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

CGAL 4.3 - Triangulated Surface Mesh Simplification

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EdgeProfile Concept Reference
Concepts

## Definition

The concept `EdgeProfile` describes the requirements for a data structure that caches the local topology and geometry in the surroundings of an undirected edge.

This profile is used by the stop, cost and placement policies.

Has Models:
  `CGAL::Surface_mesh_simplification::Edge_profile<ECM>`

## Types
typedef unspecified_type | ECM
| The type of the surface to simplify. More...
boost::graph_traits< ECM > ::vertex_descriptor | vertex_descriptor
| A Bgl vertex descriptor representing a vertex of the surface.
boost::graph_traits< ECM > ::edge_descriptor | edge_descriptor
| A Bgl edge descriptor representing an edge of the surface.
CGAL::halfedge_graph_traits < ECM >::Point | Point
| The point type for the surface vertex. More...

## Access Functions
vertex_descriptor | v0 () const
| One of vertices of the edge to be collapsed.
vertex_descriptor | v1 () const
| The other vertex of the edge to be collapsed.
edge_descriptor | v0_v1 () const
| One of the directed edges corresponding to the undirected edge being collapsed.
edge_descriptor | v1_v0 () const
| The other directed edge corresponding to the undirected edge being collapsed.
Point const & | p0 () const
| The point of vertex `v0`.
Point const & | p1 () const
| The point of vertex `v1`.
vertex_descriptor | vL () const
| If `v0v1` belongs to a finite face (is not a border edge) the third vertex of that triangular face, a null descriptor otherwise.
edge_descriptor | v1_vL () const
| If `v0v1` belongs to a finite face (is not a border edge) the directed edge from `v1` to `vL`, a null descriptor otherwise.
edge_descriptor | vL_v0 () const
| If `v0v1` belongs to a finite face (is not a border edge) the directed edge from `vL` to `v0`, a null descriptor otherwise.
vertex_descriptor | vR () const
| If `v1v0` belongs to a finite face (is not a border edge) the third vertex of that triangular face, a null descriptor otherwise.
edge_descriptor | v0_vR () const
| If `v1v0` belongs to a finite face (is not a border edge) the directed edge from `v0` to `vR`, a null descriptor otherwise.
edge_descriptor | vR_v1 () const
| If `v1v0` belongs to a finite face (is not a border edge) the directed edge from `vR` to `v1`, a null descriptor otherwise.
std::vector< vertex_descriptor > | link () const
| The unique sequence of the vertices around `v0v1` in topological order (ccw or ccw depending on the relative ordering of `v0` and `v1` in the profile).
std::vector< edge_descriptor > | border_edges () const
| The unique collection of the border directed edges incident upon `v0` and `v1`.
bool | left_face_exits () const
| Indicates if `v0v1` belongs to a finite face of the mesh (i.e, `v0v1` is not a border edge).
bool | right_face_exits () const
| Indicates if `v0v1` belongs to a finite face of the mesh (i.e, `v1v0` is not a border edge).

## Member Typedef Documentation

typedef unspecified_type EdgeProfile::ECM

The type of the surface to simplify.

Must be a model of the `EdgeCollapsableMesh` concept.

## Member Data Documentation

CGAL::halfedge_graph_traits<ECM>::Point EdgeProfile::Point

The point type for the surface vertex.

Must be a model of `Point_3`.