CGAL 4.7 - 3D Surface Mesh Generation: Mesh Generation

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

CGAL 4.7 - 3D Surface Mesh Generation

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
Functions
Mesh Generation
Functions

##

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. More...
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. More...

## Function Documentation

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.

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>`).

`#include <CGAL/make_surface_mesh.h>`

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

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.

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

`#include <CGAL/make_surface_mesh.h>`