Combinatorial face enumeration for polytopes. More...

#include <PolyhedralAlgorithms_Rn.h>

Collaboration diagram for FaceEnumeration:

Public Member Functions
	FaceEnumeration (const boost::shared_ptr< Polytope_Rn > &A)
	General Face Enumeration Algorithm. More...

const std::vector< std::vector < ListOfFaces > > &	getFacesWithVertices () throw (std::domain_error)

const std::vector< std::vector < ListOfFaces > > &	getFacesWithFacets () throw (std::domain_error)

void	clear ()

void	printFacesWithVerticesToSage (std::ostream &this_ostream) const

void	printFacesWithVertices (std::ostream &this_ostream) const

void	printFacesWithFacets (std::ostream &this_ostream) const

void	save (std::ostream &this_stream) const

Static Public Member Functions
static void	Compute (const boost::shared_ptr< Polytope_Rn > &A)

static void	Compute (const boost::shared_ptr< Polytope_Rn > &A, FaceEnumeration &FE)

static void	save (const std::string &filename, const std::vector< std::vector< ListOfFaces > > &latt)
	Save the polytope lattice. More...

static void	load (const std::string &filename, std::vector< std::vector< ListOfFaces > > &latt) throw (std::ios_base::failure)
	Load the polytope lattice. More...

static void	load (std::istream &this_stream, std::vector< std::vector< ListOfFaces > > &latt) throw (std::out_of_range)
	Load the polytope lattice 1st line : comments = "# SpaceDimension NumberOfHalfspaces" 2nd line : SpaceDimension TotalNumberOfFaces 3rd line : FiDimension k V1 ... Vk 4th line : FjDimension l Vu ... V(u+l) k-th line : ... More...

static void	save (std::ostream &this_stream, const std::vector< std::vector< ListOfFaces > > &latt)
	Save the polytope lattice 1st line : comments = "# SpaceDimension NumberOfHalfspaces" 2nd line : SpaceDimension TotalNumberOfFaces 3rd line : FiDimension k V1 ... Vk 4th line : FjDimension l Vu ... V(u+l) k-th line : ... More...

Static Protected Member Functions
static void	ComputeWithFacets (const boost::shared_ptr< Polytope_Rn > &A, FaceEnumeration &FaceEnum)

static void	ComputeWithVertices (const boost::shared_ptr< Polytope_Rn > &A, FaceEnumeration &FaceEnum)

Protected Attributes
std::vector< std::vector < ListOfFaces > >	_allFacesWithFacets

std::vector< std::vector < ListOfFaces > >	_allFacesWithVertices

const boost::shared_ptr < Polytope_Rn > &	_polytope

Detailed Description

Combinatorial face enumeration for polytopes.

Definition at line 44 of file PolyhedralAlgorithms_Rn.h.

Constructor & Destructor Documentation

FaceEnumeration::FaceEnumeration ( const boost::shared_ptr< Polytope_Rn > & A )

inline

General Face Enumeration Algorithm.

Definition at line 49 of file PolyhedralAlgorithms_Rn.h.

Member Function Documentation

void FaceEnumeration::clear ( )

inline

Definition at line 89 of file PolyhedralAlgorithms_Rn.h.

void FaceEnumeration::Compute ( const boost::shared_ptr< Polytope_Rn > & A )

static

General Face Enumeration Algorithm from Combinatorial face enumeration in convex polytopes (1994) by Komei Fukuda and Vera Rosta.
Input: the set $\mathcal{P}_0$ of vertices of a polytope P.
Output: the set $\mathcal{P}$ of vertices of a polytope P.
procedure FaceEnumeration( $\mathcal{P}_0$ : vertices)
Create a binary tree T with set of leaves $\mathcal{P}_0$
k=0; f₀ = $| \mathcal{P}_0 |$ ; $\mathcal{P}_{(0)} = \mathcal{P}_0$
WHILE f_k >= 2 DO
f_k+1 = 0 ; $\mathcal{P}_{(k+1)} = \emptyset$
FOREACH pair (F, F') in $\mathcal{P}_{(k)}$ DO
$F'' = F \cap F'$
IF $F'' \notin T$ THEN
IF $ F''== F $ or $ F''== F' $ THEN
Delete F'' from $\mathcal{P}_{(k)}$ ;
f_k = f_k - 1
ENDIF
Add F'' to T and to $\mathcal{P}_{(k+1)}$
f_k+1 = f_k+1 + 1
ENDIF
ENDFOR
Output $\mathcal{P}_{(k)}$ ; k=k+1
ENDWHILE

Definition at line 40 of file PolyhedralAlgorithms_Rn.cpp.

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void FaceEnumeration::Compute	(	const boost::shared_ptr< Polytope_Rn > &	A,
		FaceEnumeration &	FE
	)

static

Definition at line 46 of file PolyhedralAlgorithms_Rn.cpp.

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void FaceEnumeration::ComputeWithFacets	(	const boost::shared_ptr< Polytope_Rn > &	A,
		FaceEnumeration &	FaceEnum
	)

staticprotected

Definition at line 51 of file PolyhedralAlgorithms_Rn.cpp.

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void FaceEnumeration::ComputeWithVertices	(	const boost::shared_ptr< Polytope_Rn > &	A,
		FaceEnumeration &	FaceEnum
	)

staticprotected

Definition at line 124 of file PolyhedralAlgorithms_Rn.cpp.

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const std::vector< std::vector< ListOfFaces > >& FaceEnumeration::getFacesWithFacets	(		)
throw	(	std::domain_error
	)

inline

Definition at line 83 of file PolyhedralAlgorithms_Rn.h.

const std::vector< std::vector< ListOfFaces > >& FaceEnumeration::getFacesWithVertices	(		)
throw	(	std::domain_error
	)

inline

Definition at line 77 of file PolyhedralAlgorithms_Rn.h.

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void FaceEnumeration::load	(	const std::string &	filename,
		std::vector< std::vector< ListOfFaces > > &	latt
	)
throw	(	std::ios_base::failure
	)

static

Load the polytope lattice.

Definition at line 262 of file PolyhedralAlgorithms_Rn.cpp.

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void FaceEnumeration::load	(	std::istream &	this_stream,
		std::vector< std::vector< ListOfFaces > > &	latt
	)
throw	(	std::out_of_range
	)

static

Load the polytope lattice 1st line : comments = "# SpaceDimension NumberOfHalfspaces"
2nd line : SpaceDimension TotalNumberOfFaces
3rd line : FiDimension k V1 ... Vk
4th line : FjDimension l Vu ... V(u+l)
k-th line : ...

Definition at line 287 of file PolyhedralAlgorithms_Rn.cpp.

void FaceEnumeration::printFacesWithFacets ( std::ostream & this_ostream ) const

Definition at line 173 of file PolyhedralAlgorithms_Rn.cpp.

void FaceEnumeration::printFacesWithVertices ( std::ostream & this_ostream ) const

Definition at line 198 of file PolyhedralAlgorithms_Rn.cpp.

void FaceEnumeration::printFacesWithVerticesToSage ( std::ostream & this_ostream ) const

Definition at line 223 of file PolyhedralAlgorithms_Rn.cpp.

void FaceEnumeration::save	(	const std::string &	filename,
		const std::vector< std::vector< ListOfFaces > > &	latt
	)

static

Save the polytope lattice.

Definition at line 275 of file PolyhedralAlgorithms_Rn.cpp.

void FaceEnumeration::save	(	std::ostream &	this_stream,
		const std::vector< std::vector< ListOfFaces > > &	latt
	)

static

Save the polytope lattice 1st line : comments = "# SpaceDimension NumberOfHalfspaces"
2nd line : SpaceDimension TotalNumberOfFaces
3rd line : FiDimension k V1 ... Vk
4th line : FjDimension l Vu ... V(u+l)
k-th line : ...

Definition at line 321 of file PolyhedralAlgorithms_Rn.cpp.

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void FaceEnumeration::save ( std::ostream & this_stream ) const

inline

Definition at line 121 of file PolyhedralAlgorithms_Rn.h.

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Member Data Documentation

std::vector< std::vector< ListOfFaces > > FaceEnumeration::_allFacesWithFacets

protected

Definition at line 129 of file PolyhedralAlgorithms_Rn.h.

std::vector< std::vector< ListOfFaces > > FaceEnumeration::_allFacesWithVertices

protected

Definition at line 131 of file PolyhedralAlgorithms_Rn.h.

const boost::shared_ptr<Polytope_Rn>& FaceEnumeration::_polytope

protected

Definition at line 133 of file PolyhedralAlgorithms_Rn.h.

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

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

Public Member Functions

Static Public Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation