Functions
template<class K , class InputPolygonPtrIterator , class OutputPolygonWithHolesPtrIterator >
void	CGAL::arrange_offset_polygons_2 (InputPolygonPtrIterator begin, InputPolygonPtrIterator end, OutputPolygonWithHolesPtrIterator out, K const &k)
	The function `arrange_offset_polygons_2()` arranges the sequence of `Polygon_2` objects obtained by `create_offset_polygons_2()` into `Polygon_with_holes_2` objects by determining geometric parent-hole relationships using a simple algorithm based on the particular characteristics of offset polygons. More...

template<class InputIterator , class Traits >
boost::optional< typename Traits::FT >	CGAL::compute_outer_frame_margin (InputIterator first, InputIterator beyond, typename Traits::FT offset, Traits const &traits=Default_traits)
	Computes the separation required between a polygon and the outer frame used to obtain an exterior skeleton suitable for the computation of outer offset polygons at a given distance. More...

template<class Polygon , class FT , class StraightSkeleton , class K >
std::vector< boost::shared_ptr < Polygon > >	CGAL::create_offset_polygons_2 (FT offset, StraightSkeleton const &s,, K const &k=Exact_predicates_inexact_constructions_kernel)
	returns a container with the offset polygons at distance `offset` obtained from the straight skeleton `s`. More...

template<class FT , class Polygon , class OffsettingK , class SkeletonK >
std::vector< boost::shared_ptr < Polygon > >	CGAL::create_exterior_skeleton_and_offset_polygons_2 (FT offset, Polygon const &poly, OffsettingK ofk=Exact_predicates_inexact_constructions_kernel, SkeletonK ssk=Exact_predicates_inexact_constructions_kernel)
	returns a container with all the outer offset polygons at distance `offset` of the 2D polygon `poly`. More...

template<class FT , class Polygon , class HoleIterator , class OffsettingK , class SkeletonK >
std::vector< boost::shared_ptr < Polygon > >	CGAL::create_interior_skeleton_and_offset_polygons_2 (FT offset, Polygon const &outer_boundary, HoleIterator holes_begin, HoleIterator holes_end, OffsettingK ofk=CGAL::Exact_predicates_inexact_constructions_kernel, SkeletonK ssk=CGAL::Exact_predicates_inexact_constructions_kernel)
	returns a container with all the inner offset polygons at distance `offset` of the 2D polygon with holes whose outer boundary is `outer_boundary` and its holes are given by `[holes_begin,holes_end]`. More...

template<class FT , class Polygon , class OffsettingK , class SkeletonK >
std::vector< boost::shared_ptr < Polygon > >	CGAL::create_interior_skeleton_and_offset_polygons_2 (FT offset, Polygon const &poly, OffsettingK ofk=CGAL::Exact_predicates_inexact_constructions_kernel, SkeletonK ssk=CGAL::Exact_predicates_inexact_constructions_kernel)
	returns a container with all the inner offset polygons at distance `offset` of the 2D polygon `poly`. More...

template<class FT , class OffsettingK , class SkeletonK , class C >
std::vector< boost::shared_ptr < Polygon_with_holes_2 < OffsettingK, C > > >	CGAL::create_exterior_skeleton_and_offset_polygons_with_holes_2 (FT offset, CGAL::Polygon_2< OffsettingK, C > poly_with_holes, OffsettingK ofk=Exact_predicates_inexact_constructions_kernel, SkeletonK 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`. More...

template<class FT , class OffsettingK , class SkeletonK , class C >
std::vector< boost::shared_ptr < Polygon_2< OffsettingK, C > > >	CGAL::create_interior_skeleton_and_offset_polygons_2 (FT offset, CGAL::Polygon_with_holes< OffsettingK, C > poly_with_holes, OffsettingK ofk=CGAL::Exact_predicates_inexact_constructions_kernel, SkeletonK ssk=CGAL::Exact_predicates_inexact_constructions_kernel)
	returns a container with all the inner offset polygons at distance `offset` of the 2D polygon with holes `poly_with_holes`. More...

template<class FT , class OffsettingK , class SkeletonK , class C >
std::vector< boost::shared_ptr < Polygon_with_holes_2 < OffsettingK, C > > >	CGAL::create_interior_skeleton_and_offset_polygons_with_holes_2 (FT offset, CGAL::Polygon_2< OffsettingK, C > poly, OffsettingK ofk=CGAL::Exact_predicates_inexact_constructions_kernel, SkeletonK 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 `poly`. More...

template<class FT , class OffsettingK , class SkeletonK , class C >
std::vector< boost::shared_ptr < Polygon_with_holes_2 < OffsettingK, C > > >	CGAL::create_interior_skeleton_and_offset_polygons_with_holes_2 (FT offset, CGAL::Polygon_with_holes_2< OffsettingK, C > poly_with_holes, OffsettingK ofk=CGAL::Exact_predicates_inexact_constructions_kernel, SkeletonK 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`. More...

template<class FT , class PointIterator , class K >
boost::shared_ptr < Straight_skeleton_2< K > >	CGAL::create_exterior_straight_skeleton_2 (FT max_offset, PointIterator vertices_begin, PointIterator vertices_end, K const &k=Exact_predicates_inexact_constructions_kernel)
	The function `create_exterior_straight_skeleton_2()` creates a straight skeleton in the exterior of a 2D polygon with holes. More...

template<class FT , class Polygon , class K >
boost::shared_ptr < Straight_skeleton_2< K > >	CGAL::create_exterior_straight_skeleton_2 (FT max_offset, Polygon P, K const &k=Exact_predicates_inexact_constructions_kernel)
	The function `create_exterior_straight_skeleton_2()` creates a straight skeleton in the exterior of a 2D polygon with holes. More...

template<class PointIterator , class HoleIterator , class K >
boost::shared_ptr < Straight_skeleton_2< K > >	CGAL::create_interior_straight_skeleton_2 (PointIterator outer_contour_vertices_begin, PointIterator outer_contour_vertices_end, HoleIterator holes_begin, HoleIterator holes_end, K const &k=Exact_predicates_inexact_constructions_kernel)
	returns a new `Straight_skeleton_2<K>` in the interior of the 2D polygon with holes whose outer boundary is given by the point sequence `[outer_contour_vertices_begin,outer_contour_vertices_end]` and its holes given by `[holes_begin,holes_end]`. More...

template<class PointIterator , class K >
boost::shared_ptr < Straight_skeleton_2< K > >	CGAL::create_interior_straight_skeleton_2 (PointIterator outer_contour_vertices_begin, PointIterator outer_contour_vertices_end, K const &k=Exact_predicates_inexact_constructions_kernel)
	returns a new `Straight_skeleton_2<K>` in the interior of the 2D polygon whose outer boundary is given by the point sequence `[outer_contour_vertices_begin,outer_contour_vertices_end]`. More...

template<class Polygon , class K >
boost::shared_ptr < Straight_skeleton_2< K > >	CGAL::create_interior_straight_skeleton_2 (Polygon const &outer_contour, K const &k=Exact_predicates_inexact_constructions_kernel)
	returns a new `Straight_skeleton_2<K>` in the interior of the 2D polygon `outer_contour`. More...

template<class K , class C >
boost::shared_ptr < Straight_skeleton_2< K > >	CGAL::create_interior_straight_skeleton_2 (Polygon_with_holes< K, C > poly_with_holes, K const &k=Exact_predicates_inexact_constructions_kernel)
	returns a new `Straight_skeleton_2<K>` in the interior of the 2D polygon with holes `poly_with_holes`. More...

template<class Target_skeleton , class Source_skeleton , class Items_converter >
boost::shared_ptr < Target_skeleton, Source_skeleton, Items_converter >	CGAL::convert_straight_skeleton_2 (Source_skeleton const &s, Items_converted const &ic=Items_converter())
	Converts a straight skeleton instantiated using certain traits into another straight skeleton instantiated using a different traits. More...

Function Documentation

template<class K , class InputPolygonPtrIterator , class OutputPolygonWithHolesPtrIterator >

void CGAL::arrange_offset_polygons_2	(	InputPolygonPtrIterator	begin,
		InputPolygonPtrIterator	end,
		OutputPolygonWithHolesPtrIterator	out,
		K const &	k
	)

The function arrange_offset_polygons_2() arranges the sequence of Polygon_2 objects obtained by create_offset_polygons_2() into Polygon_with_holes_2 objects by determining geometric parent-hole relationships using a simple algorithm based on the particular characteristics of offset polygons.

The function determines parent-hole relationships among the polygons given by [begin,end] creating boost::shared_ptr< Polygon_with_holes_2<K> > objects added to the output sequence given out. A CLOCKWISE oriented polygon H is a hole of a COUNTERCLOCKWISE polygon P, iff at least one vertex of H is ON_BOUNDED_SIDE of P.

This function should not be used to arrange arbitrary polygons into polygons with holes unless they meet the requirements specified below.

Template Parameters

K	must be a CGAL kernel.
InputPolygonPtrIterator	must be an input iterator whose `value_type` is a smart pointer (such as `boost::shared_ptr`) whose `element_type` is `Polygon_2<K>`. The input polygons must be simple. The set of input polygons are unique and interior disjoint. That is, given distinct polygons `P` and `Q`, there are vertices of `P` which are not on the boundary of `Q` and are all on the bounded or unbounded side of `Q` (but not both).
OutputPolygonWithHolesPtrIterator	must be an output iterator whose `value_type` is a smart pointer (such as `boost::shared_ptr`) whose `element_type` is `Polygon_with_holes_2<K>`.

See Also: create_exterior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/arrange_offset_polygons_2.h>

template<class InputIterator , class Traits >

boost::optional< typename Traits::FT > CGAL::compute_outer_frame_margin	(	InputIterator	first,
		InputIterator	beyond,
		typename Traits::FT	offset,
		Traits const &	traits = `Default_traits`
	)

Computes the separation required between a polygon and the outer frame used to obtain an exterior skeleton suitable for the computation of outer offset polygons at a given distance.

Given a non-degenerate strictly-simple 2D polygon whose vertices are passed in the range [first,beyond), calculates the largest euclidean distance d between each input vertex and its corresponding offset vertex at a distance offset.

If such a distance can be approximately computed, returns an optional<FT> with the value d + (offset * 1.05). If the distance cannot be computed, not even approximately, due to overflow for instance, returns an empty optional<FT> (an absent result).

This result is the required separation between the input polygon and the rectangular frame used to construct an exterior offset contour at distance offset (which is done by placing the polygon as a hole of that frame).

Such a separation must be computed in this way because if the frame is too close to the polygon, the inward offset contour from the frame could collide with the outward offset contour of the polygon, resulting in a merged contour offset instead of two contour offsets, one of them corresponding to the frame.

Simply using 2*offset as the separation is incorrect since offset is the distance between an offset line and its original, not between an offset vertex and its original. The later, which is calculated by this function and needed to place the frame sufficiently away from the polygon, can be thousands of times larger than offset.

If the result is absent, any attempt to construct an exterior offset polygon at distance offset will fail. This will occur whenever the polygon has a vertex with an internal angle approaching 0 (because the offset vertex of a vertex whose internal angle equals 0 is at infinity ).

Precondition: offset > 0.; The range [first,beyond) contains the vertices of a non-degenerate strictly-simple 2D polygon.

The default traits class Default_traits is an instance of the class Polygon_offset_builder_traits_2<Kernel> parameterized on the kernel in which the type InputIterator::value_type is defined.

Template Parameters

InputIterator	must have a `value_type` equivalent to `Traits::Point_2`.
Traits	must be a model for `PolygonOffsetBuilderTraits_2`.

See Also: PolygonOffsetBuilderTraits_2; Polygon_offset_builder_traits_2

#include <CGAL/compute_outer_frame_margin.h>

Examples:: Straight_skeleton_2/Low_level_API.cpp.

template<class Target_skeleton , class Source_skeleton , class Items_converter >

boost::shared_ptr<Target_skeleton, Source_skeleton, Items_converter> CGAL::convert_straight_skeleton_2	(	Source_skeleton const &	s,
		Items_converted const &	ic = `Items_converter()`
	)

Converts a straight skeleton instantiated using certain traits into another straight skeleton instantiated using a different traits.

returns a new straight skeleton data structure with the same combinatorial and geometric data as s using the items converter ic to convert the geometric embedding to the types of the target skeleton.

Template Parameters

Target_skeleton	type of the target straight skeleton
Source_skeleton	type of the source straight skeleton
Items_converter	a model of `StraightSkeletonItemsConverter_2`

See Also: StraightSkeletonItemsConverter_2; Straight_skeleton_items_converter_2; Straight_skeleton_converter_2

#include <CGAL/Straight_skeleton_converter_2.h>

template<class FT , class Polygon , class OffsettingK , class SkeletonK >

std::vector< boost::shared_ptr<Polygon> > CGAL::create_exterior_skeleton_and_offset_polygons_2	(	FT	offset,
		Polygon const &	poly,
		OffsettingK	ofk = `Exact_predicates_inexact_constructions_kernel`,
		SkeletonK	ssk = `Exact_predicates_inexact_constructions_kernel`
	)

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

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

Template Parameters

OffsettingK	must be a CGAL kernel. It is used to instantiate `Polygon_offset_builder_traits_2<K>` for constructing the offset polygons.
SkeletonK	must be a CGAL kernel. It is used to instantiate `Straight_skeleton_builder_traits_2<K>` for constructing the straight skeleton. If `SkeletonK != OffsettingK` the constructed straight skeleton is converted to `Straight_skeleton_2<OffsettingK>`.
FT	must be a number type implicitly convertible to `OffsettingK::FT`. `Straight_skeleton` is `Straight_skeleton_2<K2>`. If `K != K2` the straight skeleton is converted to `Straight_skeleton_2<K>`.

See Also: create_exterior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_offset_polygons_2.h>

Examples:: Straight_skeleton_2/Create_skeleton_and_offset_polygons_2.cpp.

template<class FT , class OffsettingK , class SkeletonK , class C >

std::vector< boost::shared_ptr< Polygon_with_holes_2<OffsettingK,C> > > CGAL::create_exterior_skeleton_and_offset_polygons_with_holes_2	(	FT	offset,
		CGAL::Polygon_2< OffsettingK, C >	poly_with_holes,
		OffsettingK	ofk = `Exact_predicates_inexact_constructions_kernel`,
		SkeletonK	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.

This is equivalent to arrange_offset_polygons_2(create_exterior_skeleton_and_offset_polygons_2(offset,poly,okk,ssk)).

#include <CGAL/create_offset_polygons_from_polygon_with_holes_2.h>

template<class FT , class PointIterator , class K >

boost::shared_ptr< Straight_skeleton_2<K> > CGAL::create_exterior_straight_skeleton_2	(	FT	max_offset,
		PointIterator	vertices_begin,
		PointIterator	vertices_end,
		K const &	k = `Exact_predicates_inexact_constructions_kernel`
	)

The function create_exterior_straight_skeleton_2() creates a straight skeleton in the exterior of a 2D polygon with holes.

The function returns a new Straight_skeleton_2<K> in the limited exterior of the 2D polygon P given by the point sequence [vertices_begin,vertices_end]. The skeleton in the limited exterior of P is the skeleton in the interior of a polygon Q with P as its hole and a rectangular frame F as outer boundary. The outer boundary F is constructed by enlarging the bounding box of P a distance d. d is a margin sufficiently large to allow an outer offset at distance max_offset to be obtained from this exterior skeleton, as computed by the function compute_outer_frame_margin()

Requirements

Template Parameters

FT	a number type
K	is any CGAL Kernel
PointIterator	an `InputIterator` with `value_type` being equivalent to `K2::Point_2` `Cartesian_converter` is used to convert from `K2::Point_2` to `K::Point_2`

See Also: create_interior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_straight_skeleton_2.h>

Examples:: Straight_skeleton_2/Create_straight_skeleton_2.cpp.

template<class FT , class Polygon , class K >

boost::shared_ptr< Straight_skeleton_2<K> > CGAL::create_exterior_straight_skeleton_2	(	FT	max_offset,
		Polygon	P,
		K const &	k = `Exact_predicates_inexact_constructions_kernel`
	)

The function create_exterior_straight_skeleton_2() creates a straight skeleton in the exterior of a 2D polygon with holes.

The function returns a new Straight_skeleton_2<K> in the limited exterior of the 2D polygon P. The skeleton in the limited exterior of P is the skeleton in the interior of a polygon Q with P as its hole and a rectangular frame F as outer boundary. The outer boundary F is constructed by enlarging the bounding box of P a distance d. d is a margin sufficiently large to allow an outer offset at distance max_offset to be obtained from this exterior skeleton, as computed by the function compute_outer_frame_margin()

Requirements

Template Parameters

FT	a number type
K	is any CGAL kernel.
Polygon	is `Polygon_2<K>` or a standard container of `K::Point_2` elements.

See Also: create_interior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_straight_skeleton_2.h>

template<class FT , class OffsettingK , class SkeletonK , class C >

std::vector< boost::shared_ptr< Polygon_2<OffsettingK,C> > > CGAL::create_interior_skeleton_and_offset_polygons_2	(	FT	offset,
		CGAL::Polygon_with_holes< OffsettingK, C >	poly_with_holes,
		OffsettingK	ofk = `CGAL::Exact_predicates_inexact_constructions_kernel`,
		SkeletonK	ssk = `CGAL::Exact_predicates_inexact_constructions_kernel`
	)

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

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

OffsettingK	is the CGAL kernel used to instantiate `Polygon_offset_builder_traits_2<K>` for constructing the offset polygons.
SkeletonK	is the CGAL kernel used to instantiate `Straight_skeleton_builder_traits_2<K>` for constructing the straight skeleton. If `SkeletonK != OffsettingK` the constructed straight skeleton is converted to `Straight_skeleton_2<OffsettingK>`.
FT	is any number type implicitly convertible to `OffsettingK::FT`.
C	is the container of points in the polygons.

See Also: create_exterior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_offset_polygons_from_polygon_with_holes_2.h>

template<class FT , class Polygon , class HoleIterator , class OffsettingK , class SkeletonK >

std::vector< boost::shared_ptr<Polygon> > CGAL::create_interior_skeleton_and_offset_polygons_2	(	FT	offset,
		Polygon const &	outer_boundary,
		HoleIterator	holes_begin,
		HoleIterator	holes_end,
		OffsettingK	ofk = `CGAL::Exact_predicates_inexact_constructions_kernel`,
		SkeletonK	ssk = `CGAL::Exact_predicates_inexact_constructions_kernel`
	)

returns a container with all the inner offset polygons at distance offset of the 2D polygon with holes whose outer boundary is outer_boundary and its holes are given by [holes_begin,holes_end].

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

OffsettingK	is the CGAL kernel used to instantiate `Polygon_offset_builder_traits_2<K>` for constructing the offset polygons.
SkeletonK	is the CGAL kernel used to instantiate `Straight_skeleton_builder_traits_2<K>` for constructing the straight skeleton. If `SkeletonK != OffsettingK` the constructed straight skeleton is converted to `Straight_skeleton_2<OffsettingK>`.
FT	is any number type implicitly convertible to `OffsettingK::FT`.
Straight_skeleton	is `Straight_skeleton_2<K2>`. If `K != K2` the straight skeleton is converted to `Straight_skeleton_2<K>`.
HoleIterator	is an `InputIterator` with `value_type` being `CGAL::Polygon_2<OffsettingK>` or a standard container of `OffsettingK::Point_2` elements
Polygon	is an `InputIterator` with `value_type` being `CGAL::Polygon_2<OffsettingK>` or a standard container of `OffsettingK::Point_2` elements

See Also: create_exterior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_offset_polygons_2.h>

Examples:: Straight_skeleton_2/Create_saop_from_polygon_with_holes_2.cpp, and Straight_skeleton_2/Create_skeleton_and_offset_polygons_2.cpp.

template<class FT , class Polygon , class OffsettingK , class SkeletonK >

std::vector< boost::shared_ptr<Polygon> > CGAL::create_interior_skeleton_and_offset_polygons_2	(	FT	offset,
		Polygon const &	poly,
		OffsettingK	ofk = `CGAL::Exact_predicates_inexact_constructions_kernel`,
		SkeletonK	ssk = `CGAL::Exact_predicates_inexact_constructions_kernel`
	)

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

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

OffsettingK	is the CGAL kernel used to instantiate `Polygon_offset_builder_traits_2<K>` for constructing the offset polygons.
SkeletonK	is the CGAL kernel used to instantiate `Straight_skeleton_builder_traits_2<K>` for constructing the straight skeleton. If `SkeletonK != OffsettingK` the constructed straight skeleton is converted to `Straight_skeleton_2<OffsettingK>`.
FT	is any number type implicitly convertible to `OffsettingK::FT`.
Polygon	is an `InputIterator` with `value_type` being `CGAL::Polygon_2<OffsettingK>` or a standard container of `OffsettingK::Point_2` elements

See Also: create_exterior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_offset_polygons_2.h>

template<class FT , class OffsettingK , class SkeletonK , class C >

std::vector< boost::shared_ptr< Polygon_with_holes_2<OffsettingK,C> > > CGAL::create_interior_skeleton_and_offset_polygons_with_holes_2	(	FT	offset,
		CGAL::Polygon_2< OffsettingK, C >	poly,
		OffsettingK	ofk = `CGAL::Exact_predicates_inexact_constructions_kernel`,
		SkeletonK	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 poly.

This is equivalent to arrange_offset_polygons_2(create_interior_skeleton_and_offset_polygons_2(offset,poly,okk,ssk)).

Template Parameters

OffsettingK	is the CGAL kernel used to instantiate `Polygon_offset_builder_traits_2<K>` for constructing the offset polygons.
SkeletonK	is the CGAL kernel used to instantiate `Straight_skeleton_builder_traits_2<K>` for constructing the straight skeleton. If `SkeletonK != OffsettingK` the constructed straight skeleton is converted to `Straight_skeleton_2<OffsettingK>`.
FT	is any number type implicitly convertible to `OffsettingK::FT`.
C	is the container of points in the polygons.

See Also: create_exterior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_offset_polygons_from_polygon_with_holes_2.h>

Examples:: Straight_skeleton_2/Create_skeleton_and_offset_polygons_with_holes_2.cpp, and Straight_skeleton_2/Show_offset_polygon.cpp.

template<class FT , class OffsettingK , class SkeletonK , class C >

std::vector< boost::shared_ptr< Polygon_with_holes_2<OffsettingK,C> > > CGAL::create_interior_skeleton_and_offset_polygons_with_holes_2	(	FT	offset,
		CGAL::Polygon_with_holes_2< OffsettingK, C >	poly_with_holes,
		OffsettingK	ofk = `CGAL::Exact_predicates_inexact_constructions_kernel`,
		SkeletonK	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.

This is equivalent to arrange_offset_polygons_2(create_interior_skeleton_and_offset_polygons_2(offset,poly_with_holes,okk,ssk)).

Template Parameters

OffsettingK	is the CGAL kernel used to instantiate `Polygon_offset_builder_traits_2<K>` for constructing the offset polygons.
SkeletonK	is the CGAL kernel used to instantiate `Straight_skeleton_builder_traits_2<K>` for constructing the straight skeleton. If `SkeletonK != OffsettingK` the constructed straight skeleton is converted to `Straight_skeleton_2<OffsettingK>`.
FT	is any number type implicitly convertible to `OffsettingK::FT`.
C	is the container of points in the polygons.
Straight_skeleton	is `Straight_skeleton_2<K2>`. If `K != K2` the straight skeleton is converted to `Straight_skeleton_2<K>`.

See Also: create_exterior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_offset_polygons_from_polygon_with_holes_2.h>

template<class K , class C >

boost::shared_ptr< Straight_skeleton_2<K> > CGAL::create_interior_straight_skeleton_2	(	Polygon_with_holes< K, C >	poly_with_holes,
		K const &	k = `Exact_predicates_inexact_constructions_kernel`
	)

returns a new Straight_skeleton_2<K> in the interior of the 2D polygon with holes poly_with_holes.

See Also: create_exterior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_straight_skeleton_from_polygon_with_holes_2.h>

template<class PointIterator , class HoleIterator , class K >

boost::shared_ptr< Straight_skeleton_2<K> > CGAL::create_interior_straight_skeleton_2	(	PointIterator	outer_contour_vertices_begin,
		PointIterator	outer_contour_vertices_end,
		HoleIterator	holes_begin,
		HoleIterator	holes_end,
		K const &	k = `Exact_predicates_inexact_constructions_kernel`
	)

returns a new Straight_skeleton_2<K> in the interior of the 2D polygon with holes whose outer boundary is given by the point sequence [outer_contour_vertices_begin,outer_contour_vertices_end] and its holes given by [holes_begin,holes_end].

Template Parameters

K	is any CGAL Kernel
PointIterator	an `InputIterator` with `value_type` begin equivalent to `K2::Point_2`. `Cartesian_converter` is used to convert from `K2::Point_2` to `K::Point_2`
HoleIterator	an `InputIterator` with `value_type` being `Polygon_2<K>` or a standard container of `K2::Point_2` elements.

See Also: create_exterior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_straight_skeleton_2.h>

Examples:: Straight_skeleton_2/Create_offset_polygons_2.cpp, Straight_skeleton_2/Create_straight_skeleton_2.cpp, Straight_skeleton_2/Create_straight_skeleton_from_polygon_with_holes_2.cpp, and Straight_skeleton_2/Show_straight_skeleton.cpp.

template<class PointIterator , class K >

boost::shared_ptr< Straight_skeleton_2<K> > CGAL::create_interior_straight_skeleton_2	(	PointIterator	outer_contour_vertices_begin,
		PointIterator	outer_contour_vertices_end,
		K const &	k = `Exact_predicates_inexact_constructions_kernel`
	)

returns a new Straight_skeleton_2<K> in the interior of the 2D polygon whose outer boundary is given by the point sequence [outer_contour_vertices_begin,outer_contour_vertices_end].

Template Parameters

K	is any CGAL Kernel
PointIterator	an `InputIterator` with `value_type` begin equivalent to `K2::Point_2`. `Cartesian_converter` is used to convert from `K2::Point_2` to `K::Point_2`

See Also: create_exterior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_straight_skeleton_2.h>

template<class Polygon , class K >

boost::shared_ptr< Straight_skeleton_2<K> > CGAL::create_interior_straight_skeleton_2	(	Polygon const &	outer_contour,
		K const &	k = `Exact_predicates_inexact_constructions_kernel`
	)

returns a new Straight_skeleton_2<K> in the interior of the 2D polygon outer_contour.

Template Parameters

K	is any CGAL Kernel
Polygon	an `InputIterator` with `value_type` being `Polygon_2<K>` or a standard container of `K2::Point_2` elements.

See Also: create_exterior_straight_skeleton_2(); Straight_skeleton_builder_2

#include <CGAL/create_straight_skeleton_2.h>

template<class Polygon , class FT , class StraightSkeleton , class K >

std::vector< boost::shared_ptr<Polygon> > CGAL::create_offset_polygons_2	(	FT	offset,
		StraightSkeleton const &	s,
		K const &	k = `Exact_predicates_inexact_constructions_kernel`
	)

returns a container with the offset polygons at distance offset obtained from the straight skeleton s.

If s is the inner skeleton of a polygon with holes, the offset polygons will be generated in its interior. If s is the outer skeleton of a polygon with holes, the offset polygons will be generated in its exterior.

Template Parameters

K	is any CGAL kernel.
FT	is any number type implicitly convertible to `K::FT`.
StraightSkeleton	is `Straight_skeleton_2<K2>`. If `K != K2` the straight skeleton is converted to `Straight_skeleton_2<K>`.
Polygon	is a model of `VertexContainer_2`. If this first template parameter is omitted, `Polygon_2` is used.

See Also: create_interior_straight_skeleton_2(); create_exterior_straight_skeleton_2(); create_interior_skeleton_and_offset_polygons_2(); create_exterior_skeleton_and_offset_polygons_2()

#include <CGAL/create_offset_polygons_2.h>

Functions

Function Documentation