CGAL::Fast_winding_number< TriangleMesh, FaceNormalMap, FaceAreaMap, FaceCentroidMap, Tree, ORDER, GeomTraits, VertexPointMap > Class Template Reference

#include <CGAL/fast_winding_number.h>

Definition

template<class TriangleMesh, class FaceNormalMap, class FaceAreaMap, class FaceCentroidMap, class Tree, int ORDER = 3, class GeomTraits = Default, class VertexPointMap = Default>
class CGAL::Fast_winding_number< TriangleMesh, FaceNormalMap, FaceAreaMap, FaceCentroidMap, Tree, ORDER, GeomTraits, VertexPointMap >

Fast evaluation of the (normalized) winding number of a triangle mesh.

This class implements a hierarchical (multipole / cluster–far field) approximation of the generalized winding number for a triangle mesh.

Template Parameters

TriangleMesh	a model of FaceListGraph
FaceNormalMap	a readable property map contains the normal of each face: face_descriptor -> Vector_3
FaceAreaMap	a readable property map contains the area of each face: face_descriptor -> FT
FaceCentroidMap	a readable property map contains the centroid of each face: face_descriptor -> Point_3
Tree	a built AABB tree over the faces of TriangleMesh
ORDER	the order of the taylor expansion, must be 1, 2, or 3. Default: 3
GeomTraits	a model of Kernel Default: CGAL::Kernel_traits< boost::property_traits< boost::property_map<TriangleMesh, CGAL::vertex_point_t>::type >::value_type >::Kernel a model of ReadWritePropertyMap with boost::graph_traits<TriangleMesh_>::vertex_descriptor as key and GeomTraits_::Point_3 as value type. Default: boost::property_map<TriangleMesh_, CGAL::vertex_point_t>::const_type.

Public Member Functions
template<class NamedParameters = parameters::Default_named_parameters>
FT	evaluate_fast_winding_number (const Point_3 &p, const NamedParameters &np=parameters::default_values())
	computes the fast winding number of a given query point.
FT	exact_winding_number (const Point_3 &p) const
	computes the exact winding number of a given query point p and the input mesh.
bool	is_inside (const Point_3 &p)
	tests whether a given query point is inside the input mesh.

Constructor
The constructor of a vmas object. Template Parameters NamedParameters a sequence of Named Parameters Parameters tmesh The input triangle mesh without borders. fnm A readable property map that maps each face of tmesh to its normal vector. fam A readable property map that maps each face of tmesh to its area. fcm A readable property map that maps each face of tmesh to its centroid. tree A built AABB tree over the faces of tmesh. np An optional sequence of Named Parameters, listed below: Optional Named Parameters 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 Point_3 as value type Default: boost::get(CGAL::vertex_point, pmesh) fast_winding_number_beta The parameter to control the accuracy/speed trade-off of the fast winding number evaluation. little values lead to more accurate results, but slower evaluation. Type: FT Default: FT(2.0) Extra: The range of this parameter is (0,+inf).
template<class NamedParameters = parameters::Default_named_parameters>
	Fast_winding_number (const TriangleMesh &tmesh, const FaceNormalMap &fnm, const FaceAreaMap &fam, const FaceCentroidMap &fcm, Tree &tree, const NamedParameters &np=parameters::default_values())

Member Function Documentation

evaluate_fast_winding_number()

template<class TriangleMesh , class FaceNormalMap , class FaceAreaMap , class FaceCentroidMap , class Tree , int ORDER = 3, class GeomTraits = Default, class VertexPointMap = Default>

template<class NamedParameters = parameters::Default_named_parameters>

FT CGAL::Fast_winding_number< TriangleMesh, FaceNormalMap, FaceAreaMap, FaceCentroidMap, Tree, ORDER, GeomTraits, VertexPointMap >::evaluate_fast_winding_number	(	const Point_3 &	p,
		const NamedParameters &	np = parameters::default_values()
	)

computes the fast winding number of a given query point.

This function computes the fast winding number of a given query point p recursively. For a given query point p, we first compute its distance r to the center of root node in the AABB tree. If r is larger than beta times the radius of the root node, we consider the root node as a single dipole and use the precomputed Taylor expansion coefficients to evaluate the winding number. Otherwise, we traverse down the tree recursively and repeat the same process for each child node.

Parameters

p	the query point
np	an optional sequence of Named Parameters, listed below: Optional Named Parameters fast_winding_number_beta The parameter to control the accuracy/speed trade-off of the fast winding number evaluation. little values lead to more accurate results, but slower evaluation. Type: FT Default: FT(2.0) Extra: The range of this parameter is (0,+inf).

Returns

the fast winding number of p

exact_winding_number()

template<class TriangleMesh , class FaceNormalMap , class FaceAreaMap , class FaceCentroidMap , class Tree , int ORDER = 3, class GeomTraits = Default, class VertexPointMap = Default>

FT CGAL::Fast_winding_number< TriangleMesh, FaceNormalMap, FaceAreaMap, FaceCentroidMap, Tree, ORDER, GeomTraits, VertexPointMap >::exact_winding_number

(

const Point_3 &

p

)

const

computes the exact winding number of a given query point p and the input mesh.

Parameters

p	the query point

Returns

the exact winding number of p

is_inside()

template<class TriangleMesh , class FaceNormalMap , class FaceAreaMap , class FaceCentroidMap , class Tree , int ORDER = 3, class GeomTraits = Default, class VertexPointMap = Default>

bool CGAL::Fast_winding_number< TriangleMesh, FaceNormalMap, FaceAreaMap, FaceCentroidMap, Tree, ORDER, GeomTraits, VertexPointMap >::is_inside

(

const Point_3 &

p

)

tests whether a given query point is inside the input mesh.

Parameters

p	the query point

Returns

true if p is inside the input mesh, false otherwise.