Corrected Curvature Computation

Functions to compute the corrected curvatures of a polygon mesh.

Classes
struct	CGAL::Polygon_mesh_processing::Principal_curvatures_and_directions< GT >
	a struct for storing principal curvatures and directions. More...

Functions
template<typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::interpolated_corrected_curvatures (const PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
	computes the interpolated corrected curvatures across the mesh pmesh.
template<typename VertexDescriptor , typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::interpolated_corrected_curvatures (VertexDescriptor v, const PolygonMesh &pmesh, const NamedParameters &np=parameters::default_values())
	computes the interpolated corrected curvatures at a vertex v.

Function Documentation

interpolated_corrected_curvatures() [1/2]

template<typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>

void CGAL::Polygon_mesh_processing::interpolated_corrected_curvatures	(	const PolygonMesh &	pmesh,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/interpolated_corrected_curvatures.h>

computes the interpolated corrected curvatures across the mesh pmesh.

By providing mean, Gaussian and/or principal curvature and direction property maps as named parameters, the user can choose which quantities to compute.

Note

This function depends on the Eigen 3.1 (or later) library.

Template Parameters

PolygonMesh	a model of FaceListGraph.
NamedParameters	a sequence of Named Parameters.

Parameters

pmesh	the polygon mesh.
np	an optional sequence of Named Parameters among the ones listed below. GT stands for the type of the object provided to the named parameter geom_traits().

Optional Named Parameters

vertex_mean_curvature_map a property map associating mean curvatures to the vertices of pmesh. Type: a class model of WritablePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and GT::FT as value type Extra: If this parameter is omitted, mean curvatures will not be computed.
vertex_Gaussian_curvature_map a property map associating Gaussian curvatures to the vertices of pmesh. Type: a class model of WritablePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and GT::FT as value type. Extra: If this parameter is omitted, Gaussian curvatures will not be computed.
vertex_principal_curvatures_and_directions_map a property map associating principal curvatures and directions to the vertices of pmesh. Type: a class model of WritablePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and Principal_curvatures_and_directions<GT> as value type. Extra: If this parameter is omitted, principal curvatures and directions will not be computed.
ball_radius a strictly positive scalar value specifying the radius used for expanding curvature measures by summing measures of faces inside a ball of this radius centered at the vertex expanded from. The summed face measures are weighted by their inclusion ratio inside this ball. Type: GT::FT Default: -1 Extra: If this parameter is omitted (-1), the expansion is then just a sum of measures on faces around the vertex.
vertex_point_map a property map associating points to the vertices of pmesh. Type: a class model of ReadablePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and GT::Point_3 as value type. Default: boost::get(CGAL::vertex_point, pmesh). Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh.
vertex_normal_map a property map associating normal vectors to the vertices of pmesh. Type: a class model of ReadablePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and GT::Vector_3 as value type. Default: get(dynamic_vertex_property_t<GT::Vector_3>(), pmesh). Extra: If this parameter is omitted, vertex normals will be computed using compute_vertex_normals().
geom_traits an instance of a geometric traits class. Type: a class model of Kernel Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits. Extra: The geometric traits class must be compatible with the vertex point type.

interpolated_corrected_curvatures() [2/2]

template<typename VertexDescriptor , typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>

void CGAL::Polygon_mesh_processing::interpolated_corrected_curvatures	(	VertexDescriptor	v,
		const PolygonMesh &	pmesh,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/interpolated_corrected_curvatures.h>

computes the interpolated corrected curvatures at a vertex v.

By providing mean, Gaussian and/or principal curvature and direction property maps as named parameters, the user can choose which quantities to compute.

Note

This function depends on the Eigen 3.1 (or later) library.

Template Parameters

PolygonMesh	a model of FaceListGraph.
VertexDescriptor	must be convertible to boost::graph_traits<PolygonMesh>::vertex_descriptor.
NamedParameters	a sequence of Named Parameters.

Parameters

pmesh	the polygon mesh.
v	the vertex of pmesh to compute the curvatures at.
np	an optional sequence of Named Parameters among the ones listed below. GT stands for the type of the object provided to the named parameter geom_traits().

Optional Named Parameters

vertex_mean_curvature a reference to a scalar value to store the mean curvature at the vertex v. Type: std::reference_wrapper<GT::FT>. Extra: If this parameter is omitted, mean curvature will not be computed.
vertex_Gaussian_curvature a reference to a scalar value to store the Gaussian curvature at the vertex v. Type: std::reference_wrapper<GT::FT>. Extra: If this parameter is omitted, Gaussian curvature will not be computed.
vertex_principal_curvatures_and_directions a reference to a Principal_curvatures_and_directions<GT> object to store the principal curvatures and directions at the vertex v. Type: std::reference_wrapper<Principal_curvatures_and_directions<GT>>. Extra: If this parameter is omitted, principal curvatures and directions will not be computed.
ball_radius a scalar value specifying the radius used for expanding curvature measures by summing measures of faces inside a ball of this radius centered at the vertex expanded from. The summed face measures are weighted by their inclusion ratio inside this ball. Type: GT::FT Default: -1 Extra: If this parameter is omitted (-1), the expansion is then just a sum of measures on faces around the vertex.
vertex_point_map a property map associating points to the vertices of pmesh. Type: a class model of ReadablePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and GT::Point_3 as value type. Default: boost::get(CGAL::vertex_point, pmesh). Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh.
vertex_normal_map a property map associating normal vectors to the vertices of pmesh. Type: a class model of ReadablePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and GT::Vector_3 as value type. Default: get(dynamic_vertex_property_t<GT::Vector_3>(), pmesh). Extra: If this parameter is omitted, vertex normals will be computed using compute_vertex_normals().
geom_traits an instance of a geometric traits class. Type: a class model of Kernel Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits. Extra: The geometric traits class must be compatible with the vertex point type.