Mesh Kernel

Functions to compute kernel of polyhedra.

Functions
template<typename FaceRange , typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters, typename NamedParametersOut = parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::kernel (const FaceRange &face_range, const PolygonMesh &pm, PolygonMesh &out, const NamedParameters &np=parameters::default_values(), const NamedParametersOut &np_out=parameters::default_values())
	computes the kernel of the given faces of a polygon mesh.
template<typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters, typename NamedParametersOut = parameters::Default_named_parameters>
void	CGAL::Polygon_mesh_processing::kernel (const PolygonMesh &pm, PolygonMesh &out, const NamedParameters &np=parameters::default_values(), const NamedParametersOut &np_out=parameters::default_values())
	computes the kernel of the given polygon mesh.
template<typename FaceRange , typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
bool	CGAL::Polygon_mesh_processing::has_empty_kernel (const FaceRange &face_range, const PolygonMesh &pm, const NamedParameters &np=parameters::default_values())
	indicates whether the kernel of the given faces of a polygon mesh is empty.
template<typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
bool	CGAL::Polygon_mesh_processing::has_empty_kernel (const PolygonMesh &pm, const NamedParameters &np=parameters::default_values())
	indicates whether the kernel of the given polygon mesh is empty.
template<typename FaceRange , typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters>
std::optional< Point_3 >	CGAL::Polygon_mesh_processing::kernel_point (const FaceRange &face_range, const PolygonMesh &pm, const NamedParameters &np=parameters::default_values())
	returns a point inside the kernel of the given faces of a polygon mesh.
template<typename PolygonMesh , typename NamedParameters = CGAL::parameters::Default_named_parameters>
std::optional< Point_3 >	CGAL::Polygon_mesh_processing::kernel_point (const PolygonMesh &pm, const NamedParameters &np=parameters::default_values())
	returns a point inside the kernel of the given polygon mesh.

Function Documentation

has_empty_kernel() [1/2]

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

bool CGAL::Polygon_mesh_processing::has_empty_kernel	(	const FaceRange &	face_range,
		const PolygonMesh &	pm,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/kernel.h>

indicates whether the kernel of the given faces of a polygon mesh is empty.

The kernel is defined as the convex polyhedron that is the intersection of all the halfspaces on the negative side of the oriented planes defined by a range of faces of the input mesh.

See CGAL::Polygon_mesh_processing::kernel() for a comprehensive description of the parameters.

has_empty_kernel() [2/2]

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

bool CGAL::Polygon_mesh_processing::has_empty_kernel	(	const PolygonMesh &	pm,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/kernel.h>

indicates whether the kernel of the given polygon mesh is empty.

This is a convenience overload that calls the overload above on all faces of the mesh.

kernel() [1/2]

template<typename FaceRange , typename PolygonMesh , typename NamedParameters = parameters::Default_named_parameters, typename NamedParametersOut = parameters::Default_named_parameters>

void CGAL::Polygon_mesh_processing::kernel	(	const FaceRange &	face_range,
		const PolygonMesh &	pm,
		PolygonMesh &	out,
		const NamedParameters &	np = parameters::default_values(),
		const NamedParametersOut &	np_out = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/kernel.h>

computes the kernel of the given faces of a polygon mesh.

The kernel is defined as the convex polyhedron that is the intersection of all the halfspaces on the negative side of the oriented planes defined by a range of faces of the input mesh. The kernel may be empty or degenerate to a lower-dimensional convex shape.

In the implementation, a starting shape is iteratively clipped by the faces. By default, the bounding box of the input mesh is used as starting shape. However, the parameter out may be non-empty: In this case, it must be a convex polyhedron and will be used as starting shape.

The algorithm assumes that the faces of the input range form a closed surface as to perform a quick exit if the genus is non-zero. This precondition can be relaxed using the named parameter allow_open_input. In that case, the resulting kernel may contain faces of the starting shape.

In case of a degenerate kernel:

• If the dimension of the kernel is 2 (i.e., the kernel is a convex polygon in 3D), the output mesh consists of a single face.
• If the dimension of the kernel is 1 (i.e., the kernel is a line segment), the output mesh consists two isolated vertices.
• If the dimension of the kernel is 0 (i.e., the kernel is a single point), the output mesh contains one isolated vertex.

Template Parameters

FaceRange	a model of ConstRange with boost::graph_traits<PolygonMesh>::face_descriptor as value type
PolygonMesh	a model of VertexListGraph, HalfedgeListGraph and FaceListGraph
PolygonMeshOut	a model of MutableFaceGraph, VertexListGraph and FaceListGraph
NamedParameters	a sequence of Named Parameters
NamedParametersOut	a sequence of Named Parameters

Parameters

face_range	the range of faces used
pm	input surface mesh
out	output surface mesh
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

allow_open_input If set to true, the input mesh is allowed to have boundaries. Type: Boolean Default: false
vertex_point_map a property map associating points to the vertices of pm Type: a class model of ReadWritePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, pm) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh.
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
random_seed is used to initialize the random number generator of the algorithm. Type: unsigned int Default: use std::default_random_engine()

Parameters

np_out

an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

vertex_point_map a property map associating points to the vertices of out Type: a class model of ReadWritePropertyMap with boost::graph_traits<PolygonMesh>::vertex_descriptor as key type and Point_3 as value type Default: boost::get(CGAL::vertex_point, out) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in PolygonMesh.

face_to_face_map a property map storing, for each face of the output mesh, a face of the input mesh that defined the clipping plane that created it (or boost::graph_traits<PolygonMeshOut>::null_face if the face belongs to the starting shape) Type: a class model of ReadWritePropertyMap with boost::graph_traits<PolygonMeshOut>::face_descriptor as key type and boost::graph_traits<PolygonMesh>::face_descriptor as value type Default: unused

kernel() [2/2]

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

void CGAL::Polygon_mesh_processing::kernel	(	const PolygonMesh &	pm,
		PolygonMesh &	out,
		const NamedParameters &	np = parameters::default_values(),
		const NamedParametersOut &	np_out = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/kernel.h>

computes the kernel of the given polygon mesh.

This is a convenience overload that calls the overload above on all faces of the mesh.

kernel_point() [1/2]

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

std::optional< Point_3 > CGAL::Polygon_mesh_processing::kernel_point	(	const FaceRange &	face_range,
		const PolygonMesh &	pm,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/kernel.h>

returns a point inside the kernel of the given faces of a polygon mesh.

The kernel is defined as the convex polyhedron that is the intersection of all the halfspaces on the negative side of the oriented planes defined by a range of faces of the input mesh.

See CGAL::Polygon_mesh_processing::kernel() for a comprehensive description of the parameters.

In addition to the parameters available in CGAL::Polygon_mesh_processing::kernel(), the following parameter is also available:

Optional Named Parameters

require_strictly_inside If set to true, the returned point is required to lie strictly inside the mesh and not on its boundary. If the kernel is degenerate, this requirement cannot be satisfied and no point is returned. Type: Boolean Default: false

Returns

std::nullopt if and only if the kernel is empty.

kernel_point() [2/2]

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

std::optional< Point_3 > CGAL::Polygon_mesh_processing::kernel_point	(	const PolygonMesh &	pm,
		const NamedParameters &	np = parameters::default_values()
	)

#include <CGAL/Polygon_mesh_processing/kernel.h>

returns a point inside the kernel of the given polygon mesh.

This is a convenience overload that calls the overload above on all faces of the mesh.