Mesh Generation

The function make_surface_mesh() is a surface mesh generator, that is a function to build a two dimensional mesh approximating a surface.

Template Parameters

SurfaceMeshC2T3	must be a model of the concept SurfaceMeshComplex_2InTriangulation_3, a data structure able to represent a two dimensional complex embedded in a three dimensional triangulation. The argument c2t3 of type SurfaceMeshC2T3, passed by reference to the surface mesh generator, is used to maintain the current approximating mesh and it stores the final mesh at the end of the procedure. The type SurfaceMeshC2T3 is in particular required to provide a type SurfaceMeshC2T3::Triangulation_3 for the three dimensional triangulation embedding the surface mesh. The vertex and cell base classes of the triangulation SurfaceMeshC2T3::Triangulation_3 are required to be models of the concepts SurfaceMeshVertexBase_3 and SurfaceMeshCellBase_3 respectively.
Surface	stands for the surface type. This type has to be a model of the concept Surface_3. The knowledge on the surface, required by the surface mesh generator is encapsulated in a traits class. Actually, the mesh generator accesses the surface to be meshed through this traits class only. The traits class is required to be a model of the concept SurfaceMeshTraits_3.
FacetsCriteria	has to be a model of the concept SurfaceMeshFacetsCriteria_3. The argument of type FacetsCriteria passed to the surface mesh generator specifies the size and shape requirements on the output surface mesh.
Tag	is a tag whose type affects the behavior of the meshing algorithm. The function make_surface_mesh() has specialized versions for the following tag types: Manifold_tag: the output mesh is guaranteed to be a manifold surface without boundary. Manifold_with_boundary_tag: the output mesh is guaranteed to be manifold but may have boundaries. Non_manifold_tag: the algorithm relies on the given criteria and guarantees nothing else.

The Delaunay refinement process is started with an initial set of points which is the union of two sets: the set of vertices in the initial triangulation pointed to by the c2t3 argument and a set of points provided by the traits class. The optional parameter initial_number_of_points allows to monitor the number of points in this second set. (This parameter is passed to the operator() of the constructor object Construct_initial_points in the traits class.) The meshing algorithm requires that the initial set of points includes at least one point on each connected components of the surface to be meshed.

See also

SurfaceMeshComplex_2InTriangulation_3

SurfaceMeshCellBase_3

SurfaceMeshVertexBase_3

Surface_3

SurfaceMeshFacetsCriteria_3

Surface_mesh_default_triangulation_3

Functions
template<class SurfaceMeshC2T3 , class Surface , class FacetsCriteria , class Tag >
void	CGAL::make_surface_mesh (SurfaceMeshC2T3 &c2t3, Surface surface, FacetsCriteria criteria, Tag tag, int initial_number_of_points=20)
	In the first overloaded version of of make_surface_mesh(), the surface type is given as template parameter (Surface) and the surface to be meshed is passed as parameter to the mesh generator.
template<class SurfaceMeshC2T3 , class SurfaceMeshTraits , class FacetsCriteria , class Tag >
void	CGAL::make_surface_mesh (SurfaceMeshC2T3 &c2t3, SurfaceMeshTraits::Surface_3 surface, SurfaceMeshTraits traits, FacetsCriteria criteria, Tag tag, int initial_number_of_points=20)
	In the second overloaded version of make_surface_mesh(), the surface mesh generator traits type is provided by the template parameter SurfaceMeshTraits_3 and the surface type is obtained from this traits type.

Function Documentation

make_surface_mesh() [1/2]

template<class SurfaceMeshC2T3 , class Surface , class FacetsCriteria , class Tag >

void CGAL::make_surface_mesh	(	SurfaceMeshC2T3 &	c2t3,
		Surface	surface,
		FacetsCriteria	criteria,
		Tag	tag,
		int	initial_number_of_points = 20
	)

#include <CGAL/make_surface_mesh.h>

In the first overloaded version of of make_surface_mesh(), the surface type is given as template parameter (Surface) and the surface to be meshed is passed as parameter to the mesh generator.

In that case the surface mesh generator traits type is automatically generated form the surface type by an auxiliary class called the Surface_mesh_traits_generator_3.

The first overloaded version can be used whenever the surface type either provides a nested type Surface::Surface_mesher_traits_3 that is a model of SurfaceMeshTraits_3 or is a surface type for which a specialization of the traits generator Surface_mesh_traits_generator_3<Surface> is provided. Currently, the library provides partial specializations of Surface_mesh_traits_generator_3<Surface> for implicit surfaces (Implicit_surface_3<Traits, Function>) and gray level images (Gray_level_image_3<FT, Point>).

Examples

Surface_mesher/mesh_a_3d_gray_image.cpp, and Surface_mesher/mesh_an_implicit_function.cpp.

make_surface_mesh() [2/2]

template<class SurfaceMeshC2T3 , class SurfaceMeshTraits , class FacetsCriteria , class Tag >

void CGAL::make_surface_mesh	(	SurfaceMeshC2T3 &	c2t3,
		SurfaceMeshTraits::Surface_3	surface,
		SurfaceMeshTraits	traits,
		FacetsCriteria	criteria,
		Tag	tag,
		int	initial_number_of_points = 20
	)

#include <CGAL/make_surface_mesh.h>

In the second overloaded version of make_surface_mesh(), the surface mesh generator traits type is provided by the template parameter SurfaceMeshTraits_3 and the surface type is obtained from this traits type.

Both the surface and the traits are passed to the mesh generator as arguments.