The following functions are used to construct the inward or outward weighted offsets of a polygon.

Functions
template<typename OfKPolygon , typename FT , typename InKPolygon , typename InKWeights , typename HoleIterator , typename OfK , typename SsK >
std::vector< std::shared_ptr< OfKPolygon > >	CGAL::create_interior_weighted_skeleton_and_offset_polygons_2 (FT offset, const InKPolygon &outer_boundary, HoleIterator holes_begin, HoleIterator holes_end, const InKWeights &outer_boundary_weights, HoleWeightsIterator holes_weights_begin, HoleWeightsIterator holes_weights_end, OfK ofk=CGAL::Exact_predicates_inexact_constructions_kernel, SsK ssk=CGAL::Exact_predicates_inexact_constructions_kernel())
	returns a container with all the inner offset polygons at distance `offset` of a 2D polygon with holes.

template<typename OfKPolygon , typename FT , typename InKPolygon , typename InKWeights , typename OfK , typename SsK >
std::vector< std::shared_ptr< OfKPolygon > >	CGAL::create_interior_weighted_skeleton_and_offset_polygons_2 (FT offset, const InKPolygon &poly, const InKWeights &weights, OfK ofk=CGAL::Exact_predicates_inexact_constructions_kernel, SsK ssk=CGAL::Exact_predicates_inexact_constructions_kernel())
	returns a container with all the inner offset polygons at distance `offset` of the 2D polygon `poly`.

template<typename OfKPolygon , typename FT , typename InKPolygon , typename InKWeights , typename OfK , typename SsK >
std::vector< std::shared_ptr< OfKPolygon > >	CGAL::create_exterior_weighted_skeleton_and_offset_polygons_2 (FT offset, const InKPolygon &poly, const InKWeights &weights, OfK ofk=Exact_predicates_inexact_constructions_kernel(), SsK ssk=Exact_predicates_inexact_constructions_kernel())
	returns a container with all the outer offset polygons at distance `offset` of the 2D polygon `poly`.

template<class OfKPolygon , class FT , class InKPolygon , class OfK , class SsK >
std::vector< std::shared_ptr< OfKPolygon > >	CGAL::create_interior_weighted_skeleton_and_offset_polygons_with_holes_2 (FT offset, const InKPolygon &poly_with_holes, OfK ofk=CGAL::Exact_predicates_inexact_constructions_kernel, SsK ssk=CGAL::Exact_predicates_inexact_constructions_kernel)
	returns a container with all the inner offset polygons with holes at distance `offset` of the 2D polygon with holes `poly_with_holes`.

template<class OfKPolygon , class FT , class InKPolygon , class OfK , class SsK >
std::vector< std::shared_ptr< OfKPolygon > >	CGAL::create_exterior_weighted_skeleton_and_offset_polygons_with_holes_2 (FT offset, const InKPolygon &poly_with_holes, const InKWeights &weights, OfK ofk=Exact_predicates_inexact_constructions_kernel(), SsK ssk=Exact_predicates_inexact_constructions_kernel())
	returns a container with all the outer offset polygons with holes at distance `offset` of the 2D polygon `poly_with_holes`.

Function Documentation

◆ create_exterior_weighted_skeleton_and_offset_polygons_2()

template<typename OfKPolygon , typename FT , typename InKPolygon , typename InKWeights , typename OfK , typename SsK >

std::vector< std::shared_ptr< OfKPolygon > > CGAL::create_exterior_weighted_skeleton_and_offset_polygons_2	(	FT	offset,
		const InKPolygon &	poly,
		const InKWeights &	weights,
		OfK	ofk = `Exact_predicates_inexact_constructions_kernel()`,
		SsK	ssk = `Exact_predicates_inexact_constructions_kernel()`
	)

#include <CGAL/create_weighted_offset_polygons_2.h>

returns a container with all the outer offset polygons at distance offset of the 2D polygon poly.

Weights of the polygon are given by weights, in the same order as the vertices of the polygon: the i-th weight in the range is associated to the contour edge between the i-1-th and i-th vertices.

The exterior skeleton is limited by an outer rectangular frame placed at a margin sufficiently large to allow the offset polygons to be constructed.

Note: A temporary straight skeleton is constructed in the limited exterior of the input polygon to obtain the offsets. The construction of this skeleton is the most expensive operation, therefore, to construct offsets at more than one single distance, use the separate functions create_exterior_straight_skeleton_2() and create_offset_polygons_2() instead.

Template Parameters

OfKPolygon	is a polygon without holes type determined from `OfK` and `InKPolygon`, see Section Polygon Return Type.
FT	must be a model of `FieldNumberType` convertible to `OfK::FT` and `SsK::FT`.
InKPolygon	must be a model of `SequenceContainer` with value type `InK::Point_2` (e.g. `Polygon_2<InK>`) or a model of `GeneralPolygonWithHoles_2` (e.g. `Polygon_with_holes_2<InK>`).
InKWeights	must be a model of `SequenceContainer` whose value type is itself a model of `SequenceContainer` with value type `InK::FT`.
OfK	must be a model of `Kernel`. It is used to instantiate `Polygon_offset_builder_traits_2<OfK>` for constructing the offset polygons.
SsK	must be a model of `Kernel`. It is used to instantiate `Straight_skeleton_builder_traits_2<SsK>` for constructing the straight skeleton.

Note: If SsK != OfK the constructed straight skeleton is converted to CGAL::Straight_skeleton_2<OfK>.

Precondition: offset is positive; poly is weakly simple, counterclockwise polygon.

See also: CGAL::create_interior_skeleton_and_offset_polygons_2(); CGAL::create_exterior_skeleton_and_offset_polygons_with_holes_2(); Polygon_offset_builder_2

◆ create_exterior_weighted_skeleton_and_offset_polygons_with_holes_2()

template<class OfKPolygon , class FT , class InKPolygon , class OfK , class SsK >

std::vector< std::shared_ptr< OfKPolygon > > CGAL::create_exterior_weighted_skeleton_and_offset_polygons_with_holes_2	(	FT	offset,
		const InKPolygon &	poly_with_holes,
		const InKWeights &	weights,
		OfK	ofk = `Exact_predicates_inexact_constructions_kernel()`,
		SsK	ssk = `Exact_predicates_inexact_constructions_kernel()`
	)

#include <CGAL/create_weighted_offset_polygons_from_polygon_with_holes_2.h>

returns a container with all the outer offset polygons with holes at distance offset of the 2D polygon poly_with_holes.

Note that the offset of the outer frame is ignored.

This is equivalent to a call to CGAL::arrange_offset_polygons_2() on the output of create_exterior_weighted_skeleton_and_offset_polygons_2(offset, poly_with_holes, ofk, ssk) after having filtered out the polygon corresponding to the offset of the outer frame and having reversed the orientation of all other polygons.

Template Parameters

OfKPolygon	is a polygon without holes type determined by `OfK` and `InKPolygon`, see Section Polygon Return Type.
FT	must be a model of `FieldNumberType` convertible to `OfK::FT` and `SsK::FT`.
InKPolygon	must be a model of `SequenceContainer` with value type `InK::Point_2` (e.g. `Polygon_2<InK>`) or a model of `GeneralPolygonWithHoles_2` (e.g. `Polygon_with_holes_2<InK>`).
InKWeights	must be a model of `SequenceContainer` whose value type is itself a model of `SequenceContainer` with value type `InK::FT`.
OfK	must be a model of `Kernel`. It is used to instantiate `Polygon_offset_builder_traits_2<OfK>` for constructing the offset polygons.
SsK	must be a model of `Kernel`. It is used to instantiate `Straight_skeleton_builder_traits_2<SsK>` for constructing the straight skeleton.

Note: If SsK != OfK the constructed weighted straight skeleton is converted to CGAL::Straight_skeleton_2<OfK>.

See also: CGAL::create_exterior_weighted_skeleton_and_offset_polygons_2(); CGAL::create_interior_weighted_skeleton_and_offset_polygons_with_holes_2(); Polygon_offset_builder_2

◆ create_interior_weighted_skeleton_and_offset_polygons_2() [1/2]

template<typename OfKPolygon , typename FT , typename InKPolygon , typename InKWeights , typename HoleIterator , typename OfK , typename SsK >

std::vector< std::shared_ptr< OfKPolygon > > CGAL::create_interior_weighted_skeleton_and_offset_polygons_2	(	FT	offset,
		const InKPolygon &	outer_boundary,
		HoleIterator	holes_begin,
		HoleIterator	holes_end,
		const InKWeights &	outer_boundary_weights,
		HoleWeightsIterator	holes_weights_begin,
		HoleWeightsIterator	holes_weights_end,
		OfK	ofk = `CGAL::Exact_predicates_inexact_constructions_kernel`,
		SsK	ssk = `CGAL::Exact_predicates_inexact_constructions_kernel()`
	)

#include <CGAL/create_weighted_offset_polygons_2.h>

returns a container with all the inner offset polygons at distance offset of a 2D polygon with holes.

The outer boundary is outer_boundary and its holes are given by [holes_begin,holes_end). Weights of the outer contour are given by outer_boundary_weights and weights of the holes are given by [holes_weights_begin, holes_weights_end], in the same order as holes appear in the iterator range. Within each weight range, weights are given in the same order as the vertices of the contour: the i-th weight in the range is associated to the contour edge between the i-1-th and i-th vertices.

Note: A temporary straight skeleton is constructed in the interior of the input polygon to obtain the offsets. The construction of this skeleton is the most expensive operation, therefore, to construct offsets at more than one single distance, it is advised to use the separate functions create_interior_straight_skeleton_2() and create_offset_polygons_2() instead.

Template Parameters

OfKPolygon	is a polygon without holes type determined from `OfK` and `InKPolygon`, see Section Polygon Return Type.
FT	must be a model of `FieldNumberType` convertible to `OfK::FT` and `SsK::FT`.
InKPolygon	must be a model of `SequenceContainer` with value type `InK::Point_2` (e.g. `Polygon_2<InK>`).
HoleIterator	must be a model of `InputIterator` with value type being a model of `ConstRange` with value type `SsK::Point_2`.
InKWeights	must be a model of `SequenceContainer` whose value type is `InK::FT`.
HoleWeightsIterator	must be a model of `InputIterator` with value type being a model of `SequenceContainer` with value type `InK::FT`.
OfK	must be a model of `Kernel`. It is used to instantiate `Polygon_offset_builder_traits_2<OfK>` for constructing the offset polygons.
SsK	must be a model of `Kernel`. It is used to instantiate `Straight_skeleton_builder_traits_2<SsK>` for constructing the straight skeleton.

Note: If SsK != OfK the constructed straight skeleton is converted to CGAL::Straight_skeleton_2<OfK>.

See also: CGAL::create_exterior_skeleton_and_offset_polygons_2(); CGAL::create_interior_skeleton_and_offset_polygons_with_holes_2(); Polygon_offset_builder_2

◆ create_interior_weighted_skeleton_and_offset_polygons_2() [2/2]

template<typename OfKPolygon , typename FT , typename InKPolygon , typename InKWeights , typename OfK , typename SsK >

std::vector< std::shared_ptr< OfKPolygon > > CGAL::create_interior_weighted_skeleton_and_offset_polygons_2	(	FT	offset,
		const InKPolygon &	poly,
		const InKWeights &	weights,
		OfK	ofk = `CGAL::Exact_predicates_inexact_constructions_kernel`,
		SsK	ssk = `CGAL::Exact_predicates_inexact_constructions_kernel()`
	)

#include <CGAL/create_weighted_offset_polygons_2.h>

returns a container with all the inner offset polygons at distance offset of the 2D polygon poly.

Weights of the polygon are given by weights, in the same order as the vertices of the polygon: the i-th weight in the range is associated to the contour edge between the i-1-th and i-th vertices.

Note: A temporary straight skeleton is constructed in the interior of the input polygon to obtain the offsets. The construction of this skeleton is the most expensive operation, therefore, to construct offsets at more than one single distance, use the separate functions create_interior_straight_skeleton_2() and create_offset_polygons_2() instead.

Template Parameters

OfKPolygon	is a polygon without holes type determined by `OfK` and `InKPolygon`, see Section Polygon Return Type.
FT	must be a model of `FieldNumberType` convertible to `OfK::FT` and `SsK::FT`.
InKPolygon	must be a model of `SequenceContainer` with value type `InK::Point_2` (e.g. `Polygon_2<InK>`) or a model of `GeneralPolygonWithHoles_2` (e.g. `Polygon_with_holes_2<InK>`).
InKWeights	must be a model of `SequenceContainer` whose value type is itself a model of `SequenceContainer` with value type `InK::FT`.
OfK	must be a model of `Kernel`. It is used to instantiate `Polygon_offset_builder_traits_2<OfK>` for constructing the offset polygons.
SsK	must be a model of `Kernel`. It is used to instantiate `Straight_skeleton_builder_traits_2<SsK>` for constructing the straight skeleton.

Note: If SsK != OfK the constructed straight skeleton is converted to CGAL::Straight_skeleton_2<OfK>.

See also: CGAL::create_exterior_skeleton_and_offset_polygons_2(); CGAL::create_interior_skeleton_and_offset_polygons_with_holes_2(); Polygon_offset_builder_2

◆ create_interior_weighted_skeleton_and_offset_polygons_with_holes_2()

template<class OfKPolygon , class FT , class InKPolygon , class OfK , class SsK >

std::vector< std::shared_ptr< OfKPolygon > > CGAL::create_interior_weighted_skeleton_and_offset_polygons_with_holes_2	(	FT	offset,
		const InKPolygon &	poly_with_holes,
		OfK	ofk = `CGAL::Exact_predicates_inexact_constructions_kernel`,
		SsK	ssk = `CGAL::Exact_predicates_inexact_constructions_kernel`
	)

#include <CGAL/create_weighted_offset_polygons_from_polygon_with_holes_2.h>

returns a container with all the inner offset polygons with holes at distance offset of the 2D polygon with holes poly_with_holes.

This is equivalent to arrange_offset_polygons_2(create_interior_weighted_skeleton_and_offset_polygons_2(offset, poly_with_holes, ofk, ssk)).

Template Parameters

OfKPolygon	is a polygon without holes type determined by `OfK` and `InKPolygon`, see Section Polygon Return Type.
FT	must be a model of `FieldNumberType` convertible to `OfK::FT` and `SsK::FT`.
InKPolygon	must be a model of `SequenceContainer` with value type `InK::Point_2` (e.g. `Polygon_2<InK>`) or a model of `GeneralPolygonWithHoles_2` (e.g. `Polygon_with_holes_2<InK>`).
InKWeights	must be a model of `SequenceContainer` whose value type is itself a model of `SequenceContainer` with value type `InK::FT`.
OfK	must be a model of `Kernel`. It is used to instantiate `Polygon_offset_builder_traits_2<OfK>` for constructing the offset polygons.
SsK	must be a model of `Kernel`. It is used to instantiate `Straight_skeleton_builder_traits_2<SsK>` for constructing the weighted straight skeleton.

Note: If SsK != OfK the constructed weighted straight skeleton is converted to CGAL::Straight_skeleton_2<OfK>.

See also: CGAL::create_interior_weighted_skeleton_and_offset_polygons_2(); CGAL::create_exterior_weighted_skeleton_and_offset_polygons_with_holes_2(); Polygon_offset_builder_2

Functions

Function Documentation

◆ create_exterior_weighted_skeleton_and_offset_polygons_2()

◆ create_exterior_weighted_skeleton_and_offset_polygons_with_holes_2()

◆ create_interior_weighted_skeleton_and_offset_polygons_2() [1/2]

◆ create_interior_weighted_skeleton_and_offset_polygons_2() [2/2]

◆ create_interior_weighted_skeleton_and_offset_polygons_with_holes_2()