\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.4 - 3D Triangulation Data Structure
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TriangulationDataStructure_3::Cell Concept Reference

Definition

The concept TriangulationDataStructure_3::Cell stores four Vertex_handles to its four vertices and four Cell_handles to its four neighbors. The vertices are indexed 0, 1, 2, and 3 in consistent order. The neighbor indexed \( i\) lies opposite to vertex i.

In degenerate dimensions, cells are used to store faces of maximal dimension: in dimension 2, each cell represents only one facet of index 3, and 3 edges \( (0,1)\), \( (1,2)\) and \( (2,0)\); in dimension 1, each cell represents one edge \( (0,1)\). (See also Section Representation.)

Creation

In order to obtain new cells or destruct unused cells, the user must call the create_cell() and delete_cell() methods of the triangulation data structure.

See Also
TriangulationDataStructure_3::Vertex

Types

typedef
TriangulationDataStructure_3 
Triangulation_data_structure
 
typedef
TriangulationDataStructure_3::Vertex_handle 
Vertex_handle
 
typedef
TriangulationDataStructure_3::Cell_handle 
Cell_handle
 

Access Functions

Vertex_handle vertex (int i) const
 Returns the vertex i of c. More...
 
int index (Vertex_handle v) const
 Returns the index of vertex v in c. More...
 
bool has_vertex (Vertex_handle v) const
 Returns true if v is a vertex of c.
 
bool has_vertex (Vertex_handle v, int &i) const
 Returns true if v is a vertex of c, and computes its index i in c.
 
Cell_handle neighbor (int i) const
 Returns the neighbor i of c. More...
 
int index (Cell_handle n) const
 Returns the index corresponding to neighboring cell n. More...
 
bool has_neighbor (Cell_handle n) const
 Returns true if n is a neighbor of c.
 
bool has_neighbor (Cell_handle n, int &i) const
 Returns true if n is a neighbor of c, and computes its index i in c.
 

Setting

void set_vertex (int i, Vertex_handle v)
 Sets vertex i to v. More...
 
void set_vertices (Vertex_handle v0, Vertex_handle v1, Vertex_handle v2, Vertex_handle v3)
 Sets the vertex pointers.
 
void set_neighbor (int i, Cell_handle n)
 Sets neighbor i to n. More...
 
void set_neighbors (Cell_handle n0, Cell_handle n1, Cell_handle n2, Cell_handle n3)
 Sets the neighbors pointers.
 

Checking

bool is_valid (bool verbose=false, int level=0) const
 This is a function for debugging purpose. More...
 

Member Function Documentation

int TriangulationDataStructure_3::Cell::index ( Vertex_handle  v) const

Returns the index of vertex v in c.

Precondition
v is a vertex of c.
int TriangulationDataStructure_3::Cell::index ( Cell_handle  n) const

Returns the index corresponding to neighboring cell n.

Precondition
n is a neighbor of c.
bool TriangulationDataStructure_3::Cell::is_valid ( bool  verbose = false,
int  level = 0 
) const

This is a function for debugging purpose.

Debugging Support

User defined local validity checking function.

Cell_handle TriangulationDataStructure_3::Cell::neighbor ( int  i) const

Returns the neighbor i of c.

Precondition
\( i \in\{0, 1, 2, 3\}\).
void TriangulationDataStructure_3::Cell::set_neighbor ( int  i,
Cell_handle  n 
)

Sets neighbor i to n.

Precondition
\( i \in\{0, 1, 2, 3\}\).
void TriangulationDataStructure_3::Cell::set_vertex ( int  i,
Vertex_handle  v 
)

Sets vertex i to v.

Precondition
\( i \in\{0, 1, 2, 3\}\).
Vertex_handle TriangulationDataStructure_3::Cell::vertex ( int  i) const

Returns the vertex i of c.

Precondition
\( i \in\{0, 1, 2, 3\}\).