A data structure for 3D Voronoi cells. More...

#include <easy3d/algo/delaunay_3d.h>

Public Member Functions
	VoronoiCell3d ()
	Default constructor.

void	clear ()
	Clears the Voronoi cell.

unsigned int	nb_facets () const
	Returns the number of facets in the Voronoi cell.

unsigned int	facet_begin (unsigned int f) const
	Returns the starting index of the vertices for facet `f`.

unsigned int	facet_end (unsigned int f) const
	Returns the ending index of the vertices for facet `f`.

unsigned int	nb_vertices (unsigned int f) const
	Returns the number of vertices in facet `f`.

unsigned int	next_around_facet (unsigned int f, unsigned int i) const
	Returns the next vertex index around facet `f` starting from vertex `i`.

unsigned int	prev_around_facet (unsigned int f, unsigned int i) const
	Returns the previous vertex index around facet `f` starting from vertex `i`.

unsigned int	facet_bisector (unsigned int f) const
	Returns the bisector vertex for facet `f`.

int	edge_bisector (unsigned int i) const
	Returns the edge bisector for vertex `i`.

const vec3 &	vertex (unsigned int i) const
	Returns the coordinates of vertex `i`.

bool	vertex_is_infinite (unsigned int i) const
	Checks if vertex `i` is at infinity.

void	begin_facet (unsigned int f_bisector)
	Begins a new facet with the given bisector vertex.

void	add_to_facet (int e_bisector, const vec3 &v, bool infinite)
	Adds a vertex to the current facet.

void	add_to_facet (int e_bisector, bool infinite)
	Adds a vertex to the current facet without specifying coordinates.

void	end_facet ()
	Ends the current facet.

unsigned int	find_facet (unsigned int bisector) const
	Finds the index of the facet with the given bisector vertex.

Detailed Description

A data structure for 3D Voronoi cells.

A 3D Voronoi cell stores the dual facets in a Compressed Row Storage (CRS) array.

Each facet knows the bisector it is on, and the list of vertices/edges.
Each vertex knows the tet it is dual to.
Each edge knows the other bisector it is on (an edge is defined as the intersection between the facet bisector and the edge bisector).

Member Function Documentation

◆ add_to_facet() [1/2]

void add_to_facet	(	int	e_bisector,
		bool	infinite )

inline

Adds a vertex to the current facet without specifying coordinates.

Parameters

e_bisector	The edge bisector for the vertex.
infinite	True if the vertex is at infinity, false otherwise.

◆ add_to_facet() [2/2]

void add_to_facet	(	int	e_bisector,
		const vec3 &	v,
		bool	infinite )

inline

Adds a vertex to the current facet.

Parameters

e_bisector	The edge bisector for the vertex.
v	The coordinates of the vertex.
infinite	True if the vertex is at infinity, false otherwise.

◆ begin_facet()

void begin_facet ( unsigned int f_bisector )

inline

Begins a new facet with the given bisector vertex.

Parameters

f_bisector The bisector vertex for the new facet.

◆ edge_bisector()

int edge_bisector ( unsigned int i ) const

inline

Returns the edge bisector for vertex i.

The vertices of facet(f) are denoted by indices i in the range[facet_begin(f) ... facet_end(f) - 1]. Vertex i is the dual of a tetrahedron t incident to the edge [v1,v2]. edge_bisector(i) returns the vertex of t oriented clockwise relative to the edge [v1,v2].

Note: An infinite facet has two vertices i1 and i2 that are dual to infinite tetrahedra. Supposing the proper ordering of i1 and i2, edge_bisector(i1) returns the vertex of the boundary facet that is incident to [v1,v2], and edge_bisector(i2) returns -1 (infinite vertex). The other vertex of the other boundary facet that is incident to [v1,v2] is encountered when traversing the dual vertex/tetrahedron that precedes v2.

Parameters

i	The index of the vertex.

Returns: The edge bisector.

◆ facet_begin()

unsigned int facet_begin ( unsigned int f ) const

inline

Returns the starting index of the vertices for facet f.

Parameters

f	The index of the facet.

Returns: The starting index of the vertices.

◆ facet_bisector()

unsigned int facet_bisector ( unsigned int f ) const

inline

Returns the bisector vertex for facet f.

This VoronoiCell3d is the dual of vertex v1, Facet f lies on the bisector plane of [v1,v2], and facet_bisector(f) returns v2.

Parameters

f	The index of the facet.

Returns: The bisector vertex.

◆ facet_end()

unsigned int facet_end ( unsigned int f ) const

inline

Returns the ending index of the vertices for facet f.

Parameters

f	The index of the facet.

Returns: The ending index of the vertices.

◆ find_facet()

unsigned int find_facet ( unsigned int bisector ) const

inline

Finds the index of the facet with the given bisector vertex.

Parameters

bisector The bisector vertex.

Returns: The index of the facet.

◆ nb_facets()

unsigned int nb_facets ( ) const

inline

Returns the number of facets in the Voronoi cell.

Returns: The number of facets.

◆ nb_vertices()

unsigned int nb_vertices ( unsigned int f ) const

inline

Returns the number of vertices in facet f.

Parameters

f	The index of the facet.

Returns: The number of vertices.

◆ next_around_facet()

unsigned int next_around_facet	(	unsigned int	f,
		unsigned int	i ) const

inline

Returns the next vertex index around facet f starting from vertex i.

Parameters

f	The index of the facet.
i	The index of the current vertex.

Returns: The next vertex index.

◆ prev_around_facet()

unsigned int prev_around_facet	(	unsigned int	f,
		unsigned int	i ) const

inline

Returns the previous vertex index around facet f starting from vertex i.

Parameters

f	The index of the facet.
i	The index of the current vertex.

Returns: The previous vertex index.

◆ vertex()

const vec3 & vertex ( unsigned int i ) const

inline

Returns the coordinates of vertex i.

For finite dual vertices, returns the Voronoi vertex. For dual vertices at infinity, returns the direction (normal to primal facet on the boundary).

Parameters

i	The index of the vertex.

Returns: The coordinates of the vertex.

◆ vertex_is_infinite()

bool vertex_is_infinite ( unsigned int i ) const

inline

Checks if vertex i is at infinity.

Parameters

i	The index of the vertex.

Returns: True if the vertex is at infinity, false otherwise.

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

G:/3_code/Easy3D/easy3d/algo/delaunay_3d.h

Public Member Functions

Detailed Description

Member Function Documentation

◆ add_to_facet() [1/2]

◆ add_to_facet() [2/2]

◆ begin_facet()

◆ edge_bisector()

◆ facet_begin()

◆ facet_bisector()

◆ facet_end()

◆ find_facet()

◆ nb_facets()

◆ nb_vertices()

◆ next_around_facet()

◆ prev_around_facet()

◆ vertex()

◆ vertex_is_infinite()