\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.3 - 3D Triangulation Data Structure

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TriangulationDataStructure_3::Vertex Concept Reference
Concepts

## Definition

The concept `TriangulationDataStructure_3::Vertex` represents the vertex class of a 3D-triangulation data structure. It must define the types and operations listed in this section. Some of these requirements are of geometric nature, they are optional when using the triangulation data structure class alone. They become compulsory when the triangulation data structure is used as a layer for the geometric triangulation class. (See Section Software Design.)

Creation

In order to obtain new vertices or destruct unused vertices, the user must call the `create_vertex()` and `delete_vertex()` methods of the triangulation data structure.

See Also
  `TriangulationDataStructure_3::Cell`

## Types
The class `Vertex` defines types that are the same as some of the types defined by the triangulation data structure class `TriangulationDataStructure_3`.
typedef unspecified_type | Point
| Optional for the triangulation data structure alone.
typedef TriangulationDataStructure_3 | Triangulation_data_structure
typedef TriangulationDataStructure_3::Vertex_handle | Vertex_handle
typedef TriangulationDataStructure_3::Cell_handle | Cell_handle

## Access Functions
Cell_handle | cell () const
| Returns a cell of the triangulation having `v` as vertex.
Point | point () const
| Returns the point stored in the vertex. More...

## Setting
void | set_cell (Cell_handle c)
| Sets the incident cell to `c`.
void | set_point (const Point &p)
| Sets the point to `p`. More...

## Checking
bool | is_valid (bool verbose=false) const
| This is a function for debugging purpose. More...

## Member Function Documentation

bool TriangulationDataStructure_3::Vertex::is_valid | ( | bool | verbose = `false`) |  | const

This is a function for debugging purpose.

Debugging Support

Checks the validity of the vertex. Must check that its incident cell has this vertex. The validity of the base vertex is also checked.

When `verbose` is set to `true`, messages are printed to give a precise indication on the kind of invalidity encountered.

Point TriangulationDataStructure_3::Vertex::point | ( | ) |  | const

Returns the point stored in the vertex.

Optional for the triangulation data structure alone.

void TriangulationDataStructure_3::Vertex::set_point | ( | const Point & | p) |  |

Sets the point to `p`.

Optional for the triangulation data structure alone.