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

CGAL 4.3 - Approximation of Ridges and Umbilics on Triangulated Surface Meshes

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TriangulatedSurfaceMesh Concept Reference
Concepts

## Definition

The concept `TriangulatedSurfaceMesh` describes an oriented surface (possibly with boundary) embedded in the 3 space. It is combinatorially based on a halfedge data structure with triangular faces, geometrically 3d points associated to the vertices define the embedding.

Has Models:
  `CGAL::Polyhedron_3` with the restriction that faces are triangular.

Creation

Construction and destruction are undefined.

## Concepts
concept | Facet
| Opaque type representing a facet of the `TriangulatedSurfaceMesh` . More...
concept | Halfedge
| Opaque type representing a halfedge of the `TriangulatedSurfaceMesh` . More...
concept | Vertex
| Opaque type representing a vertex of the `TriangulatedSurfaceMesh` . More...

## Types
typedef unspecified_type | Facet_handle
| Handle to a facet. More...
typedef unspecified_type | Facet_const_handle
typedef unspecified_type | Facet_iterator
| Iterator over all mesh facets. More...
typedef unspecified_type | Facet_const_iterator
typedef unspecified_type | Vertex_handle
| Handle to a vertex. More...
typedef unspecified_type | Vertex_const_handle
typedef unspecified_type | Vertex_iterator
| Iterator over all vertices of a mesh. More...
typedef unspecified_type | Vertex_const_iterator
typedef unspecified_type | Halfedge_handle
| Handle to a halfedge. More...
typedef unspecified_type | Halfedge_const_handle
typedef unspecified_type | Halfedge_iterator
| Iterator over all halfedges of a `TriangulatedSurfaceMesh` . More...
typedef unspecified_type | Halfedge_const_iterator
typedef unspecified_type | Point_iterator
| Iterator over all points of a `TriangulatedSurfaceMesh` , its value type is `Traits::Point_3`. More...
typedef unspecified_type | Point_const_iterator

## Operations
Facet_const_iterator | facets_begin ()
| iterator over all facets (excluding holes).
Facet_const_iterator | facets_end ()
| past-the-end iterator.
Point_iterator | points_begin ()
| iterator over all points.
Point_iterator | points_end ()
| past-the-end iterator.

## Member Typedef Documentation

typedef unspecified_type TriangulatedSurfaceMesh::Facet_handle

Handle to a facet.

Model of the Handle concept.

typedef unspecified_type TriangulatedSurfaceMesh::Facet_iterator

Iterator over all mesh facets.

Model of the ForwardIterator concept.

typedef unspecified_type TriangulatedSurfaceMesh::Halfedge_handle

Handle to a halfedge.

Model of the Handle concept.

typedef unspecified_type TriangulatedSurfaceMesh::Halfedge_iterator

Iterator over all halfedges of a `TriangulatedSurfaceMesh` .

Model of the ForwardIterator concept.

typedef unspecified_type TriangulatedSurfaceMesh::Point_iterator

Iterator over all points of a `TriangulatedSurfaceMesh` , its value type is `Traits::Point_3`.

Model of the `ForwardIterator` concept.

typedef unspecified_type TriangulatedSurfaceMesh::Vertex_handle

Handle to a vertex.

Model of the Handle concept.

typedef unspecified_type TriangulatedSurfaceMesh::Vertex_iterator

Iterator over all vertices of a mesh.

Model of the ForwardIterator concept.