|
CGAL 5.1 - Surface Mesh Topology
|
|
CGAL 5.1 - Surface Mesh Topology
|
#include <CGAL/Curves_on_surface_topology.h>
The class Curves_on_surface_topology provides methods to compute shortest non contractible cycles and to test homotopy on paths.
Each object of this class is constructed from an external mesh, either a 2D combinatorial map or a model of a FaceGraph. It maintains a correspondence between this mesh and an internal representation, computed the first time an homotopy test is called. The user must not modify the input surface as long as homotopy tests are performed with this Curves_on_surface_topology.
| Mesh | a model of CombinatorialMap or of FaceGraph |
Public Types | |
| typedef unspecified_type | halfedge_descriptor |
A handle to Dart for combinatorial/generalized maps, or a halfedge descriptor for models of the FaceGraph concept. | |
Public Member Functions | |
| Curves_on_surface_topology (const Mesh &amesh) | |
creates a Curves_on_surface_topology object using amesh as input. | |
| bool | are_freely_homotopic (const Path_on_surface< Mesh > &p1, const Path_on_surface< Mesh > &p2) const |
returns true if the closed paths p1 and p2 are freely homotopic. More... | |
| bool | are_homotopic_with_fixed_endpoints (const Path_on_surface< Mesh > &p1, const Path_on_surface< Mesh > &p2) const |
returns true if the paths p1 and p2 are homotopic with fixed endpoints. More... | |
| bool | is_contractible (const Path_on_surface< Mesh > &p) const |
returns true if the closed path p is contractible. More... | |
| Path_on_surface< Mesh > | compute_edge_width () const |
returns a non-contractible cycle of type Path_on_surface with minimal number of edges. More... | |
| template<class WeightFunctor = Unit_weight_functor> | |
| Path_on_surface< Mesh > | compute_shortest_non_contractible_cycle (const WeightFunctor &wf=WeightFunctor()) const |
returns a non-contractible cycle of type Path_on_surface with minimal length, where the length of a cycle is the sum of the weights of its edges computed thanks to the WeightFunctor wf. More... | |
| template<class WeightFunctor = Unit_weight_functor> | |
| Path_on_surface< Mesh > | compute_shortest_non_contractible_cycle_with_base_point (halfedge_descriptor dh, const WeightFunctor &wf=WeightFunctor()) const |
returns a non-contractible cycle of type Path_on_surface with minimal length going through the source vertex of dh, where the length of a cycle is the sum of the weights of its edges computed thanks to the WeightFunctor wf. More... | |
| std::vector< halfedge_descriptor > | compute_face_width () const |
| returns a vector of darts representing a non-contractible curve with a minimal number of intersection with the graph of the mesh. More... | |
| bool CGAL::Surface_mesh_topology::Curves_on_surface_topology< Mesh >::are_freely_homotopic | ( | const Path_on_surface< Mesh > & | p1, |
| const Path_on_surface< Mesh > & | p2 | ||
| ) | const |
returns true if the closed paths p1 and p2 are freely homotopic.
p1 and p2 must be two paths on amesh. | bool CGAL::Surface_mesh_topology::Curves_on_surface_topology< Mesh >::are_homotopic_with_fixed_endpoints | ( | const Path_on_surface< Mesh > & | p1, |
| const Path_on_surface< Mesh > & | p2 | ||
| ) | const |
returns true if the paths p1 and p2 are homotopic with fixed endpoints.
The paths p1 and p2 must have the same endpoints but must not be closed. Equivalent to is_contractible(q) where q is the concatenation of p1 and the reverse of p2.
p1 and p2 must be two paths on amesh. | Path_on_surface<Mesh> CGAL::Surface_mesh_topology::Curves_on_surface_topology< Mesh >::compute_edge_width | ( | ) | const |
returns a non-contractible cycle of type Path_on_surface with minimal number of edges.
This number of edges is the edge width of the mesh.
| std::vector<halfedge_descriptor> CGAL::Surface_mesh_topology::Curves_on_surface_topology< Mesh >::compute_face_width | ( | ) | const |
returns a vector of darts representing a non-contractible curve with a minimal number of intersection with the graph of the mesh.
This curve can be described by the alternating sequence of faces and vertices it goes through, so that each dart in the returned vector belongs to both a face and the next vertex in the alternating sequence. (Here, faces and vertices are viewed as subsets of darts.) The size of the returned vector is the face width of the mesh.
| Path_on_surface<Mesh> CGAL::Surface_mesh_topology::Curves_on_surface_topology< Mesh >::compute_shortest_non_contractible_cycle | ( | const WeightFunctor & | wf = WeightFunctor() | ) | const |
returns a non-contractible cycle of type Path_on_surface with minimal length, where the length of a cycle is the sum of the weights of its edges computed thanks to the WeightFunctor wf.
By default, all the edge weights are set to 1 (thanks to the Unit_weight_functor functor).
| Path_on_surface<Mesh> CGAL::Surface_mesh_topology::Curves_on_surface_topology< Mesh >::compute_shortest_non_contractible_cycle_with_base_point | ( | halfedge_descriptor | dh, |
| const WeightFunctor & | wf = WeightFunctor() |
||
| ) | const |
returns a non-contractible cycle of type Path_on_surface with minimal length going through the source vertex of dh, where the length of a cycle is the sum of the weights of its edges computed thanks to the WeightFunctor wf.
By default, all the edge weights are set to 1 (thanks to the Unit_weight_functor functor).
| bool CGAL::Surface_mesh_topology::Curves_on_surface_topology< Mesh >::is_contractible | ( | const Path_on_surface< Mesh > & | p | ) | const |
returns true if the closed path p is contractible.
p must be a closed path on amesh. 
1.8.13