std::vector< Vec3 > &epaVolume, std::vector< Vec3 > &supportA, std::vector< Vec3 > &supportB, size_t indexToReplace)
	Calculates a support point of a body extended by threshold. More...

void	removeSupportMargin (std::vector< Vec3 > &epaVolume, std::vector< Vec3 > &supportA, std::vector< Vec3 > &supportB)
	Removes a support point from the volume. More...

bool	originInTetrahedron (const Vec3 &A, const Vec3 &B, const Vec3 &C, const Vec3 &D)
	TODO. More...

bool	originInTetrahedronVolumeMethod (const Vec3 &A, const Vec3 &B, const Vec3 &C, const Vec3 &D)
	Returns true, if the origin lies in the tetrahedron ABCD. More...

bool	pointInTetrahedron (const Vec3 &A, const Vec3 &B, const Vec3 &C, const Vec3 &D, const Vec3 &point)
	Returns true, if a point lies in the tetrahedron ABCD. More...

bool	searchTetrahedron (Support &geom1, Support &geom2, std::vector< Vec3 > &epaVolume, std::vector< Vec3 > &supportA, std::vector< Vec3 > &supportB, EPA_EntryBuffer &entryBuffer, real_t margin)
	Search a tetrahedron that contains the origin. More...

void	createInitialTetrahedron (size_t top, size_t frontLeft, size_t frontRight, size_t back, std::vector< Vec3 > &epaVolume, EPA_EntryBuffer &entryBuffer)
	TODO top, frontLeft ... More...

void	createInitialSimplex (size_t numPoints, Support &geom1, Support &geom2, std::vector< Vec3 > &supportA, std::vector< Vec3 > &supportB, std::vector< Vec3 > &epaVolume, EPA_EntryBuffer &entryBuffer, real_t margin)
	Create a starting tetrahedron for EPA, from the GJK Simplex. More...

real_t	calculateCircle (const Vec3 &A, const Vec3 &B, const Vec3 &C, const Vec3 &D, Vec3 &center)
	Calculate a Circle through the for Points A, B, C, D. More...

Member Typedef Documentation

◆ EPA_EdgeBuffer

using walberla::mesa_pd::collision_detection::EPA::EPA_EdgeBuffer = std::vector<EPA_Edge>

private

◆ EPA_EntryBuffer

using walberla::mesa_pd::collision_detection::EPA::EPA_EntryBuffer = std::vector<EPA_Triangle>

private

◆ EPA_EntryHeap

using walberla::mesa_pd::collision_detection::EPA::EPA_EntryHeap = std::vector<EPA_Triangle *>

private

Member Function Documentation

◆ calculateCircle()

real_t walberla::mesa_pd::collision_detection::EPA::calculateCircle	(	const Vec3 &	A,
		const Vec3 &	B,
		const Vec3 &	C,
		const Vec3 &	D,
		Vec3 &	center
	)

inlineprivate

Calculate a Circle through the for Points A, B, C, D.

Parameters

center Contains the center point of the circle after the call

Returns: The squared radius of the circle or a negative value if no such circle exists.

◆ createInitialSimplex()

void walberla::mesa_pd::collision_detection::EPA::createInitialSimplex	(	size_t	numPoints,
		Support &	geom1,
		Support &	geom2,
		std::vector< Vec3 > &	supportA,
		std::vector< Vec3 > &	supportB,
		std::vector< Vec3 > &	epaVolume,
		EPA_EntryBuffer &	entryBuffer,
		real_t	margin
	)

inlineprivate

Create a starting tetrahedron for EPA, from the GJK Simplex.

◆ createInitialTetrahedron()

void walberla::mesa_pd::collision_detection::EPA::createInitialTetrahedron	(	size_t	top,
		size_t	frontLeft,
		size_t	frontRight,
		size_t	back,
		std::vector< Vec3 > &	epaVolume,
		EPA_EntryBuffer &	entryBuffer
	)

inlineprivate

TODO top, frontLeft ...

are indices

◆ doEPA()

bool walberla::mesa_pd::collision_detection::EPA::doEPA	(	Support &	geom1,
		Support &	geom2,
		const GJK &	gjk,
		Vec3 &	normal,
		Vec3 &	contactPoint,
		real_t &	penetrationDepth,
		real_t	margin,
		real_t	eps_rel
	)

Does an epa computation with contact margin added and specified relative error.

◆ doEPAcontactThreshold() [1/2]

bool walberla::mesa_pd::collision_detection::EPA::doEPAcontactThreshold	(	Support &	geom1,
		Support &	geom2,
		const GJK &	gjk,
		Vec3 &	retNormal,
		Vec3 &	contactPoint,
		real_t &	penetrationDepth
	)

Does an EPA computation with contactthreshold added.

Use Default relative Error.

◆ doEPAcontactThreshold() [2/2]

bool walberla::mesa_pd::collision_detection::EPA::doEPAcontactThreshold	(	Support &	geom1,
		Support &	geom2,
		const GJK &	gjk,
		Vec3 &	retNormal,
		Vec3 &	contactPoint,
		real_t &	penetrationDepth,
		real_t	eps_rel
	)

Does an EPA computation with contactThreshold added.

Relative Error can be specified.

◆ doEPAmargin()

bool walberla::mesa_pd::collision_detection::EPA::doEPAmargin	(	Support &	geom1,
		Support &	geom2,
		const GJK &	gjk,
		Vec3 &	retNormal,
		Vec3 &	contactPoint,
		real_t &	penetrationDepth,
		real_t	margin
	)

Does an EPA computation with margin added.

Use Default relative Error.

◆ getMaxSupportPoints()

size_t walberla::mesa_pd::collision_detection::EPA::getMaxSupportPoints ( )

inline

◆ getMaxTriangles()

size_t walberla::mesa_pd::collision_detection::EPA::getMaxTriangles ( )

inline

◆ getNumIterations()

int walberla::mesa_pd::collision_detection::EPA::getNumIterations ( ) const

inline

◆ originInTetrahedron()

bool walberla::mesa_pd::collision_detection::EPA::originInTetrahedron	(	const Vec3 &	p0,
		const Vec3 &	p1,
		const Vec3 &	p2,
		const Vec3 &	p3
	)

inlineprivate

TODO.

see Book "collision detection in interactive 3D environments" page161 ATTENTION seems to have no consistent behavior on the surface and vertices

◆ originInTetrahedronVolumeMethod()

bool walberla::mesa_pd::collision_detection::EPA::originInTetrahedronVolumeMethod	(	const Vec3 &	A,
		const Vec3 &	B,
		const Vec3 &	C,
		const Vec3 &	D
	)

inlineprivate

Returns true, if the origin lies in the tetrahedron ABCD.

◆ pointInTetrahedron()

bool walberla::mesa_pd::collision_detection::EPA::pointInTetrahedron	(	const Vec3 &	A,
		const Vec3 &	B,
		const Vec3 &	C,
		const Vec3 &	D,
		const Vec3 &	point
	)

inlineprivate

Returns true, if a point lies in the tetrahedron ABCD.

Parameters

point The point to be checked for containment.

◆ pushSupportMargin()

void walberla::mesa_pd::collision_detection::EPA::pushSupportMargin	(	const Support &	geom1,
		const Support &	geom2,
		const Vec3 &	dir,
		const real_t	margin,
		std::vector< Vec3 > &	epaVolume,
		std::vector< Vec3 > &	supportA,
		std::vector< Vec3 > &	supportB
	)

inlineprivate

Calculates a support point of a body extended by threshold.

Adds this support and the base points at bodies A and B to the vector.

Parameters

geom1	The body A.
geom2	The body B.
dir	The support point direction.
margin	Extension of the Body.

◆ removeSupportMargin()

void walberla::mesa_pd::collision_detection::EPA::removeSupportMargin	(	std::vector< Vec3 > &	epaVolume,
		std::vector< Vec3 > &	supportA,
		std::vector< Vec3 > &	supportB
	)

inlineprivate

Removes a support point from the volume.

◆ replaceSupportMargin()

void walberla::mesa_pd::collision_detection::EPA::replaceSupportMargin	(	const Support &	geom1,
		const Support &	geom2,
		const Vec3 &	dir,
		const real_t	margin,
		std::vector< Vec3 > &	epaVolume,
		std::vector< Vec3 > &	supportA,
		std::vector< Vec3 > &	supportB,
		size_t	indexToReplace
	)

inlineprivate

Calculates a support point of a body extended by threshold.

Replaces the old value in the vectors at "IndexToReplace" with this support and the base points at bodies A and B.

Parameters

geom1	The body A.
geom2	The body B.
dir	The support point direction.
margin	Extension of the Body.

◆ searchTetrahedron()

bool walberla::mesa_pd::collision_detection::EPA::searchTetrahedron	(	Support &	geom1,
		Support &	geom2,
		std::vector< Vec3 > &	epaVolume,
		std::vector< Vec3 > &	supportA,
		std::vector< Vec3 > &	supportB,
		EPA_EntryBuffer &	entryBuffer,
		real_t	margin
	)

inlineprivate

Search a tetrahedron that contains the origin.

Start with four arbitrary support points in epaVolume that form a tetrahedron. (This needn't contain the origin.) This algorithm will search and return an altered tetrahedron containing the origin. Do only use this function if the object/body certainly contains the origin!

Returns: True, if a tetrahedron was found. False if search has been aborted.

◆ setMaxSupportPoints()

void walberla::mesa_pd::collision_detection::EPA::setMaxSupportPoints ( size_t maxSupportPoints )

inline

◆ setMaxTriangles()

void walberla::mesa_pd::collision_detection::EPA::setMaxTriangles ( size_t maxTriangles )

inline

◆ useSphereOptimization() [1/2]

bool walberla::mesa_pd::collision_detection::EPA::useSphereOptimization ( ) const

inline

◆ useSphereOptimization() [2/2]

void walberla::mesa_pd::collision_detection::EPA::useSphereOptimization ( const bool useIt )

inline

Member Data Documentation

◆ bUseSphereOptimization_

bool walberla::mesa_pd::collision_detection::EPA::bUseSphereOptimization_ = false

private

◆ contactThreshold

constexpr real_t walberla::mesa_pd::collision_detection::EPA::contactThreshold = real_t(1e-8)

staticconstexpr

◆ maxSupportPoints_

size_t walberla::mesa_pd::collision_detection::EPA::maxSupportPoints_ = 100

private

◆ maxTriangles_

size_t walberla::mesa_pd::collision_detection::EPA::maxTriangles_ = 200

private

◆ numIterations_

int walberla::mesa_pd::collision_detection::EPA::numIterations_ = 0

private

The documentation for this class was generated from the following files:

/builds/administration/walberla-website/walberla/src/mesa_pd/collision_detection/EPA.h
/builds/administration/walberla-website/walberla/src/mesa_pd/collision_detection/EPA.cpp

Detailed Description

Classes

Public Member Functions

Static Public Attributes

Private Types

Utility functions

Member Typedef Documentation

◆ EPA_EdgeBuffer

◆ EPA_EntryBuffer

◆ EPA_EntryHeap

Member Function Documentation

◆ calculateCircle()

◆ createInitialSimplex()

◆ createInitialTetrahedron()

◆ doEPA()

◆ doEPAcontactThreshold() [1/2]

◆ doEPAcontactThreshold() [2/2]

◆ doEPAmargin()

◆ getMaxSupportPoints()

◆ getMaxTriangles()

◆ getNumIterations()

◆ originInTetrahedron()

◆ originInTetrahedronVolumeMethod()

◆ pointInTetrahedron()

◆ pushSupportMargin()

◆ removeSupportMargin()

◆ replaceSupportMargin()

◆ searchTetrahedron()

◆ setMaxSupportPoints()

◆ setMaxTriangles()

◆ useSphereOptimization() [1/2]

◆ useSphereOptimization() [2/2]

Member Data Documentation

◆ bUseSphereOptimization_

◆ contactThreshold

◆ maxSupportPoints_

◆ maxTriangles_

◆ numIterations_