\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.10.1 - Triangulated Surface Mesh Simplification
 All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members | Related Functions
EdgeCollapsableSurfaceMeshWithConstraints Concept Reference
Concepts

Definition

The concept EdgeCollapsableSurfaceMeshWithConstraints describes additional requirements for the type of triangulated surface meshes that can be passed to the simplification algorithm.

Refines:
EdgeCollapsableSurfaceMesh

Valid Expressions

Let v0v1 be an edge of the triangulated surface mesh ecm and v0 and v1 being the source and target vertices of that edge. The surface mesh simplification algorithm requires the call to the function halfedge_collapse(v0v1,ecm) to be valid and to return the vertex not removed after collapsing the undirected edge (v0v1,v1v0).

For e \( \in \{\) v0v1,v1v0 \( \}\), let en and ep be the next and previous edges, that is en = next_edge(e, surface_mesh), ep = prev_edge(e,surface_mesh), and let eno and epo be their opposite edges, that is eno = opposite_edge(en, surface_mesh) and epo = opposite_edge(ep,surface_mesh).

Then, after the collapse of (v0v1,v1v0) the invariants described in the concept EdgeCollapsableSurfaceMesh hold if ep is not constrained. Otherwise, it is en that is removed from ecm.

collapse_constraints.png
Has Models:
CGAL::Polyhedron_3<Traits> (If it has only triangular faces), using the specialization boost::graph_traits< CGAL::Polyhedron_3<Traits> > .
See Also
boost::graph_traits< CGAL::Polyhedron_3<Traits> >

Related Functions

(Note that these are not member functions.)

template<class EdgeCollapsableSurfaceMeshWithConstraints , class EdgeIsConstrainedMap >
boost::graph_traits
< EdgeCollapsableSurfaceMeshWithConstraints >
::vertex_descriptor 		halfedge_collapse (typename boost::graph_traits< EdgeCollapsableSurfaceMeshWithConstraints >::edge_descriptor const &ue, EdgeCollapsableSurfaceMeshWithConstraints &surface_mesh, EdgeIsConstrainedMap edge_is_constrained_map)
 Collapses the undirected edge (v0v1,v1v0) replacing it with v0 or v1, as described in the paragraph above and guarantees that a halfedge he, for which get(edge_is_constrained_map, he)==true, is not removed after the collapse. More...
 

Friends And Related Function Documentation

template<class EdgeCollapsableSurfaceMeshWithConstraints , class EdgeIsConstrainedMap >
boost::graph_traits< EdgeCollapsableSurfaceMeshWithConstraints >::vertex_descriptor halfedge_collapse ( typename boost::graph_traits< EdgeCollapsableSurfaceMeshWithConstraints >::edge_descriptor const &  ue,
EdgeCollapsableSurfaceMeshWithConstraints &  surface_mesh,
EdgeIsConstrainedMap  edge_is_constrained_map 
)
related

Collapses the undirected edge (v0v1,v1v0) replacing it with v0 or v1, as described in the paragraph above and guarantees that a halfedge he, for which get(edge_is_constrained_map, he)==true, is not removed after the collapse.

Template Parameters
EdgeCollapsableSurfaceMeshWithConstraintsa model of HalfedgeGraph
EdgeIsConstrainedMapa model of ReadablePropertyMap with the edge descriptor of EdgeCollapsableSurfaceMeshWithConstraints as key type and a boolean as value type. It indicates if an edge is constrained or not.
Precondition
This function requires surface_mesh to be an oriented 2-manifold with or without boundaries. Furthermore, the undirected edge (v0v1,v1v0) must satisfy the link condition [1], which guarantees that the surface mesh is also 2-manifold after the edge collapse.
get(edge_is_constrained_map, v0v1)==get(edge_is_constrained_map, v1v0)==false.
v0 and v1 are not both incident to a constrained edge.