\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.5 - 3D Surface Mesh Generation
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CGAL::Surface_mesh_default_criteria_3< Tr > Class Template Reference
Mesh and Domain Classes

#include <CGAL/Surface_mesh_default_criteria_3.h>

Definition

The class Surface_mesh_default_criteria_3 implements the most commonly used combination of meshing criteria.

It involves mainly three criteria which are in order:

  • a lower bound on the minimum angle in degrees of the surface mesh facets.

  • an upper bound on the radius of surface Delaunay balls. A surface Delaunay ball is a ball circumscribing a facet, centered on the surface and empty of vertices. Such a ball exists for each facet of the current surface mesh. Indeed the current surface mesh is the Delaunay triangulation of the current sampling restricted to the surface which is just the set of facets in the three dimensional Delaunay triangulation of the sampling that have a Delaunay surface ball.

  • an upper bound on the center-center distances of the surface mesh facets. The center-center distance of a surface mesh facet is the distance between the facet circumcenter and the center of its surface Delaunay ball.
Is Model Of:
SurfaceMeshFacetsCriteria_3
See Also
make_surface_mesh
Examples:
Surface_mesher/mesh_a_3d_gray_image.cpp, Surface_mesher/mesh_an_implicit_function.cpp, and Surface_mesher/polyhedron_remesher.cpp.

Types

typedef Tr::FT FT
 The numerical type.
 

Creation

 Surface_mesh_default_criteria_3 (FT angle_bound, FT radius_bound, FT distance_bound)
 Returns a Surface_mesh_default_criteria_3 with angle_bound, radius_bound, distance_bound as bounds for the minimum facet angle in degrees, the radius of the surface Delaunay balls and the center-center distances respectively.