CGAL 4.7 - 3D Surface Mesh Generation: Refinement Relationships

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

CGAL 4.7 - 3D Surface Mesh Generation

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Refinement Relationships

Concept SurfaceMeshCellBase_3
  `TriangulationCellBase_3` The concept `SurfaceMeshCellBase_3` adds four markers to mark the facets of the triangulation that belong to the two dimensional complex, and four markers that are helpers used in some operations to mark for instance the facets that have been visited.
  This concept also provides storage for the center of a Delaunay surface ball. Given a surface and a 3D Delaunay triangulation, a Delaunay surface ball is a ball circumscribed to a facet of the triangulation and centered on the surface and empty of triangulation vertices. Such a ball does exist when the facet is part of the restriction to the surface of a three dimensional triangulation. In the following we call surface center of a facet, the center of its biggest Delaunay surface ball.
Concept SurfaceMeshVertexBase_3
  `TriangulationVertexBase_3` The surface mesher algorithm issues frequent queries about the status of the vertices with respect to the two dimensional complex that represents the current surface approximation. The class SurfaceMeshVertexBase_3 offers a caching mechanism to answer more efficiently these queries. The caching mechanism includes two cached integers, which, when they are valid, store respectively the number of complex facets incident to the vertex and the number of connected components of the adjacency graph of those facets.