Mesh_criteria

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CGAL::Mesh_criteria_3<Tr>

Definition

The class Mesh_criteria_3<Tr> is a model of both concepts MeshCriteria_3 and MeshCriteriaWithFeatures_3. It gathers the refinement criteria for mesh tetrahedra and surface facets where surface facets are facets in the mesh approximating the domain surface patches. In addition, for domain with exposed 1-dimensional features, the class Mesh_criteria_3<Tr> handles the definition of a sizing field to guide the discretization of 1-dimensional features.

#include <CGAL/Mesh_criteria_3.h>

Parameters

The parameter Tr has to be instantiated with the type used for C3T3::Triangulation, where C3T3 is the model of MeshComplex_3InTriangulation_3 used in the mesh generation process, and C3T3::Triangulation its nested triangulation type.

Is Model for the Concepts

MeshCriteria_3

Types

typedef Mesh_edge_criteria_3<Tr>	Edge_criteria;	The criteria for edges.
typedef Mesh_facet_criteria_3<Tr>	Facet_criteria;	The criteria for facets.
typedef Mesh_cell_criteria_3<Tr>	Cell_criteria;	The criteria for cells.

Creation

Mesh_criteria_3<Tr> mc ( Facet_criteria facet_criteria, Cell_criteria cell_criteria);

Construction from facet and cell criteria. The edge criteria are ignored in this case.

Mesh_criteria_3<Tr> mc ( Edge_criteria edge_criteria, Facet_criteria facet_criteria, Cell_criteria cell_criteria);

Construction from edge, facet and cell criteria.

template<typename FT, typename ...Fieldi>

Mesh_criteria_3<Tr> mc ( Field1 parameters::edge_size = ignored,
FT parameters::facet_angle = ignored,
Field2 parameters::facet_size = ignored,
Field3 parameters::facet_distance = ignored,
Mesh_facet_topology parameters::facet_topology = CGAL::FACET_VERTICES_ON_SURFACE,
FT parameters::cell_radius_edge_ratio = ignored,
Field4 parameters::cell_size = ignored);

Construction from criteria parameters. This constructor uses named parameters (from Boost.Parameter) for convenient criteria construction. See a complete description of these parameters below.

The template parameter FT should be a model of concept FieldType. The template parameters Fieldi (i ∈ {1..4}) should be either a model of the concept FieldType or a model of the concept MeshDomainField_3.

The parameters are named parameters and can be passed in any order provided their name is given (see example below). The name of each parameter is the one that is written in the description of the function (e.g. parameters::facet_size).

The description of each parameter is as follows:

-edge_size: a scalar field (resp. a constant) providing a space varying (resp. a uniform) upper bound for the lengths of curve segment edges.

-facet_angle: a lower bound for the angles (in degrees) of the surface mesh facets.
-facet_size: a scalar field (resp. a constant) describing a space varying (resp. a uniform) upper-bound or for the radii of the surface Delaunay balls.
-facet_distance: a scalar field (resp. a constant) describing a space varying (resp. a uniform) upper bound for the same distance.
-facet_topology: the set of topological constraints which have to be verified by each surface facet. The default value is CGAL::FACET_VERTICES_ON_SURFACE. See Mesh_facet_topology manual page to get all possible values.

-cell_radius_edge_ratio: an upper bound for the radius-edge ratio of the mesh tetrahedra.
-cell_size: a scalar field (resp. a constant) describing a space varying (resp. a uniform) upper-bound for the circumradii of the mesh tetrahedra.

Note that each size or distance parameter can be specified using two ways: either as scalar field or as a numerical value when the field is uniform.

Each parameter has a special default value ignored which means that the corresponding criteria will be ignored. Numerical sizing or distance values, as well as scalar fields should be given in the unit used for coordinates of points in the mesh domain class of the mesh generation process.

Example

// Create a Mesh_criteria_3<Tr> object with all cell and facet parameters set
Mesh_criteria_3<Tr> criteria (parameters::facet_angle=30,
                              parameters::facet_size=1,
                              parameters::facet_distance=0.1,
                              parameters::cell_radius_edge_ratio=2,
                              parameters::cell_size=1.5);

// Create a Mesh_criteria_3<Tr> object with size ignored (note that the order changed)
Mesh_criteria_3<Tr> criteria (parameters::cell_radius_edge_ratio=2,
                              parameters::facet_angle=30,
                              parameters::facet_distance=0.1);