CGAL 4.12.1 - Polygon Mesh Processing

Functions to triangulate faces, and to refine and fair regions of a polygon mesh.

## Functions

template<typename VertexRange , typename TriangleMesh , typename NamedParameters >
void CGAL::Polygon_mesh_processing::random_perturbation (VertexRange vertices, TriangleMesh &tmesh, const double &perturbation_max_size, const NamedParameters &np)
randomly perturbs the locations of vertices of a triangulated surface mesh. More...

template<typename TriangleMesh , typename NamedParameters >
void CGAL::Polygon_mesh_processing::random_perturbation (TriangleMesh &tmesh, const double &perturbation_max_size, const NamedParameters &np)
same as above, but all non-border vertices of tmesh are perturbed.

template<typename TriangleMesh , typename FaceRange , typename FaceOutputIterator , typename VertexOutputIterator , typename NamedParameters >
std::pair< FaceOutputIterator, VertexOutputIterator > CGAL::Polygon_mesh_processing::refine (TriangleMesh &tmesh, const FaceRange &faces, FaceOutputIterator faces_out, VertexOutputIterator vertices_out, const NamedParameters &np)
refines a region of a triangle mesh More...

template<typename TriangleMesh , typename VertexRange , typename NamedParameters >
bool CGAL::Polygon_mesh_processing::fair (TriangleMesh &tmesh, const VertexRange &vertices, const NamedParameters &np)
fairs a region on a triangle mesh. More...

template<typename PolygonMesh , typename FaceRange , typename NamedParameters >
void CGAL::Polygon_mesh_processing::isotropic_remeshing (const FaceRange &faces, const double &target_edge_length, PolygonMesh &pmesh, const NamedParameters &np)
remeshes a triangulated region of a polygon mesh. More...

template<typename PolygonMesh , typename EdgeRange , typename NamedParameters >
void CGAL::Polygon_mesh_processing::split_long_edges (const EdgeRange &edges, const double &max_length, PolygonMesh &pmesh, const NamedParameters &np)
splits the edges listed in edges into sub-edges that are not longer than the given threshold max_length. More...

template<typename PolygonMesh , typename NamedParameters >
bool CGAL::Polygon_mesh_processing::triangulate_face (typename boost::graph_traits< PolygonMesh >::face_descriptor f, PolygonMesh &pmesh, const NamedParameters &np)
triangulates a single face of a polygon mesh. More...

template<typename FaceRange , typename PolygonMesh , typename NamedParameters >
bool CGAL::Polygon_mesh_processing::triangulate_faces (FaceRange face_range, PolygonMesh &pmesh, const NamedParameters &np)
triangulates given faces of a polygon mesh. More...

template<typename PolygonMesh , typename NamedParameters >
bool CGAL::Polygon_mesh_processing::triangulate_faces (PolygonMesh &pmesh, const NamedParameters &np)
triangulates all faces of a polygon mesh. More...

## ◆ fair()

template<typename TriangleMesh , typename VertexRange , typename NamedParameters >
 bool CGAL::Polygon_mesh_processing::fair ( TriangleMesh & tmesh, const VertexRange & vertices, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/fair.h>

fairs a region on a triangle mesh.

The points of the selected vertices are relocated to yield an as-smooth-as-possible surface patch, based on solving a linear bi-Laplacian system with boundary constraints, described in [3]. The optional parameter fairing_continuity gives the ability to control the tangential continuity C n of the output mesh.

The region described by vertices might contain multiple disconnected components. Note that the mesh connectivity is not altered in any way, only vertex locations get updated.

Fairing might fail if fixed vertices, which are used as boundary conditions, do not suffice to solve constructed linear system.

Note that if the vertex range to which fairing is applied contains all the vertices of the triangle mesh, fairing does not fail, but the mesh gets shrinked to CGAL::ORIGIN.

Template Parameters
 TriangleMesh a model of FaceGraph and MutableFaceGraph VertexRange a range of vertex descriptors of TriangleMesh, model of Range. Its iterator type is InputIterator. NamedParameters a sequence of Named Parameters
Parameters
 tmesh the triangle mesh with patches to be faired vertices the vertices of the patches to be faired (the positions of only those vertices will be changed) np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of tmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available in TriangleMesh fairing_continuity tangential continuity of the output surface patch. The larger fairing_continuity gets, the more fixed vertices are required sparse_linear_solver an instance of the sparse linear solver used for fairing
Returns
true if fairing is successful, otherwise no vertices are relocated
Precondition
is_triangle_mesh(tmesh)
Warning
This function involves linear algebra, that is computed using a non-exact floating-point arithmetic.
Examples:
Polygon_mesh_processing/refine_fair_example.cpp.

## ◆ isotropic_remeshing()

template<typename PolygonMesh , typename FaceRange , typename NamedParameters >
 void CGAL::Polygon_mesh_processing::isotropic_remeshing ( const FaceRange & faces, const double & target_edge_length, PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/remesh.h>

remeshes a triangulated region of a polygon mesh.

This operation sequentially performs edge splits, edge collapses, edge flips, tangential relaxation and projection to the initial surface to generate a smooth mesh with a prescribed edge length.

Template Parameters
 PolygonMesh model of MutableFaceGraph. The descriptor types boost::graph_traits::face_descriptor and boost::graph_traits::halfedge_descriptor must be models of Hashable. If PolygonMesh has an internal property map for CGAL::face_index_t, and no face_index_map is given as a named parameter, then the internal one must be initialized FaceRange range of boost::graph_traits::face_descriptor, model of Range. Its iterator type is ForwardIterator. NamedParameters a sequence of Named Parameters
Parameters
 pmesh a polygon mesh with triangulated surface patches to be remeshed faces the range of triangular faces defining one or several surface patches to be remeshed target_edge_length the edge length that is targeted in the remeshed patch. If 0 is passed then only the edge-flip, tangential relaxation, and projection steps will be done. np optional sequence of Named Parameters among the ones listed below
Precondition
if constraints protection is activated, the constrained edges should not be longer than 4/3*target_edge_length
Named Parameters
 geom_traits a geometric traits class instance, model of Kernel. Exact constructions kernels are not supported by this function. vertex_point_map the property map with the points associated to the vertices of pmesh. Instance of a class model of ReadWritePropertyMap. face_index_map a property map containing the index of each face of pmesh number_of_iterations the number of iterations for the sequence of atomic operations performed (listed in the above description) edge_is_constrained_map a property map containing the constrained-or-not status of each edge of pmesh. A constrained edge can be split or collapsed, but not flipped, nor its endpoints moved by smoothing. Note that patch boundary edges (i.e. incident to only one face in the range) are always considered as constrained edges. vertex_is_constrained_map a property map containing the constrained-or-not status of each vertex of pmesh. A constrained vertex cannot be modified at all during remeshing protect_constraints If true, the edges set as constrained in edge_is_constrained_map (or by default the boundary edges) are not split nor collapsed during remeshing. Note that around constrained edges that have their length higher than twice target_edge_length, remeshing will fail to provide good quality results. It can even fail to terminate because of cascading vertex insertions. face_patch_map a property map with the patch id's associated to the faces of faces. Instance of a class model of ReadWritePropertyMap. It gets updated during the remeshing process while new faces are created. number_of_relaxation_steps the number of iterations of tangential relaxation that are performed at each iteration of the remeshing process relax_constraints If true, the end vertices of the edges set as constrained in edge_is_constrained_map and boundary edges move along the constrained polylines they belong to.
split_long_edges()
Examples:
Polygon_mesh_processing/corefinement_difference_remeshed.cpp, Polygon_mesh_processing/hausdorff_distance_remeshing_example.cpp, and Polygon_mesh_processing/isotropic_remeshing_example.cpp.

## ◆ random_perturbation()

template<typename VertexRange , typename TriangleMesh , typename NamedParameters >
 void CGAL::Polygon_mesh_processing::random_perturbation ( VertexRange vertices, TriangleMesh & tmesh, const double & perturbation_max_size, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/random_perturbation.h>

randomly perturbs the locations of vertices of a triangulated surface mesh.

By default, the vertices are re-projected onto the input surface after perturbation. Note that no geometric checks are done after the perturbation (face orientation might become incorrect and self-intersections might be introduced).

Template Parameters
 VertexRange model of Range, holding vertices of type boost::graph_traits::vertex_descriptor. Its iterator type is ForwardIterator. TriangleMesh model of MutableFaceGraph. NamedParameters a sequence of Named Parameters
Parameters
 vertices the range of vertices to be perturbed tmesh the triangulated surface mesh perturbation_max_size the maximal length of moves that can be applied to vertices of tmesh. np optional sequence of Named Parameters among the ones listed below
Named Parameters
 geom_traits a geometric traits class instance, model of Kernel. vertex_point_map the property map with the points associated to the vertices of tmesh. Instance of a class model of ReadWritePropertyMap. vertex_is_constrained_map a property map containing the constrained-or-not status of each vertex of tmesh. A constrained vertex cannot be modified at all during perturbation do_project a boolean that sets whether vertices should be reprojected on the input surface after their coordinates random perturbation random_seed a non-negative integer value to seed the random number generator, and make the perturbation deterministic

## ◆ refine()

template<typename TriangleMesh , typename FaceRange , typename FaceOutputIterator , typename VertexOutputIterator , typename NamedParameters >
 std::pair CGAL::Polygon_mesh_processing::refine ( TriangleMesh & tmesh, const FaceRange & faces, FaceOutputIterator faces_out, VertexOutputIterator vertices_out, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/refine.h>

refines a region of a triangle mesh

Template Parameters
 TriangleMesh model of MutableFaceGraph FaceRange range of face descriptors, model of Range. Its iterator type is InputIterator. FaceOutputIterator model of OutputIterator holding boost::graph_traits::face_descriptor for patch faces VertexOutputIterator model of OutputIterator holding boost::graph_traits::vertex_descriptor for patch vertices NamedParameters a sequence of Named Parameters
Parameters
 tmesh triangle mesh with patches to be refined faces the range of faces defining the patches to refine faces_out output iterator into which descriptors of new faces are recorded vertices_out output iterator into which descriptors of new vertices are recorded np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of tmesh Instance of a class model of ReadWritePropertyMap. If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available in TriangleMesh density_control_factor factor to control density of the output mesh, where larger values lead to denser refinements. The density of vertices of faces_out is this factor times higher than the vertices of faces.
Returns
pair of faces_out and vertices_out
Precondition
is_triangle_mesh(tmesh)
Examples:
Polygon_mesh_processing/refine_fair_example.cpp.

## ◆ split_long_edges()

template<typename PolygonMesh , typename EdgeRange , typename NamedParameters >
 void CGAL::Polygon_mesh_processing::split_long_edges ( const EdgeRange & edges, const double & max_length, PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/remesh.h>

splits the edges listed in edges into sub-edges that are not longer than the given threshold max_length.

Note this function is useful to split constrained edges before calling isotropic_remeshing() with protection of constraints activated (to match the constrained edge length required by the remeshing algorithm to be guaranteed to terminate)

Template Parameters
 PolygonMesh model of MutableFaceGraph that has an internal property map for CGAL::vertex_point_t. EdgeRange range of boost::graph_traits::edge_descriptor, model of Range. Its iterator type is InputIterator. NamedParameters a sequence of Named Parameters
Parameters
 pmesh a polygon mesh edges the range of edges to be split if they are longer than given threshold max_length the edge length above which an edge from edges is split into to sub-edges np optional Named Parameters described below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. Instance of a class model of ReadWritePropertyMap.
isotropic_remeshing()
Examples:
Polygon_mesh_processing/isotropic_remeshing_example.cpp.

## ◆ triangulate_face()

template<typename PolygonMesh , typename NamedParameters >
 bool CGAL::Polygon_mesh_processing::triangulate_face ( typename boost::graph_traits< PolygonMesh >::face_descriptor f, PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/triangulate_faces.h>

triangulates a single face of a polygon mesh.

This function depends on the package 2D Triangulation

Template Parameters
 PolygonMesh a model of FaceListGraph and MutableFaceGraph NamedParameters a sequence of Named Parameters
Parameters
 f face to be triangulated pmesh the polygon mesh to which the face to be triangulated belongs np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available in PolygonMesh geom_traits a geometric traits class instance
Returns
true if the face has been triangulated.

## ◆ triangulate_faces() [1/2]

template<typename FaceRange , typename PolygonMesh , typename NamedParameters >
 bool CGAL::Polygon_mesh_processing::triangulate_faces ( FaceRange face_range, PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/triangulate_faces.h>

triangulates given faces of a polygon mesh.

This function depends on the package 2D Triangulation

Template Parameters
 FaceRange range of boost::graph_traits::face_descriptor, model of Range. Its iterator type is InputIterator. PolygonMesh a model of FaceListGraph and MutableFaceGraph NamedParameters a sequence of Named Parameters
Parameters
 face_range the range of faces to be triangulated pmesh the polygon mesh to be triangulated np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available in PolygonMesh geom_traits a geometric traits class instance
Returns
true if all the faces have been triangulated.
triangulate_face()
Examples:
Polygon_mesh_processing/triangulate_faces_example.cpp.

## ◆ triangulate_faces() [2/2]

template<typename PolygonMesh , typename NamedParameters >
 bool CGAL::Polygon_mesh_processing::triangulate_faces ( PolygonMesh & pmesh, const NamedParameters & np )

#include <CGAL/Polygon_mesh_processing/triangulate_faces.h>

triangulates all faces of a polygon mesh.

This function depends on the package 2D Triangulation

Template Parameters
 PolygonMesh a model of FaceListGraph and MutableFaceGraph NamedParameters a sequence of Named Parameters
Parameters
 pmesh the polygon mesh to be triangulated np optional sequence of Named Parameters among the ones listed below
Named Parameters
 vertex_point_map the property map with the points associated to the vertices of pmesh. If this parameter is omitted, an internal property map for CGAL::vertex_point_t should be available in PolygonMesh geom_traits a geometric traits class instance
Returns
true if all the faces have been triangulated.