CGAL 5.6.1  3D Mesh Generation

#include <CGAL/Polyhedral_complex_mesh_domain_3.h>
The class Polyhedral_complex_mesh_domain_3
implements a domain defined by a collection of polyhedral surfaces, forming a complex.
The constraints on the complex are:
It is a model of the concept MeshDomainWithFeatures_3
. It also provides a member function to automatically detect sharp features and boundaries from the input polyhedral surface(s).
The union of the polyhedral surfaces is a nonmanifold surface, called the 2D surface of the domain. It is locally manifold, with or without borders, but at the intersections of polyhedral surfaces.
The complement of the 2D surface is decomposed into:
If the domain has subdomains, each one must be the union of one or many connected components of the complement of the 2D surface. The subdomains have indices, of integral type Subdomain_index
, and the exterior of the mesh domain is associated with the subdomain index 0
, like for any mesh domain in CGAL.
Each polyhedral surface is oriented, and has two sides. The positive side is union of the positive side of all of its facets, usually named the "exterior" of the surface. The negative side is the other side. The use of Polyhedral_complex_mesh_domain_3
assumes that for each polyhedral surface, the subdomain indices on both sides are known.
Polyhedron  stands for the type of the input polyhedral surface(s), model of FaceListGraph . 
IGT_  stands for a geometric traits class providing the types and functors required to implement the intersection tests and intersection computations for polyhedral boundary surfaces. This parameter has to be instantiated with a model of the concept IntersectionGeometricTraits_3 . 
IntersectionGeometricTraits_3
CGAL::make_mesh_3()
. CGAL::Mesh_domain_with_polyline_features_3<MeshDomain>
CGAL::Polyhedral_mesh_domain_3<Polyhedron,IGT_,TriangleAccessor>
CGAL::Mesh_polyhedron_3<IGT_>
Public Types  
typedef Polyhedron_  Polyhedron 
The base class.  
typedef Mesh_domain_with_polyline_features_3< Polyhedral_mesh_domain_3< Polyhedron, IGT_, CGAL::Default, int, Tag_true > >  Base 
typedef Base::FT  FT 
Numerical type.  
typedef Polyhedron  Polyhedron_type 
The polyhedron type.  
Public Types inherited from CGAL::Mesh_domain_with_polyline_features_3< Polyhedral_mesh_domain_3< Polyhedron_, IGT_, CGAL::Default, int, Tag_true > >  
typedef Polyhedral_mesh_domain_3< Polyhedron_, IGT_, CGAL::Default, int, Tag_true > ::Surface_patch_index  Surface_patch_index 
typedef Polyhedral_mesh_domain_3< Polyhedron_, IGT_, CGAL::Default, int, Tag_true > ::Subdomain_index  Subdomain_index 
typedef int  Curve_index 
typedef int  Corner_index 
typedef unspecified_type  Index 
typedef CGAL::Tag_true  Has_features 
typedef Polyhedral_mesh_domain_3< Polyhedron_, IGT_, CGAL::Default, int, Tag_true > ::R::FT  FT 
Public Member Functions  
template<typename InputPolyhedraIterator , typename InputPairOfSubdomainIndicesIterator >  
Polyhedral_complex_mesh_domain_3 (InputPolyhedraIterator begin, InputPolyhedraIterator end, InputPairOfSubdomainIndicesIterator indices_begin, InputPairOfSubdomainIndicesIterator indices_end)  
Constructor. More...  
void  detect_features (FT angle_bound=FT(60)) 
Detects sharp features and boundaries of the polyhedral components of the complex (including potential internal polyhedra), and inserts them as features of the domain. More...  
void  detect_borders () 
Detects border edges of the polyhedral components of the complex, and inserts them as features of the domain. More...  
Public Member Functions inherited from CGAL::Mesh_domain_with_polyline_features_3< Polyhedral_mesh_domain_3< Polyhedron_, IGT_, CGAL::Default, int, Tag_true > >  
Mesh_domain_with_polyline_features_3 (const T &...o)  
Mesh_domain_with_polyline_features_3 (const Mesh_domain_with_polyline_features_3 &)=default  
void  add_features (InputIterator first, InputIterator end) 
Add 1dimensional features in the domain. More...  
void  add_features_and_incidences (InputIterator first, InputIterator end, PolylinePMap polyline_pmap, IncidentPatchesIndicesPMap incident_patches_indices_pmap) 
Add 1dimensional features (curves) from the range [first, end) in the domain with their incidences with 2dimensional features (patches) of the domain. More...  
OutputIterator  get_corners (OutputIterator out) const 
Implements MeshDomainWithFeatures_3::get_corners() . More...  
OutputIterator  get_curves (OutputIterator out) const 
Implements MeshDomainWithFeatures_3::get_curves() . More...  
FT  curve_segment_length (const Point_3 &p, const Point_3 q, const Curve_index &curve_index, CGAL::Orientation orientation) const 
Implements MeshDomainWithFeatures_3::curve_segment_length() .  
FT  curve_length (const Curve_index &curve_index) const 
Implements MeshDomainWithFeatures_3::curve_length() .  
Point_3  construct_point_on_curve (const Point_3 &starting_point, const Curve_index &curve_index, FT distance) const 
Implements MeshDomainWithFeatures_3::construct_point_on_curve() .  
CGAL::Sign  distance_sign_along_loop (const Point_3 &p, const Point_3 &q, const Point_3 &r, const Curve_index &index) const 
Implements MeshDomainWithFeatures_3::distance_sign_along_loop() .  
CGAL::Sign  distance_sign (const Point_3 &p, const Point_3 &q, const Curve_index &index) const 
Implements MeshDomainWithFeatures_3::distance_sign() .  
bool  is_loop (const Curve_index &index) const 
Implements MeshDomainWithFeatures_3::is_loop() .  
bool  is_curve_segment_covered (const Curve_index &index, CGAL::Orientation orientation, const Point_3 &c1, const Point_3 &c2, const FT sq_r1, const FT sq_r2) const 
Implements MeshDomainWithFeatures_3::is_curve_segment_covered() .  
Index  index_from_surface_patch_index (const Surface_patch_index &index) const 
Returns the index to be stored in a vertex lying on the surface identified by index .  
Index  index_from_subdomain_index (const Subdomain_index &index) const 
Returns the index to be stored in a vertex lying in the subdomain identified by index .  
Index  index_from_curve_index (const Curve_index &index) const 
Returns an Index from a Curve_index  
Index  index_from_corner_index (const Corner_index &index) const 
Returns an Index from a Corner_index  
Surface_patch_index  surface_patch_index (const Index &index) const 
Returns the Surface_patch_index of the surface patch where lies a vertex with dimension 2 and index index .  
Subdomain_index  subdomain_index (const Index &index) const 
Returns the index of the subdomain containing a vertex with dimension 3 and index index .  
Curve_index  curve_index (const Index &index) const 
Returns a Curve_index from an Index  
Corner_index  corner_index (const Index &index) const 
Returns a Corner_index from an Index  
Public Member Functions inherited from CGAL::Polyhedral_mesh_domain_3< Polyhedron_, IGT_, CGAL::Default, int, Tag_true >  
Polyhedral_mesh_domain_3 (const Polyhedron_ &bounding_polyhedron)  
Construction from a bounding polyhedral surface which must be closed, and free of intersections. More...  
Polyhedral_mesh_domain_3 (const Polyhedron_ &polyhedron, const Polyhedron_ &bounding_polyhedron)  
Construction from a polyhedral surface, and a bounding polyhedral surface,. More...  
Index types  
typedef Base::Corner_index  Corner_index 
typedef Base::Curve_index  Curve_index 
typedef Base::Surface_patch_index  Surface_patch_index 
typedef Base::Subdomain_index  Subdomain_index 
CGAL::Polyhedral_complex_mesh_domain_3< IGT_, Polyhedron_, TriangleAccessor >::Polyhedral_complex_mesh_domain_3  (  InputPolyhedraIterator  begin, 
InputPolyhedraIterator  end,  
InputPairOfSubdomainIndicesIterator  indices_begin,  
InputPairOfSubdomainIndicesIterator  indices_end  
) 
Constructor.
Constructs a domain defined by a set of polyhedral surfaces, describing a polyhedral complex.
begin  first iterator on the input polyhedral surfaces 
end  past the end iterator on the input polyhedral surfaces 
indices_begin  first iterator on the pairs of subdomain indices (two subdomain indices per input polyhedral surface), corresponding to the first input polyhedral surface. Each pair should be ordered as follows : the first (resp. second) element is the index of the subdomain that lies on the positively oriented (resp. negatively oriented) side of the corresponding input polyhedral surface. 
indices_end  past the end iterator on the pairs of subdomain indices 
InputPolyhedraIterator  model of ForwardIterator , holding Polyhedron 's 
InputPairOfSubdomainIndicesIterator  model of ForwardIterator , holding std::pair<Subdomain_index, Subdomain_index> 
std::distance(begin, end) == std::distance(indices_begin, indices_end)
void CGAL::Polyhedral_complex_mesh_domain_3< IGT_, Polyhedron_, TriangleAccessor >::detect_borders  (  ) 
Detects border edges of the polyhedral components of the complex, and inserts them as features of the domain.
This function should be called alone only, and not before or after detect_features()
.
void CGAL::Polyhedral_complex_mesh_domain_3< IGT_, Polyhedron_, TriangleAccessor >::detect_features  (  FT  angle_bound = FT(60)  ) 
Detects sharp features and boundaries of the polyhedral components of the complex (including potential internal polyhedra), and inserts them as features of the domain.
angle_bound
gives the maximum angle (in degrees) between the two normal vectors of adjacent triangles. For an edge of the polyhedron, if the angle between the two normal vectors of its incident facets is bigger than the given bound, then the edge is considered as a feature edge, and inserted as a feature of the domain.