Intersection Test Functions

Functions
template<class PointRange , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>
FT	CGAL::Convex_hull_3::separation_distance (const PointRange &r1, const PointRange &r2, const NamedParameters_1 &np1=parameters::default_values(), const NamedParameters_2 &np2=parameters::default_values())
	computes a lower bound on the squared distance between the convex hulls of two point sets, returning zero when the hulls intersect.
template<class Graph , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>
FT	CGAL::Convex_hull_3::separation_distance (const Graph &g1, const Graph &g2, const NamedParameters_1 &np1=parameters::default_values(), const NamedParameters_2 &np2=parameters::default_values())
	computes a lower bound on the squared distance between the two convex graphs, returning zero when their hulls intersect.
template<class ConvexHullHierarchy , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>
FT	CGAL::Convex_hull_3::separation_distance (const ConvexHullHierarchy &ch1, const ConvexHullHierarchy &ch2, const NamedParameters_1 &np1=parameters::default_values(), const NamedParameters_2 &np2=parameters::default_values())
	computes a lower bound on the squared distance between the two convex hulls, returning zero when they intersect.
template<class PointRange , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>
bool	CGAL::Convex_hull_3::do_intersect (const PointRange &r1, const PointRange &r2, const NamedParameters_1 &np1=parameters::default_values(), const NamedParameters_2 &np2=parameters::default_values())
	checks if the convex hulls of the two point sets intersect or not.
template<class Graph , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>
bool	CGAL::Convex_hull_3::do_intersect (const Graph &g1, const Graph &g2, const NamedParameters_1 &np1=parameters::default_values(), const NamedParameters_2 &np2=parameters::default_values())
	checks if the two convex graphs intersect or not.
template<class ConvexHullHierarchy , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>
bool	CGAL::Convex_hull_3::do_intersect (const ConvexHullHierarchy &ch1, const ConvexHullHierarchy &ch2, const NamedParameters_1 &np1=parameters::default_values(), const NamedParameters_2 &np2=parameters::default_values())
	checks if the convex hulls intersect or not.

Function Documentation

do_intersect() [1/3]

template<class ConvexHullHierarchy , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>

bool CGAL::Convex_hull_3::do_intersect	(	const ConvexHullHierarchy &	ch1,
		const ConvexHullHierarchy &	ch2,
		const NamedParameters_1 &	np1 = parameters::default_values(),
		const NamedParameters_2 &	np2 = parameters::default_values()
	)

#include <CGAL/Convex_hull_3/do_intersect.h>

checks if the convex hulls intersect or not.

Template Parameters

ConvexHullHierarchy	an instance of CGAL::Convex_hull_hierarchy
NamedParameters_1	a sequence of Named Parameters
NamedParameters_2	a sequence of Named Parameters

Parameters

ch1	the first convex hull
ch2	the second convex hull
np1	an optional sequence of Named Parameters among the ones listed below
np2	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 ch1 (ch2) Type: a model of ReadablePropertyMap whose value types are the same for np1 and np2 Default: boost::get(CGAL::vertex_point, g) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in IncidentGraph.
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: np1 only
number_of_iterations if not 0 (no limit), indicates the maximum number of iterations performed by the algorithm. If this value is not 0, then an intersection might be reported even if the convex hulls does not intersect. However, if the convex hulls are reported not to intersect, this is guaranteed. Type: a positive integer convertible to std::size_t Extra: np1 only Default: 0

do_intersect() [2/3]

template<class Graph , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>

bool CGAL::Convex_hull_3::do_intersect	(	const Graph &	g1,
		const Graph &	g2,
		const NamedParameters_1 &	np1 = parameters::default_values(),
		const NamedParameters_2 &	np2 = parameters::default_values()
	)

#include <CGAL/Convex_hull_3/do_intersect.h>

checks if the two convex graphs intersect or not.

Template Parameters

Graph	is a model of VertexListGraph and AdjacencyGraph.
NamedParameters_1	a sequence of Named Parameters
NamedParameters_2	a sequence of Named Parameters

Parameters

g1	the first convex graph
g2	the second convex graph
np1	an optional sequence of Named Parameters among the ones listed below
np2	an optional sequence of Named Parameters among the ones listed below

Precondition

The input graph must represent a convex object to guarantee a correct answer.

Optional Named Parameters

vertex_point_map a property map associating points to the vertices of g1 (g2) Type: a model of ReadablePropertyMap whose value types are the same for np1 and np2 Default: boost::get(CGAL::vertex_point, g) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in Graph.
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: np1 only
number_of_iterations if not 0 (no limit), the maximum number of iterations performed by the algorithm. If this value is not 0, then an intersection might be reported even if the convex hulls do not intersect. However, if the convex hulls are reported not to intersect, this is guaranteed. Type: a positive integer convertible to std::size_t Extra: np1 only Default: 0

do_intersect() [3/3]

template<class PointRange , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>

bool CGAL::Convex_hull_3::do_intersect	(	const PointRange &	r1,
		const PointRange &	r2,
		const NamedParameters_1 &	np1 = parameters::default_values(),
		const NamedParameters_2 &	np2 = parameters::default_values()
	)

#include <CGAL/Convex_hull_3/do_intersect.h>

checks if the convex hulls of the two point sets intersect or not.

Template Parameters

PointRange	is a model of ConstRange. The value type of its iterator is the key type of the named parameter point_map.
NamedParameters_1	a sequence of Named Parameters
NamedParameters_2	a sequence of Named Parameters

Parameters

r1	range points of the first convex hull considered in the do-intersect test
r2	range points of the second convex hull considered in the do-intersect test
np1	an optional sequence of Named Parameters among the ones listed below
np2	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

point_map a property map associating points to the elements of r1 (r2) Type: a model of ReadablePropertyMap whose value types are the same for np1 and np2 Default: CGAL::Identity_property_map
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: np1 only
number_of_iterations if not 0 (no limit), the maximum number of iterations performed by the algorithm. If this value is not 0, then an intersection might be reported even if the convex hulls do not intersect. However, if the convex hulls are reported not to intersect, this is guaranteed. Type: a positive integer convertible to std::size_t Extra: np1 only Default: 0

• Note

  The point sets do not need to be in convex position.

Examples

Convex_hull_3/do_intersect_ch3.cpp.

separation_distance() [1/3]

template<class ConvexHullHierarchy , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>

FT CGAL::Convex_hull_3::separation_distance	(	const ConvexHullHierarchy &	ch1,
		const ConvexHullHierarchy &	ch2,
		const NamedParameters_1 &	np1 = parameters::default_values(),
		const NamedParameters_2 &	np2 = parameters::default_values()
	)

#include <CGAL/Convex_hull_3/distance.h>

computes a lower bound on the squared distance between the two convex hulls, returning zero when they intersect.

Template Parameters

ConvexHullHierarchy	an instance of CGAL::Convex_hull_hierarchy
NamedParameters_1	a sequence of Named Parameters
NamedParameters_2	a sequence of Named Parameters

Parameters

ch1	the first convex hull
ch2	the second convex hull
np1	an optional sequence of Named Parameters among the ones listed below
np2	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 ch1 (ch2) Type: a model of ReadablePropertyMap whose value types are the same for np1 and np2 Default: boost::get(CGAL::vertex_point, g) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in IncidenceGraph.
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: np1 only
number_of_iterations if not 0 (no limit), indicates the maximum number of iterations performed by the algorithm. If this value is not 0, then the return value can be zero even if the convex hulls does not intersect. However, the value reported remains a lower bound of the distance between the convex. Type: a positive integer convertible to std::size_t Extra: np1 only Default: 0

See also

CGAL::Convex_hull_3::do_intersect

separation_distance() [2/3]

template<class Graph , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>

FT CGAL::Convex_hull_3::separation_distance	(	const Graph &	g1,
		const Graph &	g2,
		const NamedParameters_1 &	np1 = parameters::default_values(),
		const NamedParameters_2 &	np2 = parameters::default_values()
	)

#include <CGAL/Convex_hull_3/distance.h>

computes a lower bound on the squared distance between the two convex graphs, returning zero when their hulls intersect.

Template Parameters

Graph	is a model of VertexListGraph and AdjacencyGraph.
NamedParameters_1	a sequence of Named Parameters
NamedParameters_2	a sequence of Named Parameters

Parameters

g1	the first convex graph
g2	the second convex graph
np1	an optional sequence of Named Parameters among the ones listed below
np2	an optional sequence of Named Parameters among the ones listed below

Warning

The input graph must represent a convex object to guarantee a correct answer.

Optional Named Parameters

vertex_point_map a property map associating points to the vertices of g1 (g2) Type: a model of ReadablePropertyMap whose value types are the same for np1 and np2 Default: boost::get(CGAL::vertex_point, g) Extra: If this parameter is omitted, an internal property map for CGAL::vertex_point_t must be available in Graph.
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: np1 only
number_of_iterations if not 0 (no limit), indicates the maximum number of iterations performed by the algorithm. if this value is not 0, then the return value can be zero even if the convex hulls does not intersect. However, the value reported remains a lower bound of the distance between the convex. Type: a positive integer convertible to std::size_t Extra: np1 only Default: 0

See also

CGAL::Convex_hull_3::do_intersect

separation_distance() [3/3]

template<class PointRange , class NamedParameters_1 = parameters::Default_named_parameters, class NamedParameters_2 = parameters::Default_named_parameters>

FT CGAL::Convex_hull_3::separation_distance	(	const PointRange &	r1,
		const PointRange &	r2,
		const NamedParameters_1 &	np1 = parameters::default_values(),
		const NamedParameters_2 &	np2 = parameters::default_values()
	)

#include <CGAL/Convex_hull_3/distance.h>

computes a lower bound on the squared distance between the convex hulls of two point sets, returning zero when the hulls intersect.

Template Parameters

PointRange	is a model of ConstRange. The value type of its iterator is the key type of the named parameter point_map.
NamedParameters_1	a sequence of Named Parameters
NamedParameters_2	a sequence of Named Parameters

Parameters

r1	first point range
r2	second point range
np1	an optional sequence of Named Parameters among the ones listed below
np2	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

point_map a property map associating points to the elements of r1 (r2) Type: a model of ReadablePropertyMap whose value types are the same for np1 and np2 Default: CGAL::Identity_property_map
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: np1 only
number_of_iterations if not 0 (no limit), indicates the maximum number of iterations performed by the algorithm. If this value is not 0, then an intersection might be reported even if the convex hulls does not intersect. However, if the convex hulls are reported not to intersect, this is guaranteed. Type: a positive integer convertible to std::size_t Extra: np1 only Default: 0

Note

The point sets do not need to be in convex position.

Examples

Convex_hull_3/do_intersect_ch3.cpp.