CGAL 5.4  2D Conforming Triangulations and Meshes

The concept MeshingCriteria_2
defines the meshing criteria to be used in the algorithm. It provides a predicate Is_bad
that tests a triangle according to criteria. The return type of Is_bad
is an enum Mesh_2::Face_badness
.
The possible values of CGAL::Mesh_2::Face_badness
are CGAL::Mesh_2::NOT_BAD
, CGAL::Mesh_2::BAD
and CGAL::Mesh_2::IMPERATIVELY_BAD
. If the predicate returns BAD
, the triangle is marked as bad and the algorithm will try to destroy it. If the predicates returns CGAL::Mesh_2::IMPERATIVELY_BAD
, the algorithm will destroy the triangle unconditionally during its execution.
The termination of the algorithm is guaranteed when criteria are shape criteria corresponding to a bound on smallest angles not less than \( 20.7\) degrees (this corresponds to a radiusedge ratio bound not less than \( \sqrt{2}\)). Any size criteria that are satisfied by small enough triangle can be added to the set of criteria without compromising the termination.
Note that, in the presence of input angles smaller than \( 60\) degrees, some bad shaped triangles can appear in the final mesh in the neighboring of small angles. To achieve termination and the respect of size criteria everywhere, the Is_bad
predicate has to return CGAL::Mesh_2::IMPERATIVELY_BAD
when size criteria are not satisfied, and CGAL::Mesh_2::BAD
when shape criteria are not satisfied.
MeshingCriteria_2
also provides a type Quality
designed to code a quality measure for triangles. The type Quality
must be lessthan comparable as the meshing algorithm will order bad triangles by quality, to split those with smallest quality first. The predicate Is_bad
computes the quality of the triangle as a byproduct.
Types  
typedef unspecified_type  Face_handle 
Handle to a face of the triangulation.  
typedef unspecified_type  Quality 
Default constructible, copy constructible, assignable, and lessthan comparable type.  
typedef unspecified_type  Is_bad 
Predicate object. More...  
Access to predicate and constructor objects  
Is_bad  is_bad_object () 
Predicate object.
Must provide two operators.
The first operator Mesh_2::Face_badness operator()(Face_handle fh, Quality& q)
returns
CGAL::Mesh_2::NOT_BAD
if it satisfies the desired criteria for mesh triangles,CGAL::Mesh_2::BAD
if it does not, andCGAL::Mesh_2::IMPERATIVELY_BAD
if it does not and should be refined unconditionally.In addition, this operator assigns to q
a value measuring the quality of the triangle pointed by fh
.
Mesh_2::Face_badness operator()(Quality q)
returnsCGAL::Mesh_2::NOT_BAD
if q
is the quality of a good triangle,CGAL::Mesh_2::BAD
if the q
represents a poor quality, andCGAL::Mesh_2::IMPERATIVELY_BAD
if q
represents the quality of a bad triangle that should be refined unconditionally.