Class dedicated to degeneration processing when looking for neighbours.
Let A be a polytope of $\mathbb{R}^n, A = H_1^+ \cap H_2^+ \cap ... H_{n-1}^+ \cap ... H_k^+$ where k>n.
Let [v_i, v_j] be a segment of two vertices of A such as: More...

#include <Neighbours_Rn.h>

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Public Member Functions
	Neighbours_Rn ()

void	addGenerator (const std::vector< unsigned int > &commonFacets, unsigned int numbergenIN, unsigned int numbergenOUT, HalfSpace_Rn::State state)
	Tell whether a pseudo neighbor is a genuine one comparing set of half-spaces. More...

void	begin ()
	Iterator function. More...

void	next ()
	Iterator function. More...

void	checkIterator ()
	Make sure we don't point on a generator with state ON. More...

bool	end ()
	Iterator function. More...

unsigned int	currentGenInNumber ()
	Iterator function. More...

unsigned int	currentGenOutNumber ()
	Iterator function. More...

void	dump (std::ostream &ofs)
	Display the content on the stream passed as an argument. More...

Protected Attributes
unsigned int	_iterator
	A runner to iterate through the list of genuine neighbors. More...

std::vector< HalfSpace_Rn::State >	_GeneratorsState
	The pair of generators state. More...

std::vector< unsigned int >	_GeneratorsInNumber
	The generator numbers IN in a global list. More...

std::vector< unsigned int >	_GeneratorsOutNumber
	The generator numbers OUT in a global list. More...

std::vector< std::vector < unsigned int > >	_HSPerNewGenerators
	For each generator, store all raw pointers on their corresponding half-spaces. More...

Detailed Description

Class dedicated to degeneration processing when looking for neighbours.
Let A be a polytope of $\mathbb{R}^n, A = H_1^+ \cap H_2^+ \cap ... H_{n-1}^+ \cap ... H_k^+$ where k>n.
Let [v_i, v_j] be a segment of two vertices of A such as:

they share (n-1) hyperplanes in common: $H_{ij} = \{ H_1, H_2, ... H_{n-1} \}$
there exists an hyperplane $\mathcal{H}$ separating [v_j, v_k]

We call [v_i, v_j] a pseudo-edge if it respects the first assumption. The question is: to which condition [v_i, v_j] is a genuine edge? Can we answer the question only by processing the pseudo-edges separated by the hyperplane $\mathcal{H}$ ? The straight line $(v_i, v_j) \subset H_1 \cap H_2 \cap ... H_{n-1} \text{~with~} \mathcal{H} \neq H_u$ , $u \in \{ 1, ..., n-1 \}$ . So $H_1 \cap H_2 \cap ... H_{n-1} \cap H_n^+ \cap ... H_k^+ = F_A$ is a face of A of dimension at least 1. Let's assume [v_i, v_j] is not an edge of A, then it is not an edge of F_A and we cannot have F_A included neither in $\mathcal{H}^+$ nor in $\mathcal{H}^-$ as $\mathcal{H}$ separates [v_i, v_j] . So $\mathcal{H}$ separates F_A and we can find an edge [v_a, v_b] of F_A such as:

$\mathcal{H}$ separates [v_a, v_b] or
$\mathcal{H}$ passes through v_a or
$\mathcal{H}$ passes through v_b

As [v_a, v_b] is an edge of F_A, v_a and v_b share in common the list of hyperplanes H_ab . H_ab contains the (n-1) half-spaces $H_1, H_2, ... H_{n-1}$ and others because the intersection $H_1 \cap H_2 \cap ... H_{n-1}$ does not define a straight line. So if [v_i, v_j] is not an edge of A, we can find a genuine edge [v_a, v_b] , intersecting with $\mathcal{H}$ , such as $H_{ij} \subset H_{ab}$

Definition at line 59 of file Neighbours_Rn.h.

Constructor & Destructor Documentation

Neighbours_Rn::Neighbours_Rn ( )

inline

Definition at line 62 of file Neighbours_Rn.h.

Member Function Documentation

void Neighbours_Rn::addGenerator	(	const std::vector< unsigned int > &	commonFacets,
		unsigned int	numbergenIN,
		unsigned int	numbergenOUT,
		HalfSpace_Rn::State	state
	)

inline

Tell whether a pseudo neighbor is a genuine one comparing set of half-spaces.

Parameters

commonFacets	the set of common half-spaces pointers between this and gen
numbergenIN	the generator number candidate to be a genuine end of edge
numbergenOUT	the generator number candidate to be the other genuine end of edge
state	equal to HalfSpace_Rn::hs_IN_OR_OUT or HalfSpace_Rn::hs_ON according to the edge property

Definition at line 69 of file Neighbours_Rn.h.

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void Neighbours_Rn::begin ( )

inline

Iterator function.

Definition at line 128 of file Neighbours_Rn.h.

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void Neighbours_Rn::checkIterator ( )

inline

Make sure we don't point on a generator with state ON.

Definition at line 134 of file Neighbours_Rn.h.

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unsigned int Neighbours_Rn::currentGenInNumber ( )

inline

Iterator function.

Definition at line 143 of file Neighbours_Rn.h.

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unsigned int Neighbours_Rn::currentGenOutNumber ( )

inline

Iterator function.

Definition at line 146 of file Neighbours_Rn.h.

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void Neighbours_Rn::dump ( std::ostream & ofs )

inline

Display the content on the stream passed as an argument.

Definition at line 149 of file Neighbours_Rn.h.

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bool Neighbours_Rn::end ( )

inline

Iterator function.

Definition at line 140 of file Neighbours_Rn.h.

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void Neighbours_Rn::next ( )

inline

Iterator function.

Definition at line 131 of file Neighbours_Rn.h.

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Member Data Documentation

std::vector< unsigned int > Neighbours_Rn::_GeneratorsInNumber

protected

The generator numbers IN in a global list.

Definition at line 169 of file Neighbours_Rn.h.

std::vector< unsigned int > Neighbours_Rn::_GeneratorsOutNumber

protected

The generator numbers OUT in a global list.

Definition at line 171 of file Neighbours_Rn.h.

std::vector< HalfSpace_Rn::State > Neighbours_Rn::_GeneratorsState

protected

The pair of generators state.

Definition at line 167 of file Neighbours_Rn.h.

std::vector< std::vector< unsigned int > > Neighbours_Rn::_HSPerNewGenerators

protected

For each generator, store all raw pointers on their corresponding half-spaces.

Definition at line 173 of file Neighbours_Rn.h.

unsigned int Neighbours_Rn::_iterator

protected

A runner to iterate through the list of genuine neighbors.

Definition at line 165 of file Neighbours_Rn.h.

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

/home/vindelos/politopix/trunk/Neighbours_Rn.h

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation