CGAL 5.6.1  3D Mesh Generation

The concept MeshDomain_3
describes the knowledge required on the object to be discretized. The concept MeshDomain_3
is the concept to be used when the input domain does not have \( 0\) or \( 1\)dimensional features that need to be accurately approximated by the mesh. In such a case, the queries issued by the meshing process concern only the faces of the input domain with dimension \( 3\) and \( 2\), that are respectively called subdomains and surface patches.
More specifically the concept MeshDomain_3
provides a method to localize a point with respect to the input domain and its subdomains. Moreover, as the concept SurfaceMeshTraits_3
, it also provides predicates to test whether a query segment (or a ray, or a line) intersects the boundary of the domain or of the subdomains, and constructors to compute some intersection point if any. It also includes a method able to provide a small set of initial points on the boundary.
In the following we consider only proper intersection with the domain and subdomain boundaries. A segment, ray or line is said to intersect properly the domain boundary (resp. a subdomain boundary) if it includes points which are strictly inside and strictly outside the domain (resp. the subdomain).
CGAL::Polyhedral_mesh_domain_3<Polyhedron,IGT,TriangleAccessor>
Types  
typedef unspecified_type  R 
Geometric traits class. More...  
typedef unspecified_type  Point_3 
Point type.  
typedef unspecified_type  Segment_3 
Segment type.  
typedef unspecified_type  Ray_3 
Ray type.  
typedef unspecified_type  Line_3 
Line type.  
typedef CGAL::Tag_false  Has_features 
A type to distinguish MeshDomain_3 models from MeshDomainWithFeatures_3 models.  
typedef unspecified_type  Subdomain_index 
Type of indices for subdomains of the input domain. More...  
typedef unspecified_type  Surface_patch_index 
Type of indices for surface patches (boundaries and interfaces) of the input domain. More...  
typedef unspecified_type  Index 
Type of indices to be stored at mesh vertices to characterize the lowest dimensional face of the input complex on which the vertex lies. More...  
typedef std::tuple< Point_3, Index, int >  Intersection 
Returns type of Construct_intersection queries. More...  
typedef unspecified_type  Construct_initial_points 
A function object to construct a set of initial points on the surface of the domain. More...  
typedef unspecified_type  Is_in_domain 
A function object to query whether a point is in the input domain or not. More...  
typedef unspecified_type  Do_intersect_surface 
A function object which answers intersection queries between the surface patches of the domain and objects of type Segment_3 , Ray_3 or Line_3 . More...  
typedef unspecified_type  Construct_intersection 
A function object to construct the intersection between an object of type Segment_3 , Ray_3 or Line_3 and an interface. More...  
Bounding box  
Since CGAL4.8, a model of  
Bbox_3  bbox () const 
Returns a bounding box of the domain.  
Operations  
The following functions give access to the function objects:  
Construct_initial_points  construct_initial_points_object () 
Is_in_domain  is_in_domain_object () 
Do_intersect_surface  do_intersect_surface_object () 
Construct_intersection  construct_intersection_object () 
Index Conversion  
Index  index_from_surface_patch_index (Surface_patch_index surface_patch_index) 
Returns the index to be stored at a vertex lying on the surface patch identified by surface_patch_index .  
Index  index_from_subdomain_index (Subdomain_index subdomain_index) 
Returns the index to be stored at a vertex lying in the subdomain identified by subdomain_index .  
Surface_patch_index  surface_patch_index (Index index) 
Returns the Surface_patch_index of the surface patch where lies a vertex with dimension 2 and index index .  
Subdomain_index  subdomain_index (Index index) 
Returns the index of the subdomain containing a vertex with dimension 3 and index index .  
A function object to construct a set of initial points on the surface of the domain.
Provides the following operators:
template<typename OutputIterator>
OutputIterator operator()(OutputIterator pts)
template<typename OutputIterator>
OutputIterator operator()(OutputIterator pts, int n)
Those two operators output a set of (n
) surface points to the output iterator pts
, as objects of type std::pair<Point_3, Index>
. If n
is not given, the functor must provide enough points to initialize the mesh generation process.
A function object to construct the intersection between an object of type Segment_3
, Ray_3
or Line_3
and an interface.
Provides the operators:
Intersection operator()(Segment_3 s)
Intersection operator()(Ray_3 r)
Intersection operator()(Line_3 l)
A function object which answers intersection queries between the surface patches of the domain and objects of type Segment_3
, Ray_3
or Line_3
.
Provides the operators:
boost::optional<Surface_patch_index> operator()(Segment_3 s)
boost::optional<Surface_patch_index> operator()(Ray_3 r)
boost::optional<Surface_patch_index> operator()(Line_3 l)
The return type of the operators tell whether or not the query intersects a surface patch. In the positive case, it provides (through operator*()) the Surface_patch_index
of one of the intersected surface patches.
typedef unspecified_type MeshDomain_3::Index 
Type of indices to be stored at mesh vertices to characterize the lowest dimensional face of the input complex on which the vertex lies.
Must be a model of CopyConstructible, Assignable, DefaultConstructible and EqualityComparable.
typedef std::tuple<Point_3, Index, int> MeshDomain_3::Intersection 
Returns type of Construct_intersection
queries.
int
represents the dimension of the lower dimensional face of the input complex on which the intersection point lies and Index
is the index of this face.
A function object to query whether a point is in the input domain or not.
In the positive case, it outputs the subdomain which includes the query point. Provides the operator:
boost::optional<Subdomain_index> operator()(Point_3 p)
typedef unspecified_type MeshDomain_3::R 
Geometric traits class.
This type is defined to ensure compatibility with CGAL::Kernel_traits<T>
.
Type of indices for subdomains of the input domain.
Must be a model of CopyConstructible, Assignable, DefaultConstructible and EqualityComparable. The default constructed value must match the label of the exterior of the domain (which contains at least the unbounded component).
Type of indices for surface patches (boundaries and interfaces) of the input domain.
Must be a model of CopyConstructible, Assignable, DefaultConstructible and EqualityComparable. The default constructed value must be the index value assigned to a non surface facet.