TriangulationDataStructure

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TriangulationDataStructure_3::Cell

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 40.1.)

Types

The class TriangulationDataStructure_3::Cell defines the following types.

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

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.

Operations

Access Functions

Vertex_handle

c.vertex ( int i) const

Returns the vertex i of c.

Precondition:

i ∈ {0, 1, 2, 3}.

int

c.index ( Vertex_handle v) const

Returns the index of vertex v in c.

Precondition:

v is a vertex of c.

bool

c.has_vertex ( Vertex_handle v) const

Returns true if v is a vertex of c.

bool

c.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

c.neighbor ( int i) const

Returns the neighbor i of c.

Precondition:

i ∈ {0, 1, 2, 3}.

int

c.index ( Cell_handle n) const

Returns the index corresponding to neighboring cell n.

Precondition:

n is a neighbor of c.

bool

c.has_neighbor ( Cell_handle n) const

Returns true if n is a neighbor of c.

bool

c.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

c.set_vertex ( int i, Vertex_handle v)

Sets vertex i to v.

Precondition:

i ∈ {0, 1, 2, 3}.

void

c.set_vertices ( Vertex_handle v0, Vertex_handle v1, Vertex_handle v2, Vertex_handle v3)

Sets the vertex pointers.

void

c.set_neighbor ( int i, Cell_handle n)

Sets neighbor i to n.

Precondition:

i ∈ {0, 1, 2, 3}.

void

c.set_neighbors ( Cell_handle n0, Cell_handle n1, Cell_handle n2, Cell_handle n3)

Sets the neighbors pointers.

Checking

bool	c.is_valid ( bool verbose = false, int level = 0) const
		User defined local validity checking function.