CGAL 5.1.2 - Triangulated Surface Mesh Skeletonization
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#include <CGAL/Mean_curvature_flow_skeletonization.h>
Function object that enables to extract the mean curvature flow skeleton of a triangulated surface mesh.
The algorithm used takes as input a triangulated surface mesh and iteratively contracts the surface mesh following the mean curvature flow [1]. The intermediate contracted surface mesh is called the meso-skeleton. After each iteration, the meso-skeleton is locally remeshed using angle split and edge contraction. The process ends when the modification of the meso-skeleton between two iterations is small.
TriangleMesh | a model of FaceListGraph |
Traits | a model of MeanCurvatureSkeletonizationTraits Default: boost::property_traits< boost::property_map<TriangleMesh, CGAL::vertex_point_t>::type >::value_type |
VertexPointMap | a model of ReadWritePropertyMap with boost::graph_traits<TriangleMesh>::vertex_descriptor as key and Traits::Point_3 as value type.Default: boost::property_map<TriangleMesh, CGAL::vertex_point_t>::const_type. |
SolverTraits_ | a model of NormalEquationSparseLinearAlgebraTraits_d .Default: If Eigen 3.2 (or greater) is available and CGAL_EIGEN3_ENABLED is defined, then an overload of Eigen_solver_traits is provided as default parameter: |
Types | |
typedef boost::adjacency_list< boost::vecS, boost::vecS, boost::undirectedS, Vmap > | Skeleton |
The graph type representing the skeleton. The vertex property Vmap is a struct with a member point of type Traits::Point_3 and a member vertices of type std::vector<boost::graph_traits<TriangleMesh>::vertex_descriptor> . See the boost documentation page for more details. | |
Constructor | |
Mean_curvature_flow_skeletonization (const TriangleMesh &tmesh, VertexPointMap vertex_point_map=get(CGAL::vertex_point, tmesh), Traits traits=Traits()) | |
The constructor of a skeletonization object. More... | |
Local Remeshing Parameters | |
double | max_triangle_angle () |
During the local remeshing step, a triangle will be split if it has an angle larger than max_triangle_angle() . | |
double | min_edge_length () |
During the local remeshing step, an edge will be collapse if it is length is less than min_edge_length() . | |
void | set_max_triangle_angle (double value) |
set function for max_triangle_angle() | |
void | set_min_edge_length (double value) |
set function for min_edge_length() | |
Algorithm Termination Parameters | |
std::size_t | max_iterations () |
Maximum number of iterations performed by contract_until_convergence() . | |
double | area_variation_factor () |
The convergence is considered to be reached if the variation of the area of the meso-skeleton after one iteration is smaller than area_variation_factor()*original_area where original_area is the area of the input triangle mesh. | |
void | set_max_iterations (std::size_t value) |
set function for max_iterations() | |
void | set_area_variation_factor (double value) |
set function for area_variation_factor() | |
Vertex Motion Parameters | |
double | quality_speed_tradeoff () |
This is an advanced function. Advanced Controls the velocity of movement and approximation quality: decreasing this value makes the mean curvature flow based contraction converge faster, but results in a skeleton of lower quality. This parameter corresponds to \( w_H \) in the original publication. | |
bool | is_medially_centered () |
If true , the meso-skeleton placement will be attracted by an approximation of the medial axis of the mesh during the contraction steps, so will be the result skeleton. | |
double | medially_centered_speed_tradeoff () |
This is an advanced function. Advanced Controls the smoothness of the medial approximation: increasing this value results in a (less smooth) skeleton closer to the medial axis, as well as a lower convergence speed. It is only used if is_medially_centered()==true . This parameter corresponds to \( w_M \) in the original publication. | |
void | set_quality_speed_tradeoff (double value) |
set function for quality_speed_tradeoff() | |
void | set_is_medially_centered (bool value) |
set function for is_medially_centered() | |
void | set_medially_centered_speed_tradeoff (double value) |
set function for medially_centered_speed_tradeoff() | |
High Level Function | |
void | operator() (Skeleton &skeleton) |
Creates the curve skeleton: the input surface mesh is iteratively contracted until convergence, and then turned into a curve skeleton. More... | |
Low Level Functions | |
Advanced
The following functions enable the user to run the mean curvature flow skeletonization algorithm step by step. | |
void | contract_geometry () |
Runs one contraction step following the mean curvature flow. | |
std::size_t | collapse_edges () |
Collapses edges of the meso-skeleton with length less than min_edge_length() and returns the number of edges collapsed. | |
std::size_t | split_faces () |
Splits faces of the meso-skeleton having one angle greater than max_triangle_angle() and returns the number of faces split. | |
std::size_t | detect_degeneracies () |
Prevents degenerate vertices to move during the following contraction steps and returns the number of newly fixed vertices. | |
void | contract () |
Performs subsequent calls to contract_geometry() , collapse_edges() , split_faces() and detect_degeneracies() | |
void | contract_until_convergence () |
Iteratively calls contract() until the change of surface area of the meso-skeleton after one iteration is smaller than area_variation_factor()*original_area where original_area is the area of the input triangle mesh, or if the maximum number of iterations has been reached. | |
void | convert_to_skeleton (Skeleton &skeleton) |
Converts the contracted surface mesh to a skeleton curve. More... | |
Access to the Meso-Skeleton | |
typedef unspecified_type | Meso_skeleton |
When using the low level API it is possible to access the intermediate results of the skeletonization process, called meso-skeleton. It is a triangulated surface mesh which is model of FaceListGraph and HalfedgeListGraph . | |
const Meso_skeleton & | meso_skeleton () const |
Reference to the collapsed triangulated surface mesh. | |
CGAL::Mean_curvature_flow_skeletonization< TriangleMesh, Traits_, VertexPointMap_, SolverTraits_ >::Mean_curvature_flow_skeletonization | ( | const TriangleMesh & | tmesh, |
VertexPointMap | vertex_point_map = get(CGAL::vertex_point, tmesh) , |
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Traits | traits = Traits() |
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The constructor of a skeletonization object.
The algorithm parameters are initialized such that:
max_triangle_angle() == 110
quality_speed_tradeoff() == 0.1
medially_centered_speed_tradeoff() == 0.2
area_variation_factor() == 0.0001
max_iterations() == 500
is_medially_centered() == true
min_edge_length()
== 0.002 * the length of the diagonal of the bounding box of tmesh
tmesh
is a triangulated surface mesh without borders and has exactly one connected component. tmesh | input triangulated surface mesh. |
vertex_point_map | property map which associates a point to each vertex of the graph. |
traits | an instance of the traits class. |
void CGAL::Mean_curvature_flow_skeletonization< TriangleMesh, Traits_, VertexPointMap_, SolverTraits_ >::convert_to_skeleton | ( | Skeleton & | skeleton | ) |
Converts the contracted surface mesh to a skeleton curve.
Skeleton | an instantiation of boost::adjacency_list as a data structure for the skeleton curve. |
skeleton | graph that will contain the skeleton of tmesh . It should be empty before passed to the function. |
void CGAL::Mean_curvature_flow_skeletonization< TriangleMesh, Traits_, VertexPointMap_, SolverTraits_ >::operator() | ( | Skeleton & | skeleton | ) |
Creates the curve skeleton: the input surface mesh is iteratively contracted until convergence, and then turned into a curve skeleton.
This is equivalent to calling contract_until_convergence()
and convert_to_skeleton()
.
skeleton | graph that will contain the skeleton of the input triangulated surface mesh. For each vertex descriptor vd of skeleton , the corresponding point and the set of input vertices that contracted to vd can be retrieved using skeleton[vd].point and skeleton[vd].vertices respectively. |