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) throw (std::invalid_argument)
	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 throw (std::out_of_range)
	For a given half-space, return its list index. More...

const boost::shared_ptr < HalfSpace_Rn > &	getHalfSpace (unsigned int i) const throw (std::out_of_range)
	Return the i-th generator. 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...

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 throw (std::out_of_range)
	Return the i-th generator. More...

unsigned int	getGeneratorNumber (boost::shared_ptr< Generator_Rn > G) const throw (std::out_of_range,std::invalid_argument)
	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)

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 throw (std::invalid_argument)

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 throw (std::invalid_argument)

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 throw (std::invalid_argument)
	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)
	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 throw (std::invalid_argument)
	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 throw (std::out_of_range)

virtual bool	checkTopologyAndGeometry () 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	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 throw (std::out_of_range)
	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 : $\forall G=(g_1,...,g_n) \in \mathbb{R}^n, \exists \, (n-1) \, \bar{H}_i = \left\{ x : \sum_{j=1}^n a_{ij}x_j \geq 0 \right\} such \, as \, G \in \bar{H}_i, i \in \{1,...,n-1\}$ . More...

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

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

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

bool	checkFacets () const
	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. $\forall \bar{H}_i, \exists \, (n-1) \, G=(g_1,...,g_n) \in \mathbb{R}^n, such \, as \, G \in \bar{H}_i$ . More...

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

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

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

boost::shared_ptr < PolyhedralCone_Rn >	computeDualPolyhedralCone () const
	Build the dual polyhedral cone of the current one whose edge are orthogonal to the primal and vice-versa. More...

virtual void	computeMinkowskiSum (const boost::shared_ptr< PolyhedralCone_Rn > &A, const boost::shared_ptr< PolyhedralCone_Rn > &B)
	Compute the Minkowski sum of two polyhedral cones. More...

void	dump (std::ostream &this_ostream) const
	Dump the polyhedral structure on std::cout. 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 polytope. 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 45 of file PolyhedralCone_Rn.h.

Constructor & Destructor Documentation

PolyhedralCone_Rn::PolyhedralCone_Rn ( )

inline

Constructor.

Definition at line 51 of file PolyhedralCone_Rn.h.

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PolyhedralCone_Rn::PolyhedralCone_Rn ( const PolyhedralCone_Rn & A )

inline

Constructor.

Definition at line 54 of file PolyhedralCone_Rn.h.

virtual PolyhedralCone_Rn::~PolyhedralCone_Rn ( )

inlinevirtual

Destructor.

Definition at line 60 of file PolyhedralCone_Rn.h.

Member Function Documentation

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

inline

Add the given generator.

Definition at line 139 of file PolyhedralCone_Rn.h.

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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 137 of file PolyhedralCone_Rn.cpp.

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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 70 of file PolyhedralCone_Rn.cpp.

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virtual bool PolyhedralCone_Rn::checkEdges ( ) const

inlinevirtual

Always true in the polyhedral cone case.

Reimplemented in Polytope_Rn.

Definition at line 518 of file PolyhedralCone_Rn.h.

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 401 of file PolyhedralCone_Rn.cpp.

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

inline

Definition at line 520 of file PolyhedralCone_Rn.h.

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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 582 of file PolyhedralCone_Rn.h.

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

inline

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

Definition at line 424 of file PolyhedralCone_Rn.h.

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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 462 of file PolyhedralCone_Rn.h.

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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
throw	(	std::invalid_argument
	)

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 215 of file PolyhedralCone_Rn.h.

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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
throw	(	std::invalid_argument
	)

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 246 of file PolyhedralCone_Rn.h.

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
throw	(	std::invalid_argument
	)

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 273 of file PolyhedralCone_Rn.h.

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
	)

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 299 of file PolyhedralCone_Rn.h.

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
throw	(	std::invalid_argument
	)

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 321 of file PolyhedralCone_Rn.h.

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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 29 of file PolyhedralCone_Rn.cpp.

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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 47 of file PolyhedralCone_Rn.cpp.

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virtual bool PolyhedralCone_Rn::checkTopologyAndGeometry ( ) 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 393 of file PolyhedralCone_Rn.h.

boost::shared_ptr< PolyhedralCone_Rn > PolyhedralCone_Rn::computeDualPolyhedralCone ( ) const

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

Definition at line 285 of file PolyhedralCone_Rn.cpp.

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void PolyhedralCone_Rn::computeMinkowskiSum	(	const boost::shared_ptr< PolyhedralCone_Rn > &	A,
		const boost::shared_ptr< PolyhedralCone_Rn > &	B
	)

virtual

Compute the Minkowski sum of two polyhedral cones.

Definition at line 280 of file PolyhedralCone_Rn.cpp.

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 656 of file PolyhedralCone_Rn.h.

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 659 of file PolyhedralCone_Rn.h.

void 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 342 of file PolyhedralCone_Rn.cpp.

virtual unsigned int PolyhedralCone_Rn::dimension ( ) const

inlinevirtual

Return the space dimension.

Definition at line 63 of file PolyhedralCone_Rn.h.

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

Dump the polyhedral structure on std::cout.

Definition at line 223 of file PolyhedralCone_Rn.cpp.

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

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 348 of file PolyhedralCone_Rn.h.

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

Return the i-th generator.

Definition at line 190 of file PolyhedralCone_Rn.cpp.

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unsigned int PolyhedralCone_Rn::getGeneratorNumber	(	boost::shared_ptr< Generator_Rn >	G	)	const
throw	(	std::out_of_range,
		std::invalid_argument
	)

For a given generator, return its list index.

Definition at line 199 of file PolyhedralCone_Rn.cpp.

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

Return the i-th generator.

Definition at line 159 of file PolyhedralCone_Rn.cpp.

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

inline

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

Definition at line 110 of file PolyhedralCone_Rn.h.

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

inline

Return the list of generators.

Definition at line 148 of file PolyhedralCone_Rn.h.

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

inline

Definition at line 150 of file PolyhedralCone_Rn.h.

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

inline

Return the list of half-spaces.

Definition at line 127 of file PolyhedralCone_Rn.h.

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

inline

Return the list of half-spaces.

Definition at line 130 of file PolyhedralCone_Rn.h.

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 79 of file PolyhedralCone_Rn.h.

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 359 of file PolyhedralCone_Rn.cpp.

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void PolyhedralCone_Rn::negate ( )

inline

Compute the symmetrical polyhedral cone.

Definition at line 627 of file PolyhedralCone_Rn.h.

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 82 of file PolyhedralCone_Rn.h.

unsigned int PolyhedralCone_Rn::numberOfGenerators ( ) const

inline

Give the total number of generators.

Definition at line 136 of file PolyhedralCone_Rn.h.

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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 85 of file PolyhedralCone_Rn.h.

unsigned int PolyhedralCone_Rn::numberOfHalfSpaces ( ) const

inline

Get the total number of half-spaces.

Definition at line 93 of file PolyhedralCone_Rn.h.

void PolyhedralCone_Rn::relocateGenerators ( )

Definition at line 375 of file PolyhedralCone_Rn.cpp.

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void PolyhedralCone_Rn::removeGenerator ( unsigned int j )

inline

Remove the generator number j from its list.

Definition at line 515 of file PolyhedralCone_Rn.h.

void PolyhedralCone_Rn::removeHalfSpace ( unsigned int j )

inline

Remove the half-space number j from its list.

Definition at line 102 of file PolyhedralCone_Rn.h.

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

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

Definition at line 168 of file PolyhedralCone_Rn.cpp.

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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 105 of file PolyhedralCone_Rn.h.

void PolyhedralCone_Rn::reset ( )

inline

Remove all half-spaces and generators.

Definition at line 88 of file PolyhedralCone_Rn.h.

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

inline

Set a new list of generators.

Definition at line 204 of file PolyhedralCone_Rn.h.

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 168 of file PolyhedralCone_Rn.h.

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Friends And Related Function Documentation

friend class constIteratorOfListOfHalfSpaces

friend

Definition at line 47 of file PolyhedralCone_Rn.h.

friend class lexIteratorOfListOfHalfSpaces

friend

Definition at line 46 of file PolyhedralCone_Rn.h.

Member Data Documentation

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

protected

The convex hull of connected points.

Definition at line 665 of file PolyhedralCone_Rn.h.

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

protected

The list of half-spaces defining the polytope.

Definition at line 663 of file PolyhedralCone_Rn.h.

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

/home/vindelos/politopix/trunk/PolyhedralCone_Rn.h
/home/vindelos/politopix/trunk/PolyhedralCone_Rn.cpp

Public Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation