Detailed Description

Wrapper for CGAL::Triangulation_Data_Structure https://doc.cgal.org/latest/TDS_2/index.html.

The Triangulation is a double-linked list of vertexes and faces. It allows for efficient traversal over neighboring vertexes, faces, or edges.

Edge objects are note stored but identified by a face and opposite vertexes.

We use the basic TDS structure with addition information stored on the vertexes.

TDS is spherical by concept. Our polygons are flat, of course. We introduce an artifical vertex acting as opposite to all outer edges of the triangulation.

If you think about projecting our polygons onto a sphere, this would be the south-pole. It is indicated by a special vertex identifier (polygon vertices being identified by non-negative indexes).

Additional edges connect the south pole to each vertex of the polygon.

Initially, the vertexes of the triangulation are identical to the polygon vertexes (plus the south-pole). The algorithm for computing Valid Placements adds (and removes) more vertexes.

Author: Peter Schäfer

Definition at line 185 of file triangulation.h.

#include <triangulation.h>

Classes
class	Edge_iterator
	edge iterator. Traverses all edges of the triangulation. Derives from TDS::Edge_iterator and supplies some additional information. More...

Public Types
typedef Vertex_base< TDS >	Vertex
	a vertex of the triangulation More...

typedef TDS::Vertex_handle	Vertex_handle
	handle to a vertex (handles are managed by TDS base class) More...

typedef TDS::Face_handle	Face_handle
	handle to a triangulation face (handles are managed by TDS base class) More...

typedef TDS::Edge	Edge
	an edge of the triangulation either an edge of the polygon, or a diagonal, or an articial "outer" edge connected to the south-pole More...

typedef TDS::Face_circulator	Face_circulator
	a circulating iterator More...

typedef std::pair< Vertex_handle, Vertex_handle >	VertexPair
	a pair of vertexes More...

typedef std::pair< Edge, Edge >	EdgePair
	a pair of edges More...

typedef std::pair< Face_handle, Face_handle >	FacePair
	a pair of faces More...

typedef std::pair< Edge_iterator, Edge_iterator >	Edge_range
	a range of edges More...

typedef std::pair< Vertex_handle, Vertex_handle >	TwoVertices
	a pair of vertex handles More...

Public Member Functions
	Triangulation (int capacity=-1)
	default constructor More...

	Triangulation (const Triangulation &that)
	copy constructor More...

	~Triangulation ()
	destructor More...

void	setPolygonSize (int n)
	set number of polygon vertexes More...

int	size () const

void	resize (int sz)
	reset number of vertexes in triangulation More...

int	countVertexes () const

int	countFaces () const

Vertex_handle	operator[] (int i)

const Vertex_handle	operator[] (int i) const

Edge_iterator	edges_begin () const

Edge_iterator	edges_end () const

Edge_range	edges () const

TDS::Vertex_iterator	vertices_begin () const

TDS::Vertex_iterator	vertices_end () const

FacePair	adjacentFaces (Segment s) const

EdgePair	adjacentEdges (Edge e) const

EdgePair	adjacentEdges (Edge e, int i1, int i2) const

void	mirror (Edge &e) const
	flip the direction of an edge. Keep in mind that Edge object are desribed as a Face + opposite vertex. For each edge, there are two valid interpretations (with opposite faces). More...

void	mirror (EdgePair &e2) const
	flip the direction of two edges. More...

Face_circulator	incidentFaces (Vertex_handle v) const
	a circular (never-ending) iterator that traverses all faces incident to a given vertex. More...

Vertex_handle	oppositeVertex (Edge e) const
	the second vertex opposite to an edge. Keep in mind that Edge object are desribed as a Face + opposite vertex. More...

int	thirdVertex (int a, int b) const
	given two vertexes, find the third vertex to complement a triangle More...

Edge	edge (int i, int j) const
	construct an edge from two vertexes More...

VertexPair	incidentVertexes (Edge e) const

TwoVertices	adjacentVertices (Segment s) const

TwoVertices	adjacentVertices (int v) const
	adjacentVertices More...

Vertex_handle	createVertex (const Point &p, int i)
	create a new triangulation vertex More...

void	createFace (int a, int b, int c)
	insert a new face. Caller is responsible for keeping the triangulation in a consistent state. For instance, all faces must be oriented counter-clockwise. More...

void	complement ()
	after all faces have been added, create the complementary "outer" edges (connected to the south-pole). More...

bool	isComplete () const

bool	assertEquals (const Triangulation &that) const
	equality assertion for debugging More...

methods for computing valid placements
Vertex_handle	insertVertexOnEdge (double x)
	split an edge into two More...

void	removeVertexFromEdge (int index)
	remove a vertex More...

void	addTargetVertices (const frechet::reach::Placements &p)
	add vertexes for computing valid placements More...

Vertex_handle	addTargetVertex (const frechet::reach::Placement *p)
	add a vertex for computing valid placements More...

Vertex_handle	addVertex (double w)
	add a triangulation vertex on the edge of the polygon (does not correspond to a polygon vertex) More...

void	clearTargets ()
	clear targets for shortest-path tree search More...

void	clearPredecessors ()
	used during shortest-paths computation: reset shortest-path tree information on all vertexes More...

Static Public Member Functions
static Segment	segment (Edge e)

static Vertex_handle	vertex1 (Edge e)

static Vertex_handle	vertex2 (Edge e)

Private Types
typedef CGAL::Triangulation_data_structure_2< Vertex_base<>, CGAL::Triangulation_ds_face_base_2<> >	TDS
	Triangulation Data Structure. Instantiates CGAL::Triangulation_data_structure_2 with our customized Vertex_base class. More...

typedef std::vector< TDS::Vertex_handle >	VertexMap
	Keeps track of Vertex handles. More...

typedef std::map< Segment, TDS::Edge >	NeighborMap

Private Member Functions
void	addVertex (Vertex_handle v, double x, Point p)
	insert a new triangulation vertex into the map More...

void	linkNeighbors (Segment s, Edge e)
	keep track of neighboring faces during construction of the triangulation. More...

Vertex_handle	third_vertex (Face_handle f, Segment s)
	given two vertexes and a face, find the third vertex of the triangle More...

Static Private Member Functions
static Vertex_handle	third_vertex (Face_handle f, Vertex_handle v1, Vertex_handle v2)
	given two vertexes and a face, find the third vertex of the triangle More...

Private Attributes
int	poly_n
	polygon size, number of vertexes in polyong More...

TDS	tds
	CGAL Triangulation Data Structure. More...

VertexMap	vertices

NeighborMap	neighbors
	Keeps track of diagonals and their neighborhood during construction. More...

TDS::Vertex_handle	south_pole
	a special vertex that completes the TDS structure More...

vertex and edge types
bool	is_ccw_face (Face_handle f)

static bool	is_south_pole (Vertex_handle v)

static bool	is_outer_face (Face_handle f)

static bool	is_inner_face (Face_handle f)

static bool	is_outer_edge (Edge e)

static bool	is_polygon_edge (Edge e)

static bool	is_diagonal (Edge e)

Member Typedef Documentation

◆ Edge

typedef TDS::Edge frechet::poly::Triangulation::Edge

an edge of the triangulation either an edge of the polygon, or a diagonal, or an articial "outer" edge connected to the south-pole

Definition at line 221 of file triangulation.h.

◆ Edge_range

typedef std::pair<Edge_iterator,Edge_iterator> frechet::poly::Triangulation::Edge_range

a range of edges

Definition at line 267 of file triangulation.h.

◆ EdgePair

typedef std::pair<Edge,Edge> frechet::poly::Triangulation::EdgePair

a pair of edges

Definition at line 228 of file triangulation.h.

◆ Face_circulator

typedef TDS::Face_circulator frechet::poly::Triangulation::Face_circulator

a circulating iterator

Definition at line 223 of file triangulation.h.

◆ Face_handle

typedef TDS::Face_handle frechet::poly::Triangulation::Face_handle

handle to a triangulation face (handles are managed by TDS base class)

Definition at line 218 of file triangulation.h.

◆ FacePair

typedef std::pair<Face_handle,Face_handle> frechet::poly::Triangulation::FacePair

a pair of faces

Definition at line 230 of file triangulation.h.

◆ NeighborMap

typedef std::map<Segment,TDS::Edge> frechet::poly::Triangulation::NeighborMap

private

Definition at line 205 of file triangulation.h.

◆ TDS

typedef CGAL::Triangulation_data_structure_2< Vertex_base<>, CGAL::Triangulation_ds_face_base_2<> > frechet::poly::Triangulation::TDS

private

Triangulation Data Structure. Instantiates CGAL::Triangulation_data_structure_2 with our customized Vertex_base class.

Definition at line 196 of file triangulation.h.

◆ TwoVertices

typedef std::pair<Vertex_handle,Vertex_handle> frechet::poly::Triangulation::TwoVertices

a pair of vertex handles

Definition at line 397 of file triangulation.h.

◆ Vertex

typedef Vertex_base<TDS> frechet::poly::Triangulation::Vertex

a vertex of the triangulation

Definition at line 214 of file triangulation.h.

◆ Vertex_handle

typedef TDS::Vertex_handle frechet::poly::Triangulation::Vertex_handle

handle to a vertex (handles are managed by TDS base class)

Definition at line 216 of file triangulation.h.

◆ VertexMap

typedef std::vector<TDS::Vertex_handle> frechet::poly::Triangulation::VertexMap

private

Keeps track of Vertex handles.

Definition at line 203 of file triangulation.h.

◆ VertexPair

typedef std::pair<Vertex_handle,Vertex_handle> frechet::poly::Triangulation::VertexPair

a pair of vertexes

Definition at line 226 of file triangulation.h.

Constructor & Destructor Documentation

◆ Triangulation() [1/2]

Triangulation::Triangulation ( int capacity = -1 )

default constructor

Parameters

capacity initial number of vertexes (optional)

Definition at line 9 of file triangulation.cpp.

◆ Triangulation() [2/2]

Triangulation::Triangulation ( const Triangulation & that )

copy constructor

Parameters

that	objet to copy from

Definition at line 18 of file triangulation.cpp.

◆ ~Triangulation()

Triangulation::~Triangulation ( )

destructor

Definition at line 40 of file triangulation.cpp.

Member Function Documentation

◆ addTargetVertex()

Triangulation::Vertex_handle Triangulation::addTargetVertex ( const frechet::reach::Placement * p )

add a vertex for computing valid placements

Parameters

p	a valid placement

Returns: handle to a newly created triangulation vertex

Definition at line 108 of file triangulation.cpp.

◆ addTargetVertices()

void Triangulation::addTargetVertices ( const frechet::reach::Placements & p )

add vertexes for computing valid placements

Parameters

p	a set of valid placements

Definition at line 89 of file triangulation.cpp.

◆ addVertex() [1/2]

Triangulation::Vertex_handle Triangulation::addVertex ( double w )

add a triangulation vertex on the edge of the polygon (does not correspond to a polygon vertex)

Parameters

w	offset on polygon

Returns: handle to a newly created triangulation vertex

Definition at line 95 of file triangulation.cpp.

◆ addVertex() [2/2]

void Triangulation::addVertex	(	Vertex_handle	v,
		double	x,
		Point	p
	)

private

insert a new triangulation vertex into the map

Parameters

v	handle to a newly created vertex
x	offset on polygon
p	point in the plane

Definition at line 290 of file triangulation.cpp.

◆ adjacentEdges() [1/2]

Triangulation::EdgePair Triangulation::adjacentEdges ( Triangulation::Edge e ) const

Parameters

e	an edge in the triangulation

Returns: the two edges that are adjacemt to a given egde

Definition at line 315 of file triangulation.cpp.

◆ adjacentEdges() [2/2]

Triangulation::EdgePair Triangulation::adjacentEdges	(	Edge	e,
		int	i1,
		int	i2
	)		const

Parameters

e	an edge in the triangulation
i1	a vertex
i2	a vertex

Returns: the two edges that are adjacemt to a given egde

Sort edges, so that i1 is incident to result.first and i2 is incident to result.second To put it another way: result.first is opposite i2 result.second is opposite i1

Definition at line 334 of file triangulation.cpp.

◆ adjacentFaces()

Triangulation::FacePair Triangulation::adjacentFaces ( Segment s ) const

Returns: the two faces that are adjacent to the segment (i,j)

Definition at line 356 of file triangulation.cpp.

◆ adjacentVertices() [1/2]

Triangulation::TwoVertices Triangulation::adjacentVertices ( Segment s ) const

Parameters

s	a segment (edge or diagonal) of the polygon

Returns: the two vertices that are opposite a polygon segment

Definition at line 435 of file triangulation.cpp.

◆ adjacentVertices() [2/2]

Triangulation::TwoVertices Triangulation::adjacentVertices ( int v ) const

adjacentVertices

Parameters

v	a polygon vertex

Returns: the two adjacent vertices

Definition at line 452 of file triangulation.cpp.

◆ assertEquals()

bool Triangulation::assertEquals ( const Triangulation & that ) const

equality assertion for debugging

Parameters

that	triangulation to compare with

Returns: true if both triangulations are equal

Definition at line 649 of file triangulation.cpp.

◆ clearPredecessors()

void Triangulation::clearPredecessors ( )

used during shortest-paths computation: reset shortest-path tree information on all vertexes

Definition at line 421 of file triangulation.cpp.

◆ clearTargets()

void Triangulation::clearTargets ( )

clear targets for shortest-path tree search

Definition at line 428 of file triangulation.cpp.

◆ complement()

void Triangulation::complement ( )

after all faces have been added, create the complementary "outer" edges (connected to the south-pole).

Definition at line 486 of file triangulation.cpp.

◆ countFaces()

int frechet::poly::Triangulation::countFaces ( ) const

inline

Returns: number of faces in triangulation

Definition at line 309 of file triangulation.h.

◆ countVertexes()

int frechet::poly::Triangulation::countVertexes ( ) const

inline

Returns: numer of vertexes in triangulation (including south-pole)

Definition at line 305 of file triangulation.h.

◆ createFace()

void Triangulation::createFace	(	int	a,
		int	b,
		int	c
	)

insert a new face. Caller is responsible for keeping the triangulation in a consistent state. For instance, all faces must be oriented counter-clockwise.

Parameters

a	first vertex
b	second vertex
c	third vertex

Definition at line 457 of file triangulation.cpp.

◆ createVertex()

Triangulation::Vertex_handle Triangulation::createVertex	(	const Point &	p,
		int	i
	)

create a new triangulation vertex

Parameters

p	a point in the plane
i	index of polygon vertex (optional)

Returns: a handle to a newly created triangulation vertex

Definition at line 147 of file triangulation.cpp.

◆ edge()

Triangulation::Edge Triangulation::edge	(	int	i,
		int	j
	)		const

construct an edge from two vertexes

Parameters

i	a triangulation vertex
j	adjacent triangulation vertex

Returns: an Edge of the triangulation, undefined if the vertexes are not adjacent

Definition at line 399 of file triangulation.cpp.

◆ edges()

Edge_range frechet::poly::Triangulation::edges ( ) const

inline

Returns: a pair of iterators

Definition at line 327 of file triangulation.h.

◆ edges_begin()

Edge_iterator frechet::poly::Triangulation::edges_begin ( ) const

inline

Returns: iterator to the egdes in the triangulation

Definition at line 323 of file triangulation.h.

◆ edges_end()

Edge_iterator frechet::poly::Triangulation::edges_end ( ) const

inline

Returns: iterator beyond the end of egdes in the triangulation

Definition at line 325 of file triangulation.h.

◆ incidentFaces()

Triangulation::Face_circulator Triangulation::incidentFaces ( Vertex_handle v ) const

a circular (never-ending) iterator that traverses all faces incident to a given vertex.

Parameters

v	a vertex in the triangulation

Returns: a circular iterator

Definition at line 376 of file triangulation.cpp.

◆ incidentVertexes()

Triangulation::VertexPair Triangulation::incidentVertexes ( Edge e ) const

Parameters

e	an edge in the triangulation

Returns: the two vertexes adjacent to an edge

Definition at line 413 of file triangulation.cpp.

◆ insertVertexOnEdge()

Triangulation::Vertex_handle Triangulation::insertVertexOnEdge ( double x )

split an edge into two

Parameters

x	offset on polygon

Returns: a handle to a newly created triangulation vertex

                      v3
                       +
                      /| \
                     / |  \
                    /  |   \
                   /   |    \
                  /    |     \
                 /     |      \
                /      |       \
               /       |        \
              /        |         \
             /         |          \
         v1 +----------+-----------+ v2
             \        v|          /
              \        |         /
               \    f  |  f(2)  /
                \      |       /
                 e     |      /
                  \    |     /
                   \   |    /
                    \  |   /
                     \ |  /
                      \|/
                       +
                  south pole

Definition at line 188 of file triangulation.cpp.

◆ is_ccw_face()

bool Triangulation::is_ccw_face ( Face_handle f )

Parameters

f	a triangulation face

Returns: true if the face is oriented counter clock-wise

Definition at line 564 of file triangulation.cpp.

◆ is_diagonal()

bool Triangulation::is_diagonal ( Edge e )

static

Parameters

e	a triangulation edge

Returns: true if e is a diagonal in the polygon

Definition at line 74 of file triangulation.cpp.

◆ is_inner_face()

bool Triangulation::is_inner_face ( Face_handle f )

static

Parameters

f	a triangulation face

Returns: true if f is an proper face of the triangulation

Definition at line 58 of file triangulation.cpp.

◆ is_outer_edge()

bool Triangulation::is_outer_edge ( Edge e )

static

Parameters

e	a triangulation edge

Returns: true if e is an artifical edge adjacent to the south-pole

Definition at line 63 of file triangulation.cpp.

◆ is_outer_face()

bool Triangulation::is_outer_face ( Face_handle f )

static

Parameters

f	a triangulation face

Returns: true if f is an artifical face adjacent to the south-pole

Definition at line 53 of file triangulation.cpp.

◆ is_polygon_edge()

bool Triangulation::is_polygon_edge ( Edge e )

static

Parameters

e	a triangulation edge

Returns: true if e is an edge of the polygon

Definition at line 68 of file triangulation.cpp.

◆ is_south_pole()

bool Triangulation::is_south_pole ( Vertex_handle v )

static

Parameters

v	a triangulation vertex

Returns: true if v is the "south-pole" vertex

Definition at line 48 of file triangulation.cpp.

◆ isComplete()

bool frechet::poly::Triangulation::isComplete ( ) const

inline

Returns: true if all neighboring faces have been inserted

Definition at line 453 of file triangulation.h.

◆ linkNeighbors()

void Triangulation::linkNeighbors	(	Segment	s,
		Edge	e
	)

private

keep track of neighboring faces during construction of the triangulation.

Parameters

s	a polygon segment (vertex indexes)
e	a triangulation edge

Definition at line 522 of file triangulation.cpp.

◆ mirror() [1/2]

void Triangulation::mirror ( Edge & e ) const

flip the direction of an edge. Keep in mind that Edge object are desribed as a Face + opposite vertex. For each edge, there are two valid interpretations (with opposite faces).

Parameters

e	reference to an edge object

Definition at line 80 of file triangulation.cpp.

◆ mirror() [2/2]

void Triangulation::mirror ( EdgePair & e2 ) const

flip the direction of two edges.

Parameters

e2	a pair of Edge objects

Definition at line 84 of file triangulation.cpp.

◆ operator[]() [1/2]

Triangulation::Vertex_handle Triangulation::operator[] ( int i )

Parameters

i	index of vertex

Returns: a handle to a triangulation vertex

Definition at line 297 of file triangulation.cpp.

◆ operator[]() [2/2]

const Triangulation::Vertex_handle Triangulation::operator[] ( int i ) const

Parameters

i	index of vertex

Returns: an immutable handle to a triangulation vertex

Definition at line 306 of file triangulation.cpp.

◆ oppositeVertex()

Triangulation::Vertex_handle Triangulation::oppositeVertex ( Edge e ) const

the second vertex opposite to an edge. Keep in mind that Edge object are desribed as a Face + opposite vertex.

Parameters

e	an edge in the triangulation

Returns: the second vertex opposite to the given edge.

Definition at line 381 of file triangulation.cpp.

◆ removeVertexFromEdge()

void Triangulation::removeVertexFromEdge ( int index )

remove a vertex

Parameters

index index of vertex, previously created by insertVertexOnEdge. Undefined if the vertex was not create by insertVertexOnEdge.

                    v3
                     +
                    /| \
                   / |  \
                  /  |   \
                 /   |    \
                /    |     \
               /     |      \
              /      |       \
             /       |        \
            /        |         \
           /         |          \
          +----------+---e-------+ v2
           \       v1|          /
            \        |         /
             \       |   f    /
              \      |       /
               \     |      /
                \    |     /
                 \   |    /
                  \  |   /
                   \ |  /
                    \|/
                     +
                south pole

Definition at line 262 of file triangulation.cpp.

◆ resize()

void Triangulation::resize ( int sz )

reset number of vertexes in triangulation

Definition at line 128 of file triangulation.cpp.

◆ segment()

Segment Triangulation::segment ( Triangulation::Edge e )

static

Parameters

e	a triangulation edge

Returns: the associated polygon Segment (polygon vertex indexes)

Definition at line 226 of file triangulation.cpp.

◆ setPolygonSize()

void Triangulation::setPolygonSize ( int n )

set number of polygon vertexes

Parameters

n	number of polygon vertexes

Definition at line 118 of file triangulation.cpp.

◆ size()

int Triangulation::size ( ) const

Returns: number of vertexes in triangulation (not including south-pole)

Definition at line 123 of file triangulation.cpp.

◆ third_vertex() [1/2]

Triangulation::Vertex_handle Triangulation::third_vertex	(	Face_handle	f,
		Vertex_handle	v1,
		Vertex_handle	v2
	)

staticprivate

given two vertexes and a face, find the third vertex of the triangle

Parameters

f	a triangulation face
v1	first vertex
v2	second vertex

Returns: third vertex that makes up the triangle

Definition at line 542 of file triangulation.cpp.

◆ third_vertex() [2/2]

Triangulation::Vertex_handle Triangulation::third_vertex	(	Face_handle	f,
		Segment	s
	)

private

given two vertexes and a face, find the third vertex of the triangle

Parameters

f	a triangulation face
s	two vertexes

Returns: third vertex that makes up the triangle

Definition at line 559 of file triangulation.cpp.

◆ thirdVertex()

int Triangulation::thirdVertex	(	int	a,
		int	b
	)		const

given two vertexes, find the third vertex to complement a triangle

Parameters

a	a triangulation vertex
b	adjacent triangulation vertex

Returns: third vertex, undefined if the vertexes are not adjacent

Definition at line 386 of file triangulation.cpp.

◆ vertex1()

Triangulation::Vertex_handle Triangulation::vertex1 ( Edge e )

static

Parameters

e	a triangulation edge

Returns: a handle to the first vertex of the edge

Definition at line 606 of file triangulation.cpp.

◆ vertex2()

Triangulation::Vertex_handle Triangulation::vertex2 ( Edge e )

static

Parameters

e	a triangulation edge

Returns: a handle to the second vertex of the edge

Definition at line 612 of file triangulation.cpp.

◆ vertices_begin()

TDS::Vertex_iterator frechet::poly::Triangulation::vertices_begin ( ) const

inline

Returns: iterator to the vertexes in the triangulation

Definition at line 330 of file triangulation.h.

◆ vertices_end()

TDS::Vertex_iterator frechet::poly::Triangulation::vertices_end ( ) const

inline

Returns: iterator beyond the end of vertexes in the triangulation

Definition at line 332 of file triangulation.h.

Member Data Documentation

◆ neighbors

NeighborMap frechet::poly::Triangulation::neighbors

private

Keeps track of diagonals and their neighborhood during construction.

Definition at line 207 of file triangulation.h.

◆ poly_n

int frechet::poly::Triangulation::poly_n

private

polygon size, number of vertexes in polyong

Definition at line 199 of file triangulation.h.

◆ south_pole

TDS::Vertex_handle frechet::poly::Triangulation::south_pole

private

a special vertex that completes the TDS structure

Definition at line 210 of file triangulation.h.

◆ tds

TDS frechet::poly::Triangulation::tds

private

CGAL Triangulation Data Structure.

Definition at line 201 of file triangulation.h.

◆ vertices

VertexMap frechet::poly::Triangulation::vertices

private

Definition at line 204 of file triangulation.h.

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

include/frechet/poly/triangulation.h
src/frechet/poly/triangulation.cpp

Detailed Description

Classes

Public Types

Public Member Functions

Static Public Member Functions

Private Types

Private Member Functions

Static Private Member Functions

Private Attributes

vertex and edge types

Member Typedef Documentation

◆ Edge

◆ Edge_range

◆ EdgePair

◆ Face_circulator

◆ Face_handle

◆ FacePair

◆ NeighborMap

◆ TDS

◆ TwoVertices

◆ Vertex

◆ Vertex_handle

◆ VertexMap

◆ VertexPair

Constructor & Destructor Documentation

◆ Triangulation() [1/2]

◆ Triangulation() [2/2]

◆ ~Triangulation()

Member Function Documentation

◆ addTargetVertex()

◆ addTargetVertices()

◆ addVertex() [1/2]

◆ addVertex() [2/2]

◆ adjacentEdges() [1/2]

◆ adjacentEdges() [2/2]

◆ adjacentFaces()

◆ adjacentVertices() [1/2]

◆ adjacentVertices() [2/2]

◆ assertEquals()

◆ clearPredecessors()

◆ clearTargets()

◆ complement()

◆ countFaces()

◆ countVertexes()

◆ createFace()

◆ createVertex()

◆ edge()

◆ edges()

◆ edges_begin()

◆ edges_end()

◆ incidentFaces()

◆ incidentVertexes()

◆ insertVertexOnEdge()

◆ is_ccw_face()

◆ is_diagonal()

◆ is_inner_face()

◆ is_outer_edge()

◆ is_outer_face()

◆ is_polygon_edge()

◆ is_south_pole()

◆ isComplete()

◆ linkNeighbors()

◆ mirror() [1/2]

◆ mirror() [2/2]

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ oppositeVertex()

◆ removeVertexFromEdge()

◆ resize()

◆ segment()

◆ setPolygonSize()

◆ size()

◆ third_vertex() [1/2]

◆ third_vertex() [2/2]

◆ thirdVertex()

◆ vertex1()

◆ vertex2()

◆ vertices_begin()

◆ vertices_end()

Member Data Documentation