Free Functions

Functions to create a wrap from point clouds, segment soups, and polygons with holes.

Functions
template<typename PointRange , typename FaceRange , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>
void	CGAL::alpha_wrap_2 (const PointRange &points, const FaceRange &faces, const double alpha, const double offset, MultipolygonWithHoles &alpha_wrap, const InputNamedParameters &np=parameters::default_values())
	computes a watertight, 1-manifold, simple multipolygon that strictly contains an input indexed face set.
template<typename TriangleRange , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>
void	CGAL::alpha_wrap_2 (const TriangleRange &triangles, const double alpha, const double offset, MultipolygonWithHoles &alpha_wrap, const InputNamedParameters &np=parameters::default_values())
	computes a watertight, 1-manifold, simple multipolygon that strictly contains an input triangle soup.
template<typename Traits_ , typename Container_ , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>
void	CGAL::alpha_wrap_2 (const CGAL::Polygon_2< Traits_, Container_ > &p, const double alpha, const double offset, MultipolygonWithHoles &alpha_wrap, const InputNamedParameters &np=parameters::default_values())
	computes a watertight, 1-manifold, simple multipolygon that strictly contains an input polygon.
template<typename Traits_ , typename Container_ , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>
void	CGAL::alpha_wrap_2 (const CGAL::Polygon_with_holes_2< Traits_, Container_ > &pwh, const double alpha, const double offset, MultipolygonWithHoles &alpha_wrap, const InputNamedParameters &np=parameters::default_values())
	computes a watertight, 1-manifold, simple multipolygon that strictly contains an input polygon with holes.
template<typename InputMultipolygonWithHoles , typename OutputMultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>
void	CGAL::alpha_wrap_2 (const InputMultipolygonWithHoles &multipolygon, const double alpha, const double offset, OutputMultipolygonWithHoles &alpha_wrap, const InputNamedParameters &np=parameters::default_values())
	computes a watertight, 1-manifold, simple multipolygon that strictly contains an input multipolygon.
template<typename SegmentRange , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>
void	CGAL::alpha_wrap_2 (const SegmentRange &segments, const double alpha, const double offset, MultipolygonWithHoles &alpha_wrap, const InputNamedParameters &np=parameters::default_values())
	computes a watertight, 1-manifold, simple multipolygon that strictly contains an input segment soup.
template<typename MultiLineString , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>
void	CGAL::alpha_wrap_2 (const MultiLineString &multilinestring, const double alpha, const double offset, MultipolygonWithHoles &alpha_wrap, const InputNamedParameters &np=parameters::default_values())
	computes a watertight, 1-manifold, simple multipolygon that strictly contains input polylines.
template<typename PointRange , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>
void	CGAL::alpha_wrap_2 (const PointRange &points, const double alpha, const double offset, MultipolygonWithHoles &alpha_wrap, const InputNamedParameters &np=parameters::default_values())
	computes a watertight, 1-manifold, simple multipolygon that strictly contains an input point set.

Function Documentation

alpha_wrap_2() [1/8]

template<typename Traits_ , typename Container_ , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>

void CGAL::alpha_wrap_2	(	const CGAL::Polygon_2< Traits_, Container_ > &	p,
		const double	alpha,
		const double	offset,
		MultipolygonWithHoles &	alpha_wrap,
		const InputNamedParameters &	np = parameters::default_values()
	)

#include <CGAL/alpha_wrap_2.h>

computes a watertight, 1-manifold, simple multipolygon that strictly contains an input polygon.

Note

This function merely inserts and wraps all edges from the outer boundary. It does not repair the polygon first. Consequently, for example, if the polygon were to not be simple, with its a subcycle with opposite orientation, then the wrap would still be constructed as to contain this subcycle. In some use cases, it may be desirable to first repair invalid inputs. We refer to the CGAL component Polygon Repair for various polygon repair functions using different strategies.

The parameters alpha and offset respectively control which features will appear in the output, and the distance from the input. See Section Choosing Parameters for a detailed breakdown of their influence.

Template Parameters

MultipolygonWithHoles	a model of MultipolygonWithHoles_2
InputNamedParameters	a sequence of Named Parameters

Parameters

p	the input polygon
alpha	the value of the parameter alpha
offset	the value of the parameter offset
alpha_wrap	the output multipolygon
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

geom_traits an instance of a geometric traits class Type: a class model of AlphaWrapTraits_2 Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the point type. The geometric traits should use a floating point number type (see Interface).

Precondition

alpha and offset are strictly positive values.

alpha_wrap_2() [2/8]

template<typename Traits_ , typename Container_ , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>

void CGAL::alpha_wrap_2	(	const CGAL::Polygon_with_holes_2< Traits_, Container_ > &	pwh,
		const double	alpha,
		const double	offset,
		MultipolygonWithHoles &	alpha_wrap,
		const InputNamedParameters &	np = parameters::default_values()
	)

#include <CGAL/alpha_wrap_2.h>

computes a watertight, 1-manifold, simple multipolygon that strictly contains an input polygon with holes.

The parameters alpha and offset respectively control which features will appear in the output, and the distance from the input. See Section Choosing Parameters for a detailed breakdown of their influence.

Note

This function merely inserts and wraps all edges from the outer boundary and from the holes of the polygon with holes. It does not repair the polygon with holes first. Consequently, for example, if the polygon with holes were to be invalid with an edge that lays outside of the region enclosed by its outer boundary, then the wrap would still be constructed as to contain this edge. In some use cases, it may be desirable to first repair invalid inputs. We refer to the CGAL component Polygon Repair for various polygon repair functions using different strategies.

Template Parameters

MultipolygonWithHoles	a model of MultipolygonWithHoles_2
InputNamedParameters	a sequence of Named Parameters

Parameters

pwh	the input polygon with holes
alpha	the value of the parameter alpha
offset	the value of the parameter offset
alpha_wrap	the output multipolygon
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

geom_traits an instance of a geometric traits class Type: a class model of AlphaWrapTraits_2 Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the point type. The geometric traits should use a floating point number type (see Interface).

Precondition

alpha and offset are strictly positive values.

alpha_wrap_2() [3/8]

template<typename InputMultipolygonWithHoles , typename OutputMultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>

void CGAL::alpha_wrap_2	(	const InputMultipolygonWithHoles &	multipolygon,
		const double	alpha,
		const double	offset,
		OutputMultipolygonWithHoles &	alpha_wrap,
		const InputNamedParameters &	np = parameters::default_values()
	)

#include <CGAL/alpha_wrap_2.h>

computes a watertight, 1-manifold, simple multipolygon that strictly contains an input multipolygon.

The parameters alpha and offset respectively control which features will appear in the output, and the distance from the input. See Section Choosing Parameters for a detailed breakdown of their influence.

Note

This function merely inserts and wraps all edges from the outer boundaries and from the holes of the multipolygon. It does not repair the multipolygon first. Consequently, for example, if a polygon were to be invalid with an edge that lays outside of the region enclosed by its outer boundary, then the wrap would still be constructed as to contain this edge. In some use cases, it may be desirable to first repair invalid polygons. We refer to the CGAL component Polygon Repair for various polygon repair functions using different strategies.

Template Parameters

InputMultipolygonWithHoles	a model of MultipolygonWithHoles_2
OutputMultipolygonWithHoles	a model of MultipolygonWithHoles_2
InputNamedParameters	a sequence of Named Parameters

Parameters

multipolygon	a multipolygon
alpha	the value of the parameter alpha
offset	the value of the parameter offset
alpha_wrap	the output multipolygon
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

geom_traits an instance of a geometric traits class Type: a class model of AlphaWrapTraits_2 Default: a CGAL Kernel deduced from the point type, using CGAL::Kernel_traits and the point type of the multipolygon Extra: The geometric traits class must be compatible with the point type. The geometric traits should use a floating point number type (see Interface).

Precondition

alpha and offset are strictly positive values.

alpha_wrap_2() [4/8]

template<typename MultiLineString , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>

void CGAL::alpha_wrap_2	(	const MultiLineString &	multilinestring,
		const double	alpha,
		const double	offset,
		MultipolygonWithHoles &	alpha_wrap,
		const InputNamedParameters &	np = parameters::default_values()
	)

#include <CGAL/alpha_wrap_2.h>

computes a watertight, 1-manifold, simple multipolygon that strictly contains input polylines.

The parameters alpha and offset respectively control which features will appear in the output, and the distance from the input. See Section Choosing Parameters for a detailed breakdown of their influence.

Template Parameters

MultiLineString	a model of RandomAccessContainer whose value type is a model of RandomAccessContainer whose value type is GeomTraits::Point_2, with GeomTraits being the type of the parameter geom_traits
MultipolygonWithHoles	a model of MultipolygonWithHoles_2
InputNamedParameters	a sequence of Named Parameters

Parameters

multilinestring	the input polylines
alpha	the value of the parameter alpha
offset	the value of the parameter offset
alpha_wrap	the output multipolygon
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

geom_traits an instance of a geometric traits class Type: a class model of AlphaWrapTraits_2 Default: a CGAL Kernel deduced from the input point type, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the segment type. The geometric traits should use a floating point number type (see Interface).

Precondition

alpha and offset are strictly positive values.

alpha_wrap_2() [5/8]

template<typename PointRange , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>

void CGAL::alpha_wrap_2	(	const PointRange &	points,
		const double	alpha,
		const double	offset,
		MultipolygonWithHoles &	alpha_wrap,
		const InputNamedParameters &	np = parameters::default_values()
	)

#include <CGAL/alpha_wrap_2.h>

computes a watertight, 1-manifold, simple multipolygon that strictly contains an input point set.

The parameters alpha and offset respectively control which features will appear in the output, and the distance from the input. See Section Choosing Parameters for a detailed breakdown of their influence.

Template Parameters

PointRange	model of Range whose value type is GeomTraits::Point_2, with GeomTraits being the type of the parameter geom_traits
MultipolygonWithHoles	model of MultipolygonWithHoles_2
InputNamedParameters	a sequence of Named Parameters

Parameters

points	the input points
alpha	the value of the parameter alpha
offset	the value of the parameter offset
alpha_wrap	the output multipolygon
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

geom_traits an instance of a geometric traits class Type: a class model of AlphaWrapTraits_2 Default: a CGAL Kernel deduced from the input point type, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the point type. The geometric traits should use a floating point number type (see Interface).

Precondition

alpha and offset are strictly positive values.

alpha_wrap_2() [6/8]

template<typename PointRange , typename FaceRange , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>

void CGAL::alpha_wrap_2	(	const PointRange &	points,
		const FaceRange &	faces,
		const double	alpha,
		const double	offset,
		MultipolygonWithHoles &	alpha_wrap,
		const InputNamedParameters &	np = parameters::default_values()
	)

#include <CGAL/alpha_wrap_2.h>

computes a watertight, 1-manifold, simple multipolygon that strictly contains an input indexed face set.

The parameters alpha and offset respectively control which features will appear in the output, and the distance from the input. See Section Choosing Parameters for a detailed breakdown of their influence.

Template Parameters

PointRange	a model of RandomAccessContainer whose value type is GeomTraits::Point_2, with GeomTraits being the type of the parameter geom_traits
FaceRange	a model of Range whose value type is a model of RandomAccessContainer whose value type is an integral type
MultipolygonWithHoles	a model of MultipolygonWithHoles_2
InputNamedParameters	a sequence of Named Parameters

Parameters

points	the input points
faces	the input faces, with each element of the range being a range of indices corresponding to points in points
alpha	the value of the parameter alpha
offset	the value of the parameter offset
alpha_wrap	the output multipolygon
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

geom_traits an instance of a geometric traits class Type: a class model of AlphaWrapTraits_2 Default: a CGAL Kernel deduced from the value type of the point range, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the point type. The geometric traits should use a floating point number type (see Interface).

Precondition

alpha and offset are strictly positive values.

Examples

Alpha_wrap_2/point_set_wrap_2.cpp, Alpha_wrap_2/polygon_wrap_2.cpp, Alpha_wrap_2/polyline_wrap_2.cpp, and Alpha_wrap_2/triangle_soup_wrap_2.cpp.

alpha_wrap_2() [7/8]

template<typename SegmentRange , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>

void CGAL::alpha_wrap_2	(	const SegmentRange &	segments,
		const double	alpha,
		const double	offset,
		MultipolygonWithHoles &	alpha_wrap,
		const InputNamedParameters &	np = parameters::default_values()
	)

#include <CGAL/alpha_wrap_2.h>

computes a watertight, 1-manifold, simple multipolygon that strictly contains an input segment soup.

The parameters alpha and offset respectively control which features will appear in the output, and the distance from the input. See Section Choosing Parameters for a detailed breakdown of their influence.

Template Parameters

SegmentRange	a model of Range whose value type is GeomTraits::Segment_2, with GeomTraits being the type of the parameter geom_traits
MultipolygonWithHoles	a model of MultipolygonWithHoles_2
InputNamedParameters	a sequence of Named Parameters

Parameters

segments	the input segments
alpha	the value of the parameter alpha
offset	the value of the parameter offset
alpha_wrap	the output multipolygon
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

geom_traits an instance of a geometric traits class Type: a class model of AlphaWrapTraits_2 Default: a CGAL Kernel deduced from the input point type, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the segment type. The geometric traits should use a floating point number type (see Interface).

Precondition

alpha and offset are strictly positive values.

alpha_wrap_2() [8/8]

template<typename TriangleRange , typename MultipolygonWithHoles , typename InputNamedParameters = parameters::Default_named_parameters>

void CGAL::alpha_wrap_2	(	const TriangleRange &	triangles,
		const double	alpha,
		const double	offset,
		MultipolygonWithHoles &	alpha_wrap,
		const InputNamedParameters &	np = parameters::default_values()
	)

#include <CGAL/alpha_wrap_2.h>

computes a watertight, 1-manifold, simple multipolygon that strictly contains an input triangle soup.

The parameters alpha and offset respectively control which features will appear in the output, and the distance from the input. See Section Choosing Parameters for a detailed breakdown of their influence.

Template Parameters

TriangleRange	a model of Range whose value type is a model of RandomAccessContainer of size 3 whose value type is GeomTraits::Point_2, with GeomTraits being the type of the parameter geom_traits
MultipolygonWithHoles	a model of MultipolygonWithHoles_2
InputNamedParameters	a sequence of Named Parameters

Parameters

triangles	the input triangles
alpha	the value of the parameter alpha
offset	the value of the parameter offset
alpha_wrap	the output multipolygon
np	an optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

geom_traits an instance of a geometric traits class Type: a class model of AlphaWrapTraits_2 Default: a CGAL Kernel deduced from the input triangle range, using CGAL::Kernel_traits Extra: The geometric traits class must be compatible with the triangle type. The geometric traits should use a floating point number type (see Interface).

Precondition

alpha and offset are strictly positive values.