Model a polyhedral cone using its two equivalent definitions : the convex hull and the half-space intersection. We store its edges in _listOfHS and the positive combination of these vectors generates the polyhedral cone. More...

#include <PolyhedralCone_Rn.h>

Inheritance diagram for PolyhedralCone_Rn:

Collaboration diagram for PolyhedralCone_Rn:

Public Member Functions
	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...

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

virtual unsigned int	neigbourhoodCondition () const
	Two edges are neighbours in a polyhedral cone <=> they share at least (n-2) facets. More...

virtual unsigned int	numberOfGeneratorsPerFacet () const
	Each facet in a polyhedral cone has got (n-1) edges. 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...

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

virtual double	createTruncatedGenerator (const boost::shared_ptr< Generator_Rn_SD > &y, const boost::shared_ptr< Generator_Rn_SD > &z, boost::shared_ptr< Generator_Rn_SD > newG, double ay, double az, double b=0.) 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...

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...

virtual void	createBoundingBox (double)
	At the moment this function is useless in the case of polyhedral cones. More...

virtual void	createBoundingSimplex (double)
	At the moment this function is useless in the case of polyhedral cones. More...

Protected Attributes
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...

Friends
class	lexIteratorOfListOfHalfSpaces

class	constIteratorOfListOfHalfSpaces

Detailed Description

Model a polyhedral cone using its two equivalent definitions : the convex hull and the half-space intersection. We store its edges in _listOfHS and the positive combination of these vectors generates the polyhedral cone.

Definition at line 47 of file PolyhedralCone_Rn.h.

Constructor & Destructor Documentation

◆ PolyhedralCone_Rn() [1/2]

PolyhedralCone_Rn::PolyhedralCone_Rn ( )

inline

Constructor.

Definition at line 53 of file PolyhedralCone_Rn.h.

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◆ PolyhedralCone_Rn() [2/2]

PolyhedralCone_Rn::PolyhedralCone_Rn ( const PolyhedralCone_Rn & A )

inline

Constructor.

Definition at line 56 of file PolyhedralCone_Rn.h.

◆ ~PolyhedralCone_Rn()

virtual PolyhedralCone_Rn::~PolyhedralCone_Rn ( )

inlinevirtual

Destructor.

Definition at line 62 of file PolyhedralCone_Rn.h.

Member Function Documentation

◆ addGenerator()

void PolyhedralCone_Rn::addGenerator ( boost::shared_ptr< Generator_Rn > vx )

inline

Add the given generator.

Definition at line 146 of file PolyhedralCone_Rn.h.

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◆ addHalfSpace()

boost::shared_ptr< HalfSpace_Rn > PolyhedralCone_Rn::addHalfSpace	(	boost::shared_ptr< HalfSpace_Rn >	hs,
		bool	check = `false`
	)

Add the current half-space in its list.

Definition at line 138 of file PolyhedralCone_Rn.cpp.

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◆ checkDuplicateGenerators()

bool PolyhedralCone_Rn::checkDuplicateGenerators	(	unsigned int &	a,
		unsigned int &	b
	)

Make sure no duplicate generators are stored.

Parameters

a	in case of equality store in this parameter the index of the first equal generator
b	in case of equality store in this parameter the index of the second equal generator

Returns: true if there are equal generators, false otherwise.

Definition at line 71 of file PolyhedralCone_Rn.cpp.

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◆ checkEdges()

virtual bool PolyhedralCone_Rn::checkEdges ( ) const

inlinevirtual

Always true in the polyhedral cone case.

Reimplemented in Polytope_Rn.

Definition at line 677 of file PolyhedralCone_Rn.h.

◆ checkEquality()

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

Check whether the current polyhedral cones and B are equal or not. If the last variable is true, print the mapping between the generators and faces of both polyhedral cones.

Definition at line 437 of file PolyhedralCone_Rn.cpp.

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◆ checkFacet()

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

inline

Definition at line 679 of file PolyhedralCone_Rn.h.

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◆ checkFacets()

bool PolyhedralCone_Rn::checkFacets ( ) const

inline

Detect redundant half spaces and make sure each facet has the right number of generators.

\[ A = Conv(G_1, ..., G_k) = \displaystyle{ \bigcap_{i=1}^m \bar{H}_i^+ } \]

Check that the polytope does not have generators violating a constraint defined by a half-space.

\[ \forall G=(g_1,...,g_n) \in \mathbb{R}^n, \nexists \, \bar{H}_i^+ = \left\{ x : \sum_{j=1}^n a_{ij}x_j \geq 0 \right\} such \, as \, G \not\in \bar{H}_i^+ \]

Check that the polytope does have at least (n-1) generators per half-space frontier.

\[ \forall \bar{H}_i, \exists \, (n-1) \, G=(g_1,...,g_n) \in \mathbb{R}^n, such \, as \, G \in \bar{H}_i \]

Returns: true if everything's OK, false otherwise.

Definition at line 741 of file PolyhedralCone_Rn.h.

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◆ checkGenerator() [1/2]

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

inline

Definition at line 462 of file PolyhedralCone_Rn.h.

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◆ checkGenerator() [2/2]

void PolyhedralCone_Rn::checkGenerator	(	unsigned int	vtxNumber,
		std::ostream &	this_ostream
	)		const

inline

Compute all distance from the current point to all half-spaces frontiers.

Definition at line 485 of file PolyhedralCone_Rn.h.

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◆ checkGenerators()

bool PolyhedralCone_Rn::checkGenerators	(	const listOfGeometricObjects< boost::shared_ptr< Generator_Rn > > &	listGenA,
		const listOfGeometricObjects< boost::shared_ptr< HalfSpace_Rn > > &	listHSB,
		bool	check_all = `false`
	)		const

inline

Check the number of facets per generator and make sure it is compliant with its current constraints. It must verify the following property :

\[ \forall G=(g_1,...,g_n) \in \mathbb{R}^n, \exists \, (n-1) \, \bar{H}_i = \left\{ x : \sum_{j=1}^n a_{ij}x_j \geq 0 \right\} such \, as \, G \in \bar{H}_i, i \in \{1,...,n-1\} \]

Returns: true if everything's OK, false otherwise.

Definition at line 523 of file PolyhedralCone_Rn.h.

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◆ checkNeighbours() [1/4]

bool PolyhedralCone_Rn::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

inline

Check for polytopes that vertices share (n-1) facets. For polyhedral cones, it must check that vectors share (n-2) facets.

Parameters

V1	the first vertex to check
V2	the second vertex to check
commonFacets	the set of common facets between V1 and V2
listOfRedundantHS	the set of half-spaces that will not be taken into account to compute commonFacets

Returns: false if they are not neighbours, true otherwise with the list of common facets.

Definition at line 229 of file PolyhedralCone_Rn.h.

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◆ checkNeighbours() [2/4]

bool PolyhedralCone_Rn::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

inline

Check for polytopes that vertices share (n-1) facets. For polyhedral cones, it must check that vectors share (n-2) facets.

Parameters

V1	the first vertex to check
V2	the second vertex to check
commonFacets	the set of common facets between V1 and V2
topologicalCode	model the level of neighborhood: 1 for an edge, ..., (n-1) for a facet in a n-dimensional space

Returns: false if they are not neighbours, true otherwise with the list of common facets.

Definition at line 260 of file PolyhedralCone_Rn.h.

◆ checkNeighbours() [3/4]

bool PolyhedralCone_Rn::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

inline

Check for polytopes that vertices share (n-1) facets. For polyhedral cones, it must check that vectors share (n-2) facets.

Parameters

V1	the first vertex to check
V2	the second vertex to check
commonFacets	the list of common facets between V1 and V2
topologicalCode	model the level of neighborhood: 1 for an edge, ..., (n-1) for a facet in a n-dimensional space

Returns: false if they are not neighbours, true otherwise with the list of common facets.

Definition at line 287 of file PolyhedralCone_Rn.h.

◆ checkNeighbours() [4/4]

bool PolyhedralCone_Rn::checkNeighbours	(	const boost::shared_ptr< Generator_Rn_SD > &	genIn,
		const boost::shared_ptr< Generator_Rn_SD > &	genOut,
		std::vector< unsigned int > &	commonFacets
	)		const

inline

Check for polytopes that vertices share (n-1) facets. For polyhedral cones, it must check that vectors share (n-2) facets.

Parameters

genIn	the first vertex to check
genOut	the second vertex to check
commonFacets	the list of common facets indices between genIn and genOut

Definition at line 313 of file PolyhedralCone_Rn.h.

◆ checkNeighboursWithHSnumbers()

bool PolyhedralCone_Rn::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

inline

Check for polytopes that vertices share (n-1) facets. For polyhedral cones, it must check that vectors share (n-2) facets.

Parameters

V1	the first vertex to check
V2	the second vertex to check
commonFacets	the list of common facets between V1 and V2
listOfRedundantHS	the list of facets to ignore when we process V1 and V2
topologicalCode	model the level of neighborhood: 1 for an edge, ..., (n-1) for a facet in a n-dimensional space

Returns: false if they are not neighbours, true otherwise with the list of common facets.

Definition at line 335 of file PolyhedralCone_Rn.h.

◆ checkPoint() [1/2]

HalfSpace_Rn::State PolyhedralCone_Rn::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.

Returns: HalfSpace_Rn::OUT, HalfSpace_Rn::IN or HalfSpace_Rn::ON.

Definition at line 48 of file PolyhedralCone_Rn.cpp.

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◆ checkPoint() [2/2]

HalfSpace_Rn::State PolyhedralCone_Rn::checkPoint ( const Point_Rn & thisPoint ) const

Check a point state against the whole polyhedron.

Returns: HalfSpace_Rn::OUT, HalfSpace_Rn::IN or HalfSpace_Rn::ON.

Definition at line 30 of file PolyhedralCone_Rn.cpp.

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◆ checkTopologyAndGeometry()

virtual bool PolyhedralCone_Rn::checkTopologyAndGeometry ( bool check_all = false ) const

inlinevirtual

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 :

check all the generators are inside the H-representation
check that all generators have at least (n-1) facets in the case of a polyhedral cone (n for a polytope)
check that all facets have at least (n-1) generators in the case of a polyhedral cone (n for a polytope).

Definition at line 443 of file PolyhedralCone_Rn.h.

◆ checkVolumeEquality()

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

inline

Definition at line 587 of file PolyhedralCone_Rn.h.

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◆ computeDualPolyhedralCone()

boost::shared_ptr< PolyhedralCone_Rn > 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 :

\[ newG = \displaystyle{\frac{\langle a, z \rangle}{\langle a, z-y \rangle} y - \frac{\langle a, y \rangle}{\langle a, z-y \rangle} z, H = \left\{ x : \langle a, x \rangle = \sum_{j=1}^n a_{j}x_j \geq 0 \right\}} \]

Parameters

y	The generator outside the current half-space \( \langle a, y \rangle < 0\)
z	The generator inside the current half-space \( \langle a, z \rangle > 0\)
newG	The new generator is the intersection between the 2-face created by y and z, and the current halfspace hyperplane
ay	Scalar product \( \langle a, y \rangle \)
az	Scalar product \( \langle a, z \rangle \)
b	Half-space constant, null in the polyhedral cone case.

Build the dual polyhedral cone of the current one whose edge are orthogonal to the primal and vice-versa.

Definition at line 304 of file PolyhedralCone_Rn.cpp.

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◆ createBoundingBox()

virtual void PolyhedralCone_Rn::createBoundingBox ( double )

inlinevirtual

At the moment this function is useless in the case of polyhedral cones.

Reimplemented in Polytope_Rn.

Definition at line 848 of file PolyhedralCone_Rn.h.

◆ createBoundingSimplex()

virtual void PolyhedralCone_Rn::createBoundingSimplex ( double )

inlinevirtual

At the moment this function is useless in the case of polyhedral cones.

Reimplemented in Polytope_Rn.

Definition at line 851 of file PolyhedralCone_Rn.h.

◆ createTruncatedGenerator()

double PolyhedralCone_Rn::createTruncatedGenerator	(	const boost::shared_ptr< Generator_Rn_SD > &	y,
		const boost::shared_ptr< Generator_Rn_SD > &	z,
		boost::shared_ptr< Generator_Rn_SD >	newG,
		double	ay,
		double	az,
		double	b = `0.`
	)		const

virtual

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 :

\[ newG = \displaystyle{\frac{\langle a, z \rangle}{\langle a, z-y \rangle} y - \frac{\langle a, y \rangle}{\langle a, z-y \rangle} z, H = \left\{ x : \langle a, x \rangle = \sum_{j=1}^n a_{j}x_j \geq 0 \right\}} \]

Parameters

y	The generator outside the current half-space \( \langle a, y \rangle < 0\)
z	The generator inside the current half-space \( \langle a, z \rangle > 0\)
newG	The new generator is the intersection between the 2-face created by y and z, and the current halfspace hyperplane
ay	Scalar product \( \langle a, y \rangle \)
az	Scalar product \( \langle a, z \rangle \)
b	Half-space constant, null in the polyhedral cone case.

Reimplemented in Polytope_Rn.

Definition at line 361 of file PolyhedralCone_Rn.cpp.

◆ dimension()

virtual unsigned int PolyhedralCone_Rn::dimension ( ) const

inlinevirtual

Return the space dimension.

Definition at line 65 of file PolyhedralCone_Rn.h.

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◆ dump()

void PolyhedralCone_Rn::dump ( std::ostream & this_ostream ) const

virtual

Dump the polyhedral structure on the stream passed as an argument.

Definition at line 224 of file PolyhedralCone_Rn.cpp.

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◆ dumpScilab()

void PolyhedralCone_Rn::dumpScilab ( std::ostream & this_ostream ) const

Dump the generators on on the stream passed as an argument for outputting in Scilab.

Definition at line 279 of file PolyhedralCone_Rn.cpp.

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◆ fillIrredundantNeighbourMatrix()

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

inline

Compute and store all neighborhood relations between generators.

Parameters

neighboursA an array of arrays where each line models a generator and provide its neighbours.

Definition at line 402 of file PolyhedralCone_Rn.h.

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◆ fillNeighbourMatrix()

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

inline

Compute and store all neighborhood relations between generators.

Parameters

neighboursA	a sparse matrix where each line models a generator
topologicalCode	model the level of neighborhood: 1 for an edge, ..., (n-1) for a facet in a n-dimensional space

Definition at line 362 of file PolyhedralCone_Rn.h.

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◆ getGenerator()

const boost::shared_ptr< Generator_Rn > & PolyhedralCone_Rn::getGenerator ( unsigned int i ) const

Return the i-th generator.

Definition at line 191 of file PolyhedralCone_Rn.cpp.

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◆ getGeneratorNumber()

unsigned int PolyhedralCone_Rn::getGeneratorNumber ( boost::shared_ptr< Generator_Rn > G ) const

For a given generator, return its list index.

Definition at line 200 of file PolyhedralCone_Rn.cpp.

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◆ getGeneratorsPerFacet()

void PolyhedralCone_Rn::getGeneratorsPerFacet ( std::vector< std::vector< unsigned int > > & listOfGeneratorsPerFacet ) const

inline

Get topological connections: for each facet, list its generators.

Definition at line 783 of file PolyhedralCone_Rn.h.

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◆ getHalfSpace()

const boost::shared_ptr< HalfSpace_Rn > & PolyhedralCone_Rn::getHalfSpace ( unsigned int i ) const

Return the i-th half-space.

Definition at line 160 of file PolyhedralCone_Rn.cpp.

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◆ getHalfSpaceNumber()

unsigned int PolyhedralCone_Rn::getHalfSpaceNumber ( const boost::shared_ptr< HalfSpace_Rn > & F ) const

inline

For a given half-space, return its list index.

Definition at line 112 of file PolyhedralCone_Rn.h.

◆ getListOfGenerators()

const listOfGeometricObjects< boost::shared_ptr<Generator_Rn> >& PolyhedralCone_Rn::getListOfGenerators ( ) const

inline

Return the list of generators.

Definition at line 155 of file PolyhedralCone_Rn.h.

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◆ getListOfGeneratorsSD()

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

inline

Definition at line 157 of file PolyhedralCone_Rn.h.

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◆ getListOfHalfSpaces() [1/2]

listOfGeometricObjects< boost::shared_ptr<HalfSpace_Rn> >& PolyhedralCone_Rn::getListOfHalfSpaces ( )

inline

Return the list of half-spaces.

Definition at line 131 of file PolyhedralCone_Rn.h.

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◆ getListOfHalfSpaces() [2/2]

const listOfGeometricObjects< boost::shared_ptr<HalfSpace_Rn> >& PolyhedralCone_Rn::getListOfHalfSpaces ( ) const

inline

Return the list of half-spaces.

Definition at line 134 of file PolyhedralCone_Rn.h.

◆ isBounded()

virtual bool PolyhedralCone_Rn::isBounded ( ) const

inlinevirtual

Tell whether this polyhedron is bounded or not, polyhedral cones are not.

Reimplemented in Polytope_Rn.

Definition at line 81 of file PolyhedralCone_Rn.h.

◆ isIncluded()

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

Test whether the current polytope V-description is inside the polytope B H-description.

Parameters

B	The H-polytope

Returns: true if
\[ this \subset B \]
, false otherwise.

Definition at line 395 of file PolyhedralCone_Rn.cpp.

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◆ negate()

void PolyhedralCone_Rn::negate ( )

inline

Compute the symmetrical polyhedral cone.

Definition at line 806 of file PolyhedralCone_Rn.h.

◆ neigbourhoodCondition()

virtual unsigned int PolyhedralCone_Rn::neigbourhoodCondition ( ) const

inlinevirtual

Two edges are neighbours in a polyhedral cone <=> they share at least (n-2) facets.

Reimplemented in Polytope_Rn.

Definition at line 84 of file PolyhedralCone_Rn.h.

◆ numberOfGenerators()

unsigned int PolyhedralCone_Rn::numberOfGenerators ( ) const

inline

Give the total number of generators.

Definition at line 143 of file PolyhedralCone_Rn.h.

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◆ numberOfGeneratorsPerFacet()

virtual unsigned int PolyhedralCone_Rn::numberOfGeneratorsPerFacet ( ) const

inlinevirtual

Each facet in a polyhedral cone has got (n-1) edges.

Reimplemented in Polytope_Rn.

Definition at line 87 of file PolyhedralCone_Rn.h.

◆ numberOfHalfSpaces()

unsigned int PolyhedralCone_Rn::numberOfHalfSpaces ( ) const

inline

Get the total number of half-spaces.

Definition at line 95 of file PolyhedralCone_Rn.h.

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◆ relocateGenerators()

void PolyhedralCone_Rn::relocateGenerators ( )

Definition at line 411 of file PolyhedralCone_Rn.cpp.

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◆ removeGenerator()

void PolyhedralCone_Rn::removeGenerator ( unsigned int j )

inline

Remove the generator number j from its list.

Definition at line 671 of file PolyhedralCone_Rn.h.

◆ removeGenerators()

void PolyhedralCone_Rn::removeGenerators ( const std::set< boost::shared_ptr< Generator_Rn > > & setToRemove )

inline

Remove the generators contained in setToRemove.

Definition at line 674 of file PolyhedralCone_Rn.h.

◆ removeHalfSpace()

void PolyhedralCone_Rn::removeHalfSpace ( unsigned int j )

inline

Remove the half-space number j from its list.

Definition at line 104 of file PolyhedralCone_Rn.h.

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◆ removeHalfSpaceFromListAndGenerators()

void PolyhedralCone_Rn::removeHalfSpaceFromListAndGenerators ( const boost::shared_ptr< HalfSpace_Rn > & hs )

Remove the half-space given as parameter from its list and from all generators.

Definition at line 169 of file PolyhedralCone_Rn.cpp.

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◆ removeHalfSpaces()

void PolyhedralCone_Rn::removeHalfSpaces ( const std::set< boost::shared_ptr< HalfSpace_Rn > > & setOfRedundantHS )

inline

Remove the half-space number j from its list.

Definition at line 107 of file PolyhedralCone_Rn.h.

◆ reset()

void PolyhedralCone_Rn::reset ( )

inline

Remove all half-spaces and generators.

Definition at line 90 of file PolyhedralCone_Rn.h.

◆ setListOfGenerators()

void PolyhedralCone_Rn::setListOfGenerators ( const listOfGeometricObjects< boost::shared_ptr< Generator_Rn > > & gnList )

inline

Set a new list of generators.

Definition at line 218 of file PolyhedralCone_Rn.h.

◆ setListOfGeneratorsSD()

void PolyhedralCone_Rn::setListOfGeneratorsSD ( const std::vector< boost::shared_ptr< Generator_Rn_SD > > & gnList )

inline

Set a new list of generators. The list of half-spaces should have been previously set.

Definition at line 179 of file PolyhedralCone_Rn.h.

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◆ setListOfHalfSpaces()

void PolyhedralCone_Rn::setListOfHalfSpaces ( const listOfGeometricObjects< boost::shared_ptr< HalfSpace_Rn > > & hsList )

inline

Set a new list of half-spaces.

Definition at line 137 of file PolyhedralCone_Rn.h.

Friends And Related Function Documentation

◆ constIteratorOfListOfHalfSpaces

friend class constIteratorOfListOfHalfSpaces

friend

Definition at line 49 of file PolyhedralCone_Rn.h.

◆ lexIteratorOfListOfHalfSpaces

friend class lexIteratorOfListOfHalfSpaces

friend

Definition at line 48 of file PolyhedralCone_Rn.h.

Member Data Documentation

◆ _listOfGenerators

listOfGeometricObjects< boost::shared_ptr<Generator_Rn> > PolyhedralCone_Rn::_listOfGenerators

protected

The convex hull of connected points.

Definition at line 858 of file PolyhedralCone_Rn.h.

◆ _listOfHalfSpaces

listOfGeometricObjects< boost::shared_ptr<HalfSpace_Rn> > PolyhedralCone_Rn::_listOfHalfSpaces

protected

The list of half-spaces defining the polyhedron.

Definition at line 856 of file PolyhedralCone_Rn.h.

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

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

Public Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ PolyhedralCone_Rn() [1/2]

◆ PolyhedralCone_Rn() [2/2]

◆ ~PolyhedralCone_Rn()

Member Function Documentation

◆ addGenerator()

◆ addHalfSpace()

◆ checkDuplicateGenerators()

◆ checkEdges()

◆ checkEquality()

◆ checkFacet()

◆ checkFacets()

◆ checkGenerator() [1/2]

◆ checkGenerator() [2/2]

◆ checkGenerators()

◆ checkNeighbours() [1/4]

◆ checkNeighbours() [2/4]

◆ checkNeighbours() [3/4]

◆ checkNeighbours() [4/4]

◆ checkNeighboursWithHSnumbers()

◆ checkPoint() [1/2]

◆ checkPoint() [2/2]

◆ checkTopologyAndGeometry()

◆ checkVolumeEquality()

◆ computeDualPolyhedralCone()

◆ createBoundingBox()

◆ createBoundingSimplex()

◆ createTruncatedGenerator()

◆ dimension()

◆ dump()

◆ dumpScilab()

◆ fillIrredundantNeighbourMatrix()

◆ fillNeighbourMatrix()

◆ getGenerator()

◆ getGeneratorNumber()

◆ getGeneratorsPerFacet()

◆ getHalfSpace()

◆ getHalfSpaceNumber()

◆ getListOfGenerators()

◆ getListOfGeneratorsSD()

◆ getListOfHalfSpaces() [1/2]

◆ getListOfHalfSpaces() [2/2]

◆ isBounded()

◆ isIncluded()

◆ negate()

◆ neigbourhoodCondition()

◆ numberOfGenerators()

◆ numberOfGeneratorsPerFacet()

◆ numberOfHalfSpaces()

◆ relocateGenerators()

◆ removeGenerator()

◆ removeGenerators()

◆ removeHalfSpace()

◆ removeHalfSpaceFromListAndGenerators()

◆ removeHalfSpaces()

◆ reset()

◆ setListOfGenerators()

◆ setListOfGeneratorsSD()

◆ setListOfHalfSpaces()

Friends And Related Function Documentation

◆ constIteratorOfListOfHalfSpaces

◆ lexIteratorOfListOfHalfSpaces

Member Data Documentation

◆ _listOfGenerators

◆ _listOfHalfSpaces