The induced subcomplex of a facet between two simplices is the set of all simplices in the triangulation whose vertices are composed of those from the two simplices in question. More...

#include <edelsbrunner96/induced_subcomplex.h>

Classes
struct	BreadthFirstNode
	We do a breadthfirst search for simplices in the induced subcomplex. This data structure is what we queue in the search. More...

Public Types
typedef Traits::PointRef	PointRef

typedef Traits::Scalar	Scalar

typedef Traits::Simplex	Simplex

typedef Traits::SimplexRef	SimplexRef

typedef Traits::Storage	Storage

Public Member Functions
void	Build (Storage &storage)
	Fill the induced simplex by breadth-first search of the neighborhood about s[0] and s[1]. More...

uint8_t	FindIndexOfPeakVertex (Simplex &s)
	Given a simplex s which borders the hull of V (i.e. s shares a facet with hull(V)), then find the vertex of s which is not in V, and return it's index in S.V;. More...

void	Flip (Storage &storage)
	Flip the subcomplex. More...

void	Init (Storage &storage, SimplexRef s0_ref, SimplexRef s1_ref)
	Initialize the data structure with the two simplices and build the vertex set for the common facet. More...

void	Init (Storage &storage, const std::array< SimplexRef, 2 > &s)
	Initialize the data structure with the two simplices and build the vertex set for the common facet. More...

bool	IsFlippable (Storage &storage)
	Return true if the facet is flippable. More...

bool	IsLocallyRegular (Storage &storage)
	Return true if the facet is locally regular. More...

Public Attributes
std::array< PointRef, 2 >	e
	the two vertices in V which are not part of the facet. e[i] is the vertex missing from s[i] More...

std::array< PointRef, Traits::NDim >	f
	the vertices of facet for which this subcomplex is induced. More...

std::array< SimplexRef, Traits::NDim+2 >	S
	if S[i] is not null then it is the simplex in the triangulation composed of all the vertices in V except for the i'th More...

std::array< SimplexRef, 2 >	s
	the two simplices bounding the facet More...

std::array< PointRef, Traits::NDim+2 >	V
	the (sorted) vertices of the subcomplex More...

Detailed Description

template<typename Traits>
class edelsbrunner96::InducedSubcomplex< Traits >

The induced subcomplex of a facet between two simplices is the set of all simplices in the triangulation whose vertices are composed of those from the two simplices in question.

The concept is confusing at first, but this ascii art may help:

     \
      \
       \
        \
         \ v3
          |\\         s4
          | \   \
          |  \     \
    s5    |   \       \
          |    \  s1     \
          |   v1\___________\ ________________________
          |     /           / v2
          | s2 /  s0     /
          |   /       /
          |  /     /
          | /   /
        v0|//       s3
          /
         /
        /
       /
      /

In 2d a "simplex" is a triangle, and a "facet" is a line segment. Note the
facet between simplices s0 and s1 (the line segment v1 -> v2). If we take
all the vertices of the two simplices that
border that facet (i.e. union of the vertices of s0 and s1), we get the
set {v[0], v[1], v[2], v[3]}. The induced subcomplex of this facet is
the set of all simplices whose three vertices are all found in that set.
Namely, in this case, the induced subcomplex is the set {s0, s1, s2}.

Definition at line 74 of file induced_subcomplex.h.

Member Typedef Documentation

template<typename Traits>

typedef Traits::PointRef edelsbrunner96::InducedSubcomplex< Traits >::PointRef

Definition at line 78 of file induced_subcomplex.h.

template<typename Traits>

typedef Traits::Scalar edelsbrunner96::InducedSubcomplex< Traits >::Scalar

Definition at line 76 of file induced_subcomplex.h.

template<typename Traits>

typedef Traits::Simplex edelsbrunner96::InducedSubcomplex< Traits >::Simplex

Definition at line 80 of file induced_subcomplex.h.

template<typename Traits>

typedef Traits::SimplexRef edelsbrunner96::InducedSubcomplex< Traits >::SimplexRef

Definition at line 79 of file induced_subcomplex.h.

template<typename Traits>

typedef Traits::Storage edelsbrunner96::InducedSubcomplex< Traits >::Storage

Definition at line 77 of file induced_subcomplex.h.

Member Function Documentation

template<typename Traits >

void edelsbrunner96::InducedSubcomplex< Traits >::Build ( Storage & storage )

Fill the induced simplex by breadth-first search of the neighborhood about s[0] and s[1].

Definition at line 88 of file induced_subcomplex.hpp.

template<typename Traits >

uint8_t edelsbrunner96::InducedSubcomplex< Traits >::FindIndexOfPeakVertex ( typename Traits::Simplex & s )

Given a simplex s which borders the hull of V (i.e. s shares a facet with hull(V)), then find the vertex of s which is not in V, and return it's index in S.V;.

Definition at line 247 of file induced_subcomplex.hpp.

template<typename Traits >

void edelsbrunner96::InducedSubcomplex< Traits >::Flip ( Storage & storage )

Flip the subcomplex.

Definition at line 292 of file induced_subcomplex.hpp.

template<typename Traits >

void edelsbrunner96::InducedSubcomplex< Traits >::Init	(	Storage &	storage,
		SimplexRef	s0_ref,
		SimplexRef	s1_ref
	)

Initialize the data structure with the two simplices and build the vertex set for the common facet.

Definition at line 41 of file induced_subcomplex.hpp.

template<typename Traits >

void edelsbrunner96::InducedSubcomplex< Traits >::Init	(	Storage &	storage,
		const std::array< SimplexRef, 2 > &	s
	)

Initialize the data structure with the two simplices and build the vertex set for the common facet.

Definition at line 67 of file induced_subcomplex.hpp.

template<typename Traits >

bool edelsbrunner96::InducedSubcomplex< Traits >::IsFlippable ( Storage & storage )

Return true if the facet is flippable.

A facet is flippable if all reflex edges are filled by a simplex in the induced subcomplex.

Definition at line 165 of file induced_subcomplex.hpp.

template<class Traits >

bool edelsbrunner96::InducedSubcomplex< Traits >::IsLocallyRegular ( Storage & storage )

Return true if the facet is locally regular.

Definition at line 73 of file induced_subcomplex.hpp.

Member Data Documentation

template<typename Traits>

std::array<PointRef, 2> edelsbrunner96::InducedSubcomplex< Traits >::e

the two vertices in V which are not part of the facet. e[i] is the vertex missing from s[i]

Definition at line 106 of file induced_subcomplex.h.

template<typename Traits>

std::array<PointRef, Traits::NDim> edelsbrunner96::InducedSubcomplex< Traits >::f

the vertices of facet for which this subcomplex is induced.

Definition at line 102 of file induced_subcomplex.h.

template<typename Traits>

std::array<SimplexRef, Traits::NDim + 2> edelsbrunner96::InducedSubcomplex< Traits >::S

if S[i] is not null then it is the simplex in the triangulation composed of all the vertices in V except for the i'th

Definition at line 99 of file induced_subcomplex.h.

template<typename Traits>

std::array<SimplexRef, 2> edelsbrunner96::InducedSubcomplex< Traits >::s

the two simplices bounding the facet

Definition at line 109 of file induced_subcomplex.h.

template<typename Traits>

std::array<PointRef, Traits::NDim + 2> edelsbrunner96::InducedSubcomplex< Traits >::V

the (sorted) vertices of the subcomplex

Definition at line 95 of file induced_subcomplex.h.

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

include/edelsbrunner96/induced_subcomplex.h
include/edelsbrunner96/induced_subcomplex.hpp

Classes

Public Types

Public Member Functions

Public Attributes

Detailed Description

template<typename Traits> class edelsbrunner96::InducedSubcomplex< Traits >

Member Typedef Documentation

Member Function Documentation

Member Data Documentation

template<typename Traits>
class edelsbrunner96::InducedSubcomplex< Traits >