Model a polytope using its two equivalent definitions : the convex hull and the half-space intersection. More...

#include <Polytope_Rn.h>

Inheritance diagram for Polytope_Rn:

Collaboration diagram for Polytope_Rn:

Public Member Functions
	Polytope_Rn ()
	Constructor for polytopes i.e. bounded convex polyhedra. More...

virtual	~Polytope_Rn ()
	Destructor. More...

virtual bool	isBounded () const
	Tell whether this polyhedron is bounded or not, polytopes are bounded. More...

virtual unsigned int	neigbourhoodCondition () const
	Two vertices are neighbours in a polytope <=> they share at least (n-1) facets. More...

virtual unsigned int	numberOfGeneratorsPerFacet () const
	Each facet in a polytope has got n vertices. More...

virtual void	createBoundingSimplex (double M)
	Initialize the truncating algorithm building a M-sized simplex around the polytope. More...

virtual void	createBoundingBox (double M)
	Initialize the truncating algorithm building a M-sized bounding box around the polytope. More...

virtual bool	checkEdges () const
	Always true in the polyhedral cone case. More...

bool	checkEqualityOfVertices (const boost::shared_ptr< Polytope_Rn > &B, bool printOnScreen=false) const
	Check whether two V-polytopes are identical Check whether the sets of vertices of A and B are equal. More...

virtual double	createTruncatedGenerator (const boost::shared_ptr< Generator_Rn_SD > &in, const boost::shared_ptr< Generator_Rn_SD > &out, boost::shared_ptr< Generator_Rn_SD > newV, double ay, double az, double b=0.) const
	This is the intersection vertex in the truncating algorithm, defined by the intersection between an edge and an hyperplane. More...

boost::shared_ptr< PolyhedralCone_Rn >	getPrimalCone (unsigned int u, const std::vector< unsigned int > &allNgb) const

boost::shared_ptr< PolyhedralCone_Rn >	getPrimalCone (unsigned int i) const

boost::shared_ptr< Polytope_Rn >	sum (const boost::shared_ptr< Polytope_Rn > &pol2sum)

boost::shared_ptr< Polytope_Rn >	intersect (const boost::shared_ptr< Polytope_Rn > &pol2intersect)

bool	isIncluded (const boost::shared_ptr< Polytope_Rn > &B) const

bool	isIncluded (const boost::shared_ptr< Polytope_Rn > &B, double &minmaxDistance) const

std::string	getName () const

std::string	getFileExtension () const

Public Member Functions inherited from PolyhedralCone_Rn
	PolyhedralCone_Rn ()
	Constructor. More...

	PolyhedralCone_Rn (const PolyhedralCone_Rn &A)
	Constructor. More...

virtual	~PolyhedralCone_Rn ()
	Destructor. More...

virtual unsigned int	dimension () const
	Return the space dimension. More...

void	reset ()
	Remove all half-spaces and generators. More...

unsigned int	numberOfHalfSpaces () const
	Get the total number of half-spaces. More...

boost::shared_ptr< HalfSpace_Rn >	addHalfSpace (boost::shared_ptr< HalfSpace_Rn > hs, bool check=false)
	Add the current half-space in its list. More...

void	removeHalfSpaceFromListAndGenerators (const boost::shared_ptr< HalfSpace_Rn > &hs)
	Remove the half-space given as parameter from its list and from all generators. More...

void	removeHalfSpace (unsigned int j)
	Remove the half-space number j from its list. More...

void	removeHalfSpaces (const std::set< boost::shared_ptr< HalfSpace_Rn > > &setOfRedundantHS)
	Remove the half-space number j from its list. More...

unsigned int	getHalfSpaceNumber (const boost::shared_ptr< HalfSpace_Rn > &F) const
	For a given half-space, return its list index. More...

const boost::shared_ptr< HalfSpace_Rn > &	getHalfSpace (unsigned int i) const
	Return the i-th half-space. More...

listOfGeometricObjects< boost::shared_ptr< HalfSpace_Rn > > &	getListOfHalfSpaces ()
	Return the list of half-spaces. More...

const listOfGeometricObjects< boost::shared_ptr< HalfSpace_Rn > > &	getListOfHalfSpaces () const
	Return the list of half-spaces. More...

void	setListOfHalfSpaces (const listOfGeometricObjects< boost::shared_ptr< HalfSpace_Rn > > &hsList)
	Set a new list of half-spaces. More...

unsigned int	numberOfGenerators () const
	Give the total number of generators. More...

void	addGenerator (boost::shared_ptr< Generator_Rn > vx)
	Add the given generator. More...

const boost::shared_ptr< Generator_Rn > &	getGenerator (unsigned int i) const
	Return the i-th generator. More...

unsigned int	getGeneratorNumber (boost::shared_ptr< Generator_Rn > G) const
	For a given generator, return its list index. More...

const listOfGeometricObjects< boost::shared_ptr< Generator_Rn > > &	getListOfGenerators () const
	Return the list of generators. More...

unsigned int	getListOfGeneratorsSD (std::vector< boost::shared_ptr< Generator_Rn_SD > > &currentListOfGeneratorsSD) const

void	setListOfGeneratorsSD (const std::vector< boost::shared_ptr< Generator_Rn_SD > > &gnList)
	Set a new list of generators. The list of half-spaces should have been previously set. More...

void	relocateGenerators ()

void	setListOfGenerators (const listOfGeometricObjects< boost::shared_ptr< Generator_Rn > > &gnList)
	Set a new list of generators. More...

bool	checkNeighbours (const boost::shared_ptr< Generator_Rn > &V1, const boost::shared_ptr< Generator_Rn > &V2, std::vector< boost::shared_ptr< HalfSpace_Rn > > &commonFacets, const std::set< boost::shared_ptr< HalfSpace_Rn > > &listOfRedundantHS) const

bool	isIncluded (const boost::shared_ptr< PolyhedralCone_Rn > &B) const
	Test whether the current polytope V-description is inside the polytope B H-description. More...

bool	checkNeighbours (const boost::shared_ptr< Generator_Rn > &V1, const boost::shared_ptr< Generator_Rn > &V2, std::vector< boost::shared_ptr< HalfSpace_Rn > > &commonFacets, unsigned int topologicalCode=1) const

bool	checkNeighbours (const boost::shared_ptr< Generator_Rn > &V1, const boost::shared_ptr< Generator_Rn > &V2, std::vector< HalfSpace_Rn * > &commonFacets, unsigned int topologicalCode=1) const
	Check for polytopes that vertices share (n-1) facets. For polyhedral cones, it must check that vectors share (n-2) facets. More...

bool	checkNeighbours (const boost::shared_ptr< Generator_Rn_SD > &genIn, const boost::shared_ptr< Generator_Rn_SD > &genOut, std::vector< unsigned int > &commonFacets) const
	Check for polytopes that vertices share (n-1) facets. For polyhedral cones, it must check that vectors share (n-2) facets. More...

bool	checkNeighboursWithHSnumbers (const boost::shared_ptr< Generator_Rn > &V1, const boost::shared_ptr< Generator_Rn > &V2, std::vector< HalfSpace_Rn * > &commonFacets, const std::set< boost::shared_ptr< HalfSpace_Rn > > &listOfRedundantHS, unsigned int topologicalCode=1) const
	Check for polytopes that vertices share (n-1) facets. For polyhedral cones, it must check that vectors share (n-2) facets. More...

void	fillNeighbourMatrix (std::vector< std::vector< unsigned int > > &neighboursA, unsigned int topologicalCode=1) const

void	fillIrredundantNeighbourMatrix (std::vector< std::vector< unsigned int > > &neighboursA) const

virtual bool	checkTopologyAndGeometry (bool check_all=false) const
	As stated by Komei Fukuda "the complexity of the polyhedral verification problem is unknown. Is it in P or in coNP-complete?" So only 3 verifications are made in Rⁿ : More...

HalfSpace_Rn::State	checkPoint (const Point_Rn &thisPoint) const
	Check a point state against the whole polyhedron. More...

HalfSpace_Rn::State	checkGenerator (const boost::shared_ptr< Generator_Rn > &thisGen) const

HalfSpace_Rn::State	checkPoint (const boost::shared_ptr< Generator_Rn > &point, const boost::shared_ptr< HalfSpace_Rn > &halfSpace, double halfSpaceNorm) const
	Check a point state against a half-space. More...

bool	checkDuplicateGenerators (unsigned int &a, unsigned int &b)
	Make sure no duplicate generators are stored. More...

void	checkGenerator (unsigned int vtxNumber, std::ostream &this_ostream) const
	Compute all distance from the current point to all half-spaces frontiers. More...

bool	checkGenerators (const listOfGeometricObjects< boost::shared_ptr< Generator_Rn > > &listGenA, const listOfGeometricObjects< boost::shared_ptr< HalfSpace_Rn > > &listHSB, bool check_all=false) const
	Check the number of facets per generator and make sure it is compliant with its current constraints. It must verify the following property : More...

double	checkVolumeEquality (const boost::shared_ptr< PolyhedralCone_Rn > &B) const

void	removeGenerator (unsigned int j)
	Remove the generator number j from its list. More...

void	removeGenerators (const std::set< boost::shared_ptr< Generator_Rn > > &setToRemove)
	Remove the generators contained in setToRemove. More...

void	checkFacet (unsigned int fctNumber, std::ostream &this_ostream) const

bool	checkFacets () const
	Detect redundant half spaces and make sure each facet has the right number of generators. More...

bool	checkEquality (const boost::shared_ptr< PolyhedralCone_Rn > &B, bool getFaceMapping=false) const

void	getGeneratorsPerFacet (std::vector< std::vector< unsigned int > > &listOfGeneratorsPerFacet) const
	Get topological connections: for each facet, list its generators. More...

void	negate ()
	Compute the symmetrical polyhedral cone. More...

boost::shared_ptr< PolyhedralCone_Rn >	computeDualPolyhedralCone () const
	Create the intersection edge in the truncating algorithm. It is defined by the intersection between a 2-face and a hyperplane, i.e. a (n-1)-face. The new egde is given by this formula where H is the current half space : More...

virtual void	dump (std::ostream &this_ostream) const
	Dump the polyhedral structure on the stream passed as an argument. More...

void	dumpScilab (std::ostream &this_ostream) const
	Dump the generators on on the stream passed as an argument for outputting in Scilab. More...

Static Public Member Functions
static boost::shared_ptr< Polytope_Rn >	create ()
	Return s shared pointer on an empty polytope. More...

Additional Inherited Members
Protected Attributes inherited from PolyhedralCone_Rn
listOfGeometricObjects< boost::shared_ptr< HalfSpace_Rn > >	_listOfHalfSpaces
	The list of half-spaces defining the polyhedron. More...

listOfGeometricObjects< boost::shared_ptr< Generator_Rn > >	_listOfGenerators
	The convex hull of connected points. More...

Detailed Description

Model a polytope using its two equivalent definitions : the convex hull and the half-space intersection.

Definition at line 36 of file Polytope_Rn.h.

Constructor & Destructor Documentation

◆ Polytope_Rn()

Polytope_Rn::Polytope_Rn ( )

inline

Constructor for polytopes i.e. bounded convex polyhedra.

Definition at line 40 of file Polytope_Rn.h.

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◆ ~Polytope_Rn()

virtual Polytope_Rn::~Polytope_Rn ( )

inlinevirtual

Destructor.

Definition at line 43 of file Polytope_Rn.h.

Member Function Documentation

◆ checkEdges()

bool Polytope_Rn::checkEdges ( ) const

virtual

Always true in the polyhedral cone case.

Reimplemented from PolyhedralCone_Rn.

Definition at line 32 of file Polytope_Rn.cpp.

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◆ checkEqualityOfVertices()

bool Polytope_Rn::checkEqualityOfVertices	(	const boost::shared_ptr< Polytope_Rn > &	B,
		bool	printOnScreen = `false`
	)		const

Check whether two V-polytopes are identical Check whether the sets of vertices of A and B are equal.

Parameters

A	The V-polytope

Returns: true if
\[ \mathcal{V}_A = \mathcal{V}_B \]
, false otherwise.

Definition at line 242 of file Polytope_Rn.cpp.

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◆ create()

static boost::shared_ptr<Polytope_Rn> Polytope_Rn::create ( )

inlinestatic

Return s shared pointer on an empty polytope.

Definition at line 46 of file Polytope_Rn.h.

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◆ createBoundingBox()

void Polytope_Rn::createBoundingBox ( double M )

virtual

Initialize the truncating algorithm building a M-sized bounding box around the polytope.

When only the polytope facets are given, include it in a huge cube that we are going to truncate.

Reimplemented from PolyhedralCone_Rn.

Definition at line 154 of file Polytope_Rn.cpp.

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◆ createBoundingSimplex()

void Polytope_Rn::createBoundingSimplex ( double M )

virtual

Initialize the truncating algorithm building a M-sized simplex around the polytope.

When only the polytope facets are given, include it in a huge simplex that we are going to truncate.

Reimplemented from PolyhedralCone_Rn.

Definition at line 79 of file Polytope_Rn.cpp.

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◆ createTruncatedGenerator()

double Polytope_Rn::createTruncatedGenerator	(	const boost::shared_ptr< Generator_Rn_SD > &	in,
		const boost::shared_ptr< Generator_Rn_SD > &	out,
		boost::shared_ptr< Generator_Rn_SD >	newV,
		double	ay,
		double	az,
		double	b = `0.`
	)		const

virtual

This is the intersection vertex in the truncating algorithm, defined by the intersection between an edge and an hyperplane.

This is the intersection vertex in the truncating algorithm. It is defined by the intersection between an edge, i.e. a 1-face, and an hyperplane, i.e. a (n-1)-face.

Reimplemented from PolyhedralCone_Rn.

Definition at line 226 of file Polytope_Rn.cpp.

◆ getFileExtension()

std::string Polytope_Rn::getFileExtension ( ) const

inline

Definition at line 146 of file Polytope_Rn.h.

◆ getName()

std::string Polytope_Rn::getName ( ) const

inline

Definition at line 144 of file Polytope_Rn.h.

◆ getPrimalCone() [1/2]

boost::shared_ptr<PolyhedralCone_Rn> Polytope_Rn::getPrimalCone ( unsigned int i ) const

Return the i-th primal cone C(i) of the polytope A. If A has k vertices then \( A = \displaystyle{ \bigcap_{i=1}^k C(i) }\) where \( C(i) = \displaystyle{ \bigcap_{i=1}^l \bar{H}_i^+ } \)

◆ getPrimalCone() [2/2]

boost::shared_ptr< PolyhedralCone_Rn > Polytope_Rn::getPrimalCone	(	unsigned int	u,
		const std::vector< unsigned int > &	allNgb
	)		const

Definition at line 284 of file Polytope_Rn.cpp.

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◆ intersect()

boost::shared_ptr< Polytope_Rn > Polytope_Rn::intersect ( const boost::shared_ptr< Polytope_Rn > & pol2intersect )

Definition at line 328 of file Polytope_Rn.cpp.

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◆ isBounded()

virtual bool Polytope_Rn::isBounded ( ) const

inlinevirtual

Tell whether this polyhedron is bounded or not, polytopes are bounded.

Reimplemented from PolyhedralCone_Rn.

Definition at line 49 of file Polytope_Rn.h.

◆ isIncluded() [1/2]

bool Polytope_Rn::isIncluded ( const boost::shared_ptr< Polytope_Rn > & B ) const

inline

Definition at line 88 of file Polytope_Rn.h.

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◆ isIncluded() [2/2]

bool Polytope_Rn::isIncluded	(	const boost::shared_ptr< Polytope_Rn > &	B,
		double &	minmaxDistance
	)		const

inline

Definition at line 103 of file Polytope_Rn.h.

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◆ neigbourhoodCondition()

virtual unsigned int Polytope_Rn::neigbourhoodCondition ( ) const

inlinevirtual

Two vertices are neighbours in a polytope <=> they share at least (n-1) facets.

Reimplemented from PolyhedralCone_Rn.

Definition at line 52 of file Polytope_Rn.h.

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◆ numberOfGeneratorsPerFacet()

virtual unsigned int Polytope_Rn::numberOfGeneratorsPerFacet ( ) const

inlinevirtual

Each facet in a polytope has got n vertices.

Reimplemented from PolyhedralCone_Rn.

Definition at line 55 of file Polytope_Rn.h.

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◆ sum()

boost::shared_ptr< Polytope_Rn > Polytope_Rn::sum ( const boost::shared_ptr< Polytope_Rn > & pol2sum )

Definition at line 320 of file Polytope_Rn.cpp.

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

/mnt/c/Users/vindelos/Documents/TEST/TEST/co/politopix/trunk/Polytope_Rn.h
/mnt/c/Users/vindelos/Documents/TEST/TEST/co/politopix/trunk/Polytope_Rn.cpp

Public Member Functions

Static Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Polytope_Rn()

◆ ~Polytope_Rn()

Member Function Documentation

◆ checkEdges()

◆ checkEqualityOfVertices()

◆ create()

◆ createBoundingBox()

◆ createBoundingSimplex()

◆ createTruncatedGenerator()

◆ getFileExtension()

◆ getName()

◆ getPrimalCone() [1/2]

◆ getPrimalCone() [2/2]

◆ intersect()

◆ isBounded()

◆ isIncluded() [1/2]

◆ isIncluded() [2/2]

◆ neigbourhoodCondition()

◆ numberOfGeneratorsPerFacet()

◆ sum()