1102 lines
50 KiB
C
1102 lines
50 KiB
C
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// Copyright (c) 2006 Tel-Aviv University (Israel).
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// All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org).
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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/Minkowski_sum_2/include/CGAL/minkowski_sum_2.h $
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// $Id: minkowski_sum_2.h 254d60f 2019-10-19T15:23:19+02:00 Sébastien Loriot
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// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
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//
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// Author(s) : Ron Wein <wein_r@yahoo.com>
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// Efi Fogel <efifogel@gmail.com>
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#ifndef CGAL_MINKOWSKI_SUM_2_H
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#define CGAL_MINKOWSKI_SUM_2_H
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#include <CGAL/license/Minkowski_sum_2.h>
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#include <CGAL/basic.h>
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#include <CGAL/Polygon_with_holes_2.h>
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#include <CGAL/Minkowski_sum_2/Hole_filter_2.h>
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#include <CGAL/Minkowski_sum_2/Minkowski_sum_by_reduced_convolution_2.h>
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#include <CGAL/Minkowski_sum_2/Minkowski_sum_conv_2.h>
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#include <CGAL/Minkowski_sum_2/Minkowski_sum_decomp_2.h>
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#include <CGAL/Polygon_nop_decomposition_2.h>
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#include <CGAL/Gps_segment_traits_2.h>
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#include <list>
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namespace CGAL {
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/*!
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* Computes the Minkowski sum \f$ P \oplus Q\f$ of two given polygons.
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* The function computes the reduced convolution of the two polygons and
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* extracts those loops of the convolution which are part of the Minkowsi
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* sum. This method works very efficiently, regardless of whether `P` and
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* `Q` are convex or non-convex.
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* Note that as the input polygons may not be convex, their Minkowski
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* sum may not be a simple polygon. The result is therefore represented
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* as a polygon with holes.
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* \param[in] pgn1 The first polygon.
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* \param[in] pgn2 The second polygon.
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* \pre Both `P` and `Q` are simple, counterclockwise-oriented polygons.
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*/
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template <typename Kernel_, typename Container_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_by_reduced_convolution_2(const Polygon_2<Kernel_,
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Container_>& pgn1,
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const Polygon_2<Kernel_,
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Container_>& pgn2)
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{
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typedef Kernel_ Kernel;
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typedef Container_ Container;
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Minkowski_sum_by_reduced_convolution_2<Kernel, Container> mink_sum;
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Polygon_2<Kernel, Container> sum_bound;
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std::list<Polygon_2<Kernel, Container> > sum_holes;
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if (pgn1.size() > pgn2.size())
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mink_sum(pgn1, pgn2, sum_bound, std::back_inserter(sum_holes));
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else mink_sum(pgn2, pgn1, sum_bound, std::back_inserter(sum_holes));
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return (Polygon_with_holes_2<Kernel,Container>(sum_bound,
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sum_holes.begin(),
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sum_holes.end()));
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}
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/*!
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* Computes the Minkowski sum \f$ P \oplus Q\f$ of two given polygons with
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* holes.
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* The function computes the reduced convolution of the two polygons and
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* extracts those loops of the convolution which are part of the Minkowsi
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* sum. This method works very efficiently, regardless of whether `P` and
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* `Q` are convex or non-convex.
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* The result is also represented as a polygon with holes.
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* \param[in] pgn1 The first polygon.
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* \param[in] pgn2 The second polygon.
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*/
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template <typename Kernel_, typename Container_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_by_reduced_convolution_2
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(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
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const Polygon_with_holes_2<Kernel_, Container_>& pgn2)
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{
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typedef Kernel_ Kernel;
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typedef Container_ Container;
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Hole_filter_2<Kernel, Container> hole_filter;
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Polygon_with_holes_2<Kernel, Container> filtered_pgn1;
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Polygon_with_holes_2<Kernel, Container> filtered_pgn2;
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hole_filter(pgn1, pgn2, filtered_pgn1);
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hole_filter(pgn2, pgn1, filtered_pgn2);
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Minkowski_sum_by_reduced_convolution_2<Kernel, Container> mink_sum;
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Polygon_2<Kernel, Container> sum_bound;
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std::list<Polygon_2<Kernel, Container> > sum_holes;
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mink_sum(filtered_pgn1, filtered_pgn2, sum_bound,
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std::back_inserter(sum_holes));
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return (Polygon_with_holes_2<Kernel,Container>(sum_bound,
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sum_holes.begin(),
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sum_holes.end()));
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}
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/*!
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* Computes the Minkowski sum \f$ P \oplus Q\f$ of a simple polygon and a
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* polygon with holes.
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* The function computes the reduced convolution of the two polygons and
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* extracts those loops of the convolution which are part of the Minkowsi
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* sum. This method works very efficiently, regardless of whether `P` and
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* `Q` are convex or non-convex.
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* The result is also represented as a polygon with holes.
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* \param[in] pgn1 The simple polygon.
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* \param[in] pgn2 The polygon with holes.
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*/
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template <typename Kernel_, typename Container_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_by_reduced_convolution_2
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(const Polygon_2<Kernel_, Container_>& pgn1,
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const Polygon_with_holes_2<Kernel_, Container_>& pgn2)
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{
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typedef Kernel_ Kernel;
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typedef Container_ Container;
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Hole_filter_2<Kernel, Container> hole_filter;
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Polygon_with_holes_2<Kernel, Container> filtered_pgn2;
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hole_filter(pgn2, pgn1, filtered_pgn2);
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Minkowski_sum_by_reduced_convolution_2<Kernel, Container> mink_sum;
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Polygon_2<Kernel, Container> sum_bound;
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std::list<Polygon_2<Kernel, Container> > sum_holes;
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mink_sum(pgn1, filtered_pgn2, sum_bound, std::back_inserter(sum_holes));
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return (Polygon_with_holes_2<Kernel,Container>(sum_bound,
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sum_holes.begin(),
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sum_holes.end()));
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}
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/*!
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* Computes the Minkowski sum \f$ P \oplus Q\f$ of a simple polygon and a
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* polygon with holes.
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* The function computes the reduced convolution of the two polygons and
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* extracts those loops of the convolution which are part of the Minkowsi
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* sum. This method works very efficiently, regardless of whether `P` and
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* `Q` are convex or non-convex.
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* The result is also represented as a polygon with holes.
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* \param[in] pgn1 The polygon with holes.
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* \param[in] pgn2 The simple polygon.
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*/
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template <typename Kernel_, typename Container_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_by_reduced_convolution_2
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(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
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const Polygon_2<Kernel_, Container_>& pgn2)
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{ return minkowski_sum_by_reduced_convolution_2(pgn2, pgn1); }
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/*!
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* Compute the Minkowski sum of two simple polygons using the (full)
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* convolution method.
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* Note that as the input polygons may not be convex, their Minkowski sum may
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* not be a simple polygon. The result is therefore represented as a polygon
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* with holes.
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* \param[in] pgn1 The first polygon.
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* \param[in] pgn2 The second polygon.
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* \return The resulting polygon with holes, representing the sum.
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*/
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template <typename Kernel_, typename Container_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_by_full_convolution_2(const Polygon_2<Kernel_, Container_>& pgn1,
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const Polygon_2<Kernel_, Container_>& pgn2)
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{
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typedef Kernel_ Kernel;
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typedef Container_ Container;
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Minkowski_sum_by_convolution_2<Kernel, Container> mink_sum;
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Polygon_2<Kernel, Container> sum_bound;
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std::list<Polygon_2<Kernel, Container> > sum_holes;
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if (pgn1.size() > pgn2.size())
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mink_sum(pgn1, pgn2, sum_bound, std::back_inserter(sum_holes));
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else mink_sum(pgn2, pgn1, sum_bound, std::back_inserter(sum_holes));
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return (Polygon_with_holes_2<Kernel, Container>(sum_bound,
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sum_holes.begin(),
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sum_holes.end()));
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}
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/*!
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* Compute the Minkowski sum of two simple polygons using the convolution
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* method. This function defaults to calling the reduced convolution method,
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* as it is more efficient in most cases.
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* Note that as the input polygons may not be convex, their Minkowski sum may
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* not be a simple polygon. The result is therefore represented as a polygon
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* with holes.
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* \param[in] pgn1 The first polygon.
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* \param[in] pgn2 The second polygon.
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* \return The resulting polygon with holes, representing the sum.
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*
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* \sa `CGAL::minkowski_sum_by_reduced_convolution_2()`
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* \sa `CGAL::minkowski_sum_by_full_convolution_2()`
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*/
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template <typename Kernel_, typename Container_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
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const Polygon_2<Kernel_, Container_>& pgn2)
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{ return minkowski_sum_by_reduced_convolution_2(pgn1, pgn2); }
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/*!
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* Compute the Minkowski sum of two polygons with holes using the convolution
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* method. This function defaults to calling the reduced convolution method,
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* as it is more efficient in most cases.
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* Note that the result may not be a simple polygon. The result is therefore
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* represented as a polygon with holes.
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* \param[in] pgn1 The first polygon with holes.
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* \param[in] pgn2 The second polygon with holes.
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* \return The resulting polygon with holes, representing the sum.
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*
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* \sa `CGAL::minkowski_sum_by_reduced_convolution_2()`
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* \sa `CGAL::minkowski_sum_by_full_convolution_2()`
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*/
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template <typename Kernel_, typename Container_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
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const Polygon_with_holes_2<Kernel_, Container_>& pgn2)
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{ return minkowski_sum_by_reduced_convolution_2(pgn1, pgn2); }
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/*!
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* Compute the Minkowski sum of a simple polygon and a polygon with holes
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* using the convolution method. This function defaults to calling the reduced
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* convolution method, as it is more efficient in most cases.
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* Note that the result may not be a simple polygon. The result is therefore
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* represented as a polygon with holes.
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* \param[in] pgn1 The simple polygon.
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* \param[in] pgn2 The polygon with holes.
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* \return The resulting polygon with holes, representing the sum.
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*
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* \sa `CGAL::minkowski_sum_by_reduced_convolution_2()`
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* \sa `CGAL::minkowski_sum_by_full_convolution_2()`
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*/
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template <typename Kernel_, typename Container_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
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const Polygon_with_holes_2<Kernel_, Container_>& pgn2)
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{ return minkowski_sum_by_reduced_convolution_2(pgn1, pgn2); }
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/*!
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* Compute the Minkowski sum of a simple polygon and a polygon with holes
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* using the convolution method. This function defaults to calling the reduced
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* convolution method, as it is more efficient in most cases.
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* Note that the result may not be a simple polygon. The result is therefore
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* represented as a polygon with holes.
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* \param[in] pgn1 The polygon with holes.
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* \param[in] pgn2 The simple polygon.
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* \return The resulting polygon with holes, representing the sum.
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*
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* \sa `CGAL::minkowski_sum_by_reduced_convolution_2()`
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* \sa `CGAL::minkowski_sum_by_full_convolution_2()`
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*/
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template <typename Kernel_, typename Container_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
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const Polygon_2<Kernel_, Container_>& pgn2)
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{ return minkowski_sum_by_reduced_convolution_2(pgn1, pgn2); }
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/*!
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* \defgroup Minkowski sum by decomposition
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* @{
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*/
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/*! Compute the Minkowski sum of two simple polygons by decomposing each
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* polygon to convex sub-polygons and computing the union of the pairwise
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* Minkowski sums of the sub-polygons.
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* Note that as the input polygons may not be convex, their Minkowski sum may
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* not be a simple polygon. The result is therefore represented as a polygon
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* with holes.
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* \param[in] pgn1 The first polygon.
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* \param[in] pgn2 The second polygon.
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* \param[in] decomposition_strategy A functor for decomposing polygons.
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* \return The resulting polygon with holes, representing the sum.
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*/
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template <typename Kernel_, typename Container_,
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typename DecompositionStrategy1_, typename DecompositionStrategy2_>
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Polygon_with_holes_2<Kernel_, Container_>
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minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
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const Polygon_2<Kernel_, Container_>& pgn2,
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const DecompositionStrategy1_& decomposition_strategy1,
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const DecompositionStrategy2_& decomposition_strategy2)
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{
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typename Minkowski_sum_by_decomposition_2<DecompositionStrategy1_,
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DecompositionStrategy2_,
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Container_>::Traits_2 traits;
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return minkowski_sum_2(pgn1, pgn2,
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decomposition_strategy1, decomposition_strategy2,
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traits);
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}
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/*! Compute the Minkowski sum of two simple polygons by decomposing each
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* polygon to convex sub-polygons and computing the union of the pairwise
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* Minkowski sums of the sub-polygons.
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* Note that as the input polygons may not be convex, their Minkowski sum may
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* not be a simple polygon. The result is therefore represented as a polygon
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* with holes.
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* \param[in] pgn1 The first polygon.
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* \param[in] pgn2 The second polygon.
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* \param[in] decomposition_strategy A functor for decomposing polygons.
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* \param[in] traits The traits.
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* \return The resulting polygon with holes, representing the sum.
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*
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* The type of the last argument, namely,
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* Gps_segment_traits_2<Kernel_, Container_>
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* and the type
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* const typename Minkowski_sum_by_decomposition_2<DecompositionStrategy1_,
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* DecompositionStrategy2_,
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* Container_>::Traits_2>
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* are exchangeable except for in one case, where there is an ambiguity.
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* Thus, we use the former, even though it is less generic, as change to the
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* traits type in Minkowski_sum_by_decomposition_2 would require a similar
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* change here.
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*/
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template <typename Kernel_, typename Container_,
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|
|
typename DecompositionStrategy1_, typename DecompositionStrategy2_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1,
|
||
|
|
const DecompositionStrategy2_& decomposition_strategy2,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
typedef Container_ Container;
|
||
|
|
typedef DecompositionStrategy1_ Decomposition_strategy1;
|
||
|
|
typedef DecompositionStrategy2_ Decomposition_strategy2;
|
||
|
|
|
||
|
|
Minkowski_sum_by_decomposition_2<Decomposition_strategy1,
|
||
|
|
Decomposition_strategy2, Container>
|
||
|
|
mink_sum(decomposition_strategy1, decomposition_strategy2, traits);
|
||
|
|
return mink_sum(pgn1, pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*!
|
||
|
|
* Compute the Minkowski sum of two polygon with holes by decomposing each
|
||
|
|
* polygon to convex sub-polygons and computing the union of the pairwise
|
||
|
|
* Minkowski sums of the sub-polygons.
|
||
|
|
* The result is also represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_, typename DecompositionStrategy2_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1,
|
||
|
|
const DecompositionStrategy2_& decomposition_strategy2)
|
||
|
|
{
|
||
|
|
typename Minkowski_sum_by_decomposition_2<DecompositionStrategy1_,
|
||
|
|
DecompositionStrategy2_,
|
||
|
|
Container_>::Traits_2 traits;
|
||
|
|
return minkowski_sum_2(pgn1, pgn2,
|
||
|
|
decomposition_strategy1, decomposition_strategy2,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of two polygon with holes by decomposing each
|
||
|
|
* polygon to convex sub-polygons and computing the union of the pairwise
|
||
|
|
* Minkowski sums of the sub-polygons.
|
||
|
|
* The result is also represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \param[in] traits The traits.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_, typename DecompositionStrategy2_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1,
|
||
|
|
const DecompositionStrategy2_& decomposition_strategy2,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
typedef Kernel_ Kernel;
|
||
|
|
typedef Container_ Container;
|
||
|
|
typedef DecompositionStrategy1_ Decomposition_strategy1;
|
||
|
|
typedef DecompositionStrategy2_ Decomposition_strategy2;
|
||
|
|
|
||
|
|
Minkowski_sum_by_decomposition_2<Decomposition_strategy1,
|
||
|
|
Decomposition_strategy2, Container>
|
||
|
|
mink_sum(decomposition_strategy1, decomposition_strategy2, traits);
|
||
|
|
Hole_filter_2<Kernel, Container> hole_filter;
|
||
|
|
Polygon_with_holes_2<Kernel,Container> filtered_pgn1;
|
||
|
|
Polygon_with_holes_2<Kernel,Container> filtered_pgn2;
|
||
|
|
hole_filter(pgn1, pgn2, filtered_pgn1);
|
||
|
|
hole_filter(pgn2, pgn1, filtered_pgn2);
|
||
|
|
return mink_sum(filtered_pgn1, filtered_pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_, typename DecompositionStrategy2_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1,
|
||
|
|
const DecompositionStrategy2_& decomposition_strategy2)
|
||
|
|
{
|
||
|
|
typename Minkowski_sum_by_decomposition_2<DecompositionStrategy1_,
|
||
|
|
DecompositionStrategy2_,
|
||
|
|
Container_>::Traits_2 traits;
|
||
|
|
return minkowski_sum_2(pgn1, pgn2,
|
||
|
|
decomposition_strategy1, decomposition_strategy2,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The simple polygon.
|
||
|
|
* \param[in] pgn2 The polygon with holes.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \param[in] traits The traits.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_, typename DecompositionStrategy2_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1,
|
||
|
|
const DecompositionStrategy2_& decomposition_strategy2,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
typedef Kernel_ Kernel;
|
||
|
|
typedef Container_ Container;
|
||
|
|
typedef DecompositionStrategy1_ Decomposition_strategy1;
|
||
|
|
typedef DecompositionStrategy2_ Decomposition_strategy2;
|
||
|
|
|
||
|
|
Minkowski_sum_by_decomposition_2<Decomposition_strategy1,
|
||
|
|
Decomposition_strategy2, Container>
|
||
|
|
mink_sum(decomposition_strategy1, decomposition_strategy2, traits);
|
||
|
|
Hole_filter_2<Kernel, Container> hole_filter;
|
||
|
|
Polygon_with_holes_2<Kernel, Container> filtered_pgn2;
|
||
|
|
hole_filter(pgn2, pgn1, filtered_pgn2);
|
||
|
|
return mink_sum(pgn1, filtered_pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The second polygon.
|
||
|
|
* \param[in] pgn2 The first polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_, typename DecompositionStrategy2_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1,
|
||
|
|
const DecompositionStrategy2_& decomposition_strategy2)
|
||
|
|
{
|
||
|
|
typename Minkowski_sum_by_decomposition_2<DecompositionStrategy1_,
|
||
|
|
DecompositionStrategy2_,
|
||
|
|
Container_>::Traits_2 traits;
|
||
|
|
return minkowski_sum_2(pgn1, pgn2,
|
||
|
|
decomposition_strategy1, decomposition_strategy2,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The polygon with holes.
|
||
|
|
* \param[in] pgn2 The simple polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \param[in] traits The traits.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_, typename DecompositionStrategy2_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1,
|
||
|
|
const DecompositionStrategy2_& decomposition_strategy2,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
return minkowski_sum_2(pgn2, pgn1,
|
||
|
|
decomposition_strategy2, decomposition_strategy1,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of two simple polygons by decomposing each
|
||
|
|
* polygon to convex sub-polygons and computing the union of the pairwise
|
||
|
|
* Minkowski sums of the sub-polygons.
|
||
|
|
* Note that as the input polygons may not be convex, their Minkowski sum may
|
||
|
|
* not be a simple polygon. The result is therefore represented as a polygon
|
||
|
|
* with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1)
|
||
|
|
{
|
||
|
|
typename Minkowski_sum_by_decomposition_2<DecompositionStrategy1_,
|
||
|
|
DecompositionStrategy1_,
|
||
|
|
Container_>::Traits_2 traits;
|
||
|
|
return minkowski_sum_2(pgn1, pgn2,
|
||
|
|
decomposition_strategy1, decomposition_strategy1,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of two simple polygons by decomposing each
|
||
|
|
* polygon to convex sub-polygons and computing the union of the pairwise
|
||
|
|
* Minkowski sums of the sub-polygons.
|
||
|
|
* Note that as the input polygons may not be convex, their Minkowski sum may
|
||
|
|
* not be a simple polygon. The result is therefore represented as a polygon
|
||
|
|
* with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \param[in] traits The traits.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
typedef Container_ Container;
|
||
|
|
typedef DecompositionStrategy1_ Decomposition_strategy1;
|
||
|
|
|
||
|
|
Minkowski_sum_by_decomposition_2<Decomposition_strategy1,
|
||
|
|
Decomposition_strategy1, Container>
|
||
|
|
mink_sum(decomposition_strategy1, decomposition_strategy1, traits);
|
||
|
|
return mink_sum(pgn1, pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*!
|
||
|
|
* Compute the Minkowski sum of two polygon with holes by decomposing each
|
||
|
|
* polygon to convex sub-polygons and computing the union of the pairwise
|
||
|
|
* Minkowski sums of the sub-polygons.
|
||
|
|
* The result is also represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1)
|
||
|
|
{
|
||
|
|
typename Minkowski_sum_by_decomposition_2<DecompositionStrategy1_,
|
||
|
|
DecompositionStrategy1_,
|
||
|
|
Container_>::Traits_2 traits;
|
||
|
|
return minkowski_sum_2(pgn1, pgn2,
|
||
|
|
decomposition_strategy1, decomposition_strategy1,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of two polygon with holes by decomposing each
|
||
|
|
* polygon to convex sub-polygons and computing the union of the pairwise
|
||
|
|
* Minkowski sums of the sub-polygons.
|
||
|
|
* The result is also represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \param[in] traits The traits.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
typedef Kernel_ Kernel;
|
||
|
|
typedef Container_ Container;
|
||
|
|
typedef DecompositionStrategy1_ Decomposition_strategy1;
|
||
|
|
|
||
|
|
Minkowski_sum_by_decomposition_2<Decomposition_strategy1,
|
||
|
|
Decomposition_strategy1, Container>
|
||
|
|
mink_sum(decomposition_strategy1, decomposition_strategy1, traits);
|
||
|
|
Hole_filter_2<Kernel, Container> hole_filter;
|
||
|
|
Polygon_with_holes_2<Kernel,Container> filtered_pgn1;
|
||
|
|
Polygon_with_holes_2<Kernel,Container> filtered_pgn2;
|
||
|
|
hole_filter(pgn1, pgn2, filtered_pgn1);
|
||
|
|
hole_filter(pgn2, pgn1, filtered_pgn2);
|
||
|
|
return mink_sum(filtered_pgn1, filtered_pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1)
|
||
|
|
{
|
||
|
|
typename Minkowski_sum_by_decomposition_2<DecompositionStrategy1_,
|
||
|
|
DecompositionStrategy1_,
|
||
|
|
Container_>::Traits_2 traits;
|
||
|
|
return minkowski_sum_2(pgn1, pgn2,
|
||
|
|
decomposition_strategy1, decomposition_strategy1,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The simple polygon.
|
||
|
|
* \param[in] pgn2 The polygon with holes.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \param[in] traits The traits.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
typedef Kernel_ Kernel;
|
||
|
|
typedef Container_ Container;
|
||
|
|
typedef DecompositionStrategy1_ Decomposition_strategy1;
|
||
|
|
|
||
|
|
Minkowski_sum_by_decomposition_2<Decomposition_strategy1,
|
||
|
|
Decomposition_strategy1, Container>
|
||
|
|
mink_sum(decomposition_strategy1, decomposition_strategy1, traits);
|
||
|
|
Hole_filter_2<Kernel, Container> hole_filter;
|
||
|
|
Polygon_with_holes_2<Kernel,Container> filtered_pgn2;
|
||
|
|
hole_filter(pgn2, pgn1, filtered_pgn2);
|
||
|
|
return mink_sum(pgn1, filtered_pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The second polygon.
|
||
|
|
* \param[in] pgn2 The first polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1)
|
||
|
|
{
|
||
|
|
typename Minkowski_sum_by_decomposition_2<DecompositionStrategy1_,
|
||
|
|
DecompositionStrategy1_,
|
||
|
|
Container_>::Traits_2 traits;
|
||
|
|
return minkowski_sum_2(pgn1, pgn2,
|
||
|
|
decomposition_strategy1, decomposition_strategy1,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The polygon with holes.
|
||
|
|
* \param[in] pgn2 The simple polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \param[in] traits The traits.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename DecompositionStrategy1_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_2(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_2<Kernel_, Container_>& pgn2,
|
||
|
|
const DecompositionStrategy1_& decomposition_strategy1,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
return minkowski_sum_2(pgn2, pgn1,
|
||
|
|
decomposition_strategy1, decomposition_strategy1,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of two simple polygons by decomposing each
|
||
|
|
* polygon to convex sub-polygons and computing the union of the pairwise
|
||
|
|
* Minkowski sums of the sub-polygons.
|
||
|
|
* Note that as the input polygons may not be convex, their Minkowski sum may
|
||
|
|
* not be a simple polygon. The result is therefore represented as a polygon
|
||
|
|
* with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition_strategy A functor for decomposing polygons.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_, typename Decomposition_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_by_decomposition_2(const Polygon_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_2<Kernel_, Container_>& pgn2,
|
||
|
|
const Decomposition_& decomp)
|
||
|
|
{
|
||
|
|
typename Minkowski_sum_by_decomposition_2<Decomposition_, Decomposition_,
|
||
|
|
Container_>::Traits_2 traits;
|
||
|
|
return minkowski_sum_by_decomposition_2(pgn1, pgn2, decomp, traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of two simple polygons by decomposing each
|
||
|
|
* polygon to convex sub-polygons and computing the union of the pairwise
|
||
|
|
* Minkowski sums of the sub-polygons.
|
||
|
|
* Note that as the input polygons may not be convex, their Minkowski sum may
|
||
|
|
* not be a simple polygon. The result is therefore represented as a polygon
|
||
|
|
* with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition A functor for decomposing polygons.
|
||
|
|
* \param[in] traits The traits.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_, typename Decomposition_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_by_decomposition_2
|
||
|
|
(const Polygon_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_2<Kernel_, Container_>& pgn2,
|
||
|
|
const Decomposition_& decomp,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
typedef Kernel_ Kernel;
|
||
|
|
typedef Container_ Container;
|
||
|
|
typedef Decomposition_ Decomposition;
|
||
|
|
typedef Polygon_nop_decomposition_2<Kernel> Nop_decomposition;
|
||
|
|
|
||
|
|
if (pgn1.is_convex()) {
|
||
|
|
Nop_decomposition decomp_nop;
|
||
|
|
if (pgn2.is_convex()) {
|
||
|
|
Minkowski_sum_by_decomposition_2<Nop_decomposition, Nop_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_nop, decomp_nop, traits);
|
||
|
|
return mink_sum(pgn1, pgn2);
|
||
|
|
}
|
||
|
|
Minkowski_sum_by_decomposition_2<Nop_decomposition, Decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_nop, decomp, traits);
|
||
|
|
return mink_sum(pgn1, pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
if (pgn2.is_convex()) {
|
||
|
|
Nop_decomposition decomp_nop;
|
||
|
|
Minkowski_sum_by_decomposition_2<Decomposition, Nop_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp, decomp_nop, traits);
|
||
|
|
return mink_sum(pgn1, pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
Minkowski_sum_by_decomposition_2<Decomposition, Decomposition, Container>
|
||
|
|
mink_sum(decomp, decomp, traits);
|
||
|
|
return mink_sum(pgn1, pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of two polygon with holes by decomposing each
|
||
|
|
* polygon to convex sub-polygons and computing the union of the pairwise
|
||
|
|
* Minkowski sums of the sub-polygons.
|
||
|
|
* The result is also represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition A functor for decomposing polygons.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename NoHolesDecomposition_, typename WithHolesDecomposition_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_by_decomposition_2
|
||
|
|
(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const NoHolesDecomposition_& decomp_no_holes,
|
||
|
|
const WithHolesDecomposition_& decomp_with_holes)
|
||
|
|
{
|
||
|
|
typename Minkowski_sum_by_decomposition_2<NoHolesDecomposition_,
|
||
|
|
WithHolesDecomposition_,
|
||
|
|
Container_>::Traits_2 traits;
|
||
|
|
return minkowski_sum_by_decomposition_2(pgn1, pgn2,
|
||
|
|
decomp_no_holes, decomp_with_holes,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of two polygon with holes by decomposing each
|
||
|
|
* polygon to convex sub-polygons and computing the union of the pairwise
|
||
|
|
* Minkowski sums of the sub-polygons.
|
||
|
|
* The result is also represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition A functor for decomposing polygons.
|
||
|
|
* \param[in] traits The traits.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename NoHolesDecomposition_, typename WithHolesDecomposition_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_by_decomposition_2
|
||
|
|
(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const NoHolesDecomposition_& decomp_no_holes,
|
||
|
|
const WithHolesDecomposition_& decomp_with_holes,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
typedef Kernel_ Kernel;
|
||
|
|
typedef Container_ Container;
|
||
|
|
typedef NoHolesDecomposition_ No_holes_decomposition;
|
||
|
|
typedef WithHolesDecomposition_ With_holes_decomposition;
|
||
|
|
typedef Polygon_nop_decomposition_2<Kernel> Nop_decomposition;
|
||
|
|
|
||
|
|
Hole_filter_2<Kernel, Container> hole_filter;
|
||
|
|
Polygon_with_holes_2<Kernel, Container> filtered_pgn1;
|
||
|
|
Polygon_with_holes_2<Kernel, Container> filtered_pgn2;
|
||
|
|
hole_filter(pgn1, pgn2, filtered_pgn1);
|
||
|
|
hole_filter(pgn2, pgn1, filtered_pgn2);
|
||
|
|
|
||
|
|
if (0 == filtered_pgn1.number_of_holes()) {
|
||
|
|
const Polygon_2<Kernel, Container>& pnh1 = filtered_pgn1.outer_boundary();
|
||
|
|
if (pnh1.is_convex()) {
|
||
|
|
// pnh1 is convex
|
||
|
|
Nop_decomposition decomp_nop;
|
||
|
|
if (0 == filtered_pgn2.number_of_holes()) {
|
||
|
|
const Polygon_2<Kernel, Container>& pnh2 =
|
||
|
|
filtered_pgn2.outer_boundary();
|
||
|
|
if (pnh2.is_convex()) {
|
||
|
|
// pnh2 is convex
|
||
|
|
Minkowski_sum_by_decomposition_2<Nop_decomposition, Nop_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_nop, decomp_nop, traits);
|
||
|
|
return mink_sum(pnh1, pnh2);
|
||
|
|
}
|
||
|
|
// pnh2 is concave
|
||
|
|
Minkowski_sum_by_decomposition_2<Nop_decomposition,
|
||
|
|
No_holes_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_nop, decomp_no_holes, traits);
|
||
|
|
return mink_sum(pnh1, pnh2);
|
||
|
|
}
|
||
|
|
// pnh2 has holes
|
||
|
|
Minkowski_sum_by_decomposition_2<Nop_decomposition,
|
||
|
|
With_holes_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_nop, decomp_with_holes, traits);
|
||
|
|
return mink_sum(pnh1, filtered_pgn2);
|
||
|
|
}
|
||
|
|
// pnh1 is concave
|
||
|
|
if (0 == filtered_pgn2.number_of_holes()) {
|
||
|
|
const Polygon_2<Kernel, Container>& pnh2 =
|
||
|
|
filtered_pgn2.outer_boundary();
|
||
|
|
if (pnh2.is_convex()) {
|
||
|
|
// pnh2 is convex
|
||
|
|
Nop_decomposition decomp_nop;
|
||
|
|
Minkowski_sum_by_decomposition_2<No_holes_decomposition,
|
||
|
|
Nop_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_no_holes, decomp_nop, traits);
|
||
|
|
return mink_sum(pnh1, pnh2);
|
||
|
|
}
|
||
|
|
// pnh2 is concave
|
||
|
|
Minkowski_sum_by_decomposition_2<No_holes_decomposition,
|
||
|
|
No_holes_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_no_holes, decomp_no_holes, traits);
|
||
|
|
return mink_sum(pnh1, pnh2);
|
||
|
|
}
|
||
|
|
// pnh2 has holes
|
||
|
|
Minkowski_sum_by_decomposition_2<No_holes_decomposition,
|
||
|
|
With_holes_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_no_holes, decomp_with_holes, traits);
|
||
|
|
return mink_sum(pnh1, filtered_pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
// filtered_pgn1 has holes
|
||
|
|
if (0 == filtered_pgn2.number_of_holes()) {
|
||
|
|
const Polygon_2<Kernel, Container>& pnh2 =
|
||
|
|
filtered_pgn2.outer_boundary();
|
||
|
|
if (pnh2.is_convex()) {
|
||
|
|
// pnh2 is convex
|
||
|
|
Nop_decomposition decomp_nop;
|
||
|
|
Minkowski_sum_by_decomposition_2<Nop_decomposition,
|
||
|
|
With_holes_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_nop, decomp_with_holes, traits);
|
||
|
|
return mink_sum(pnh2, filtered_pgn1);
|
||
|
|
}
|
||
|
|
// pnh2 is concave
|
||
|
|
Minkowski_sum_by_decomposition_2<No_holes_decomposition,
|
||
|
|
With_holes_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_no_holes, decomp_with_holes, traits);
|
||
|
|
return mink_sum(pnh2, filtered_pgn1);
|
||
|
|
}
|
||
|
|
// pnh2 has holes
|
||
|
|
Minkowski_sum_by_decomposition_2<With_holes_decomposition,
|
||
|
|
With_holes_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_with_holes, decomp_with_holes, traits);
|
||
|
|
return mink_sum(filtered_pgn1, filtered_pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The first polygon.
|
||
|
|
* \param[in] pgn2 The second polygon.
|
||
|
|
* \param[in] decomposition A functor for decomposing polygons.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename NoHolesDecomposition_, typename WithHolesDecomposition_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_by_decomposition_2
|
||
|
|
(const Polygon_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const NoHolesDecomposition_& decomp_no_holes,
|
||
|
|
const WithHolesDecomposition_& decomp_with_holes)
|
||
|
|
{
|
||
|
|
typename Minkowski_sum_by_decomposition_2<NoHolesDecomposition_,
|
||
|
|
WithHolesDecomposition_,
|
||
|
|
Container_>::Traits_2 traits;
|
||
|
|
return minkowski_sum_by_decomposition_2(pgn1, pgn2,
|
||
|
|
decomp_no_holes, decomp_with_holes,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The simple polygon.
|
||
|
|
* \param[in] pgn2 The polygon with holes.
|
||
|
|
* \param[in] decomposition A functor for decomposing polygons.
|
||
|
|
* \param[in] traits The traits.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename NoHolesDecomposition_, typename WithHolesDecomposition_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_by_decomposition_2
|
||
|
|
(const Polygon_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_with_holes_2<Kernel_, Container_>& pgn2,
|
||
|
|
const NoHolesDecomposition_& decomp_no_holes,
|
||
|
|
const WithHolesDecomposition_& decomp_with_holes,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
typedef Kernel_ Kernel;
|
||
|
|
typedef Container_ Container;
|
||
|
|
typedef NoHolesDecomposition_ No_holes_decomposition;
|
||
|
|
typedef WithHolesDecomposition_ With_holes_decomposition;
|
||
|
|
typedef Polygon_nop_decomposition_2<Kernel> Nop_decomposition;
|
||
|
|
|
||
|
|
Hole_filter_2<Kernel, Container> hole_filter;
|
||
|
|
Polygon_with_holes_2<Kernel,Container> filtered_pgn2;
|
||
|
|
hole_filter(pgn2, pgn1, filtered_pgn2);
|
||
|
|
|
||
|
|
if (pgn1.is_convex()) {
|
||
|
|
Nop_decomposition decomp_nop;
|
||
|
|
if (0 == filtered_pgn2.number_of_holes()) {
|
||
|
|
const Polygon_2<Kernel, Container>& pnh2 = filtered_pgn2.outer_boundary();
|
||
|
|
if (pnh2.is_convex()) {
|
||
|
|
Minkowski_sum_by_decomposition_2<Nop_decomposition, Nop_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_nop, decomp_nop, traits);
|
||
|
|
return mink_sum(pgn1, pnh2);
|
||
|
|
}
|
||
|
|
// pnh2 is concave
|
||
|
|
Minkowski_sum_by_decomposition_2<Nop_decomposition,
|
||
|
|
No_holes_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_nop, decomp_no_holes, traits);
|
||
|
|
return mink_sum(pgn1, pnh2);
|
||
|
|
}
|
||
|
|
// pnh2 has holes
|
||
|
|
Minkowski_sum_by_decomposition_2<Nop_decomposition,
|
||
|
|
With_holes_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_nop, decomp_with_holes, traits);
|
||
|
|
return mink_sum(pgn1, filtered_pgn2);
|
||
|
|
}
|
||
|
|
// pgn1 is concave
|
||
|
|
if (0 == filtered_pgn2.number_of_holes()) {
|
||
|
|
const Polygon_2<Kernel, Container>& pnh2 = filtered_pgn2.outer_boundary();
|
||
|
|
if (pnh2.is_convex()) {
|
||
|
|
// pnh2 is convex
|
||
|
|
Nop_decomposition decomp_nop;
|
||
|
|
Minkowski_sum_by_decomposition_2<No_holes_decomposition,
|
||
|
|
Nop_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_no_holes, decomp_nop, traits);
|
||
|
|
return mink_sum(pgn1, pnh2);
|
||
|
|
}
|
||
|
|
// pnh2 is concave
|
||
|
|
Minkowski_sum_by_decomposition_2<No_holes_decomposition,
|
||
|
|
No_holes_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_no_holes, decomp_no_holes, traits);
|
||
|
|
return mink_sum(pgn1, pnh2);
|
||
|
|
}
|
||
|
|
// pnh2 has holes
|
||
|
|
Minkowski_sum_by_decomposition_2<No_holes_decomposition,
|
||
|
|
With_holes_decomposition,
|
||
|
|
Container>
|
||
|
|
mink_sum(decomp_no_holes, decomp_with_holes, traits);
|
||
|
|
return mink_sum(pgn1, filtered_pgn2);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The second polygon.
|
||
|
|
* \param[in] pgn2 The first polygon.
|
||
|
|
* \param[in] decomposition A functor for decomposing polygons.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename NoHolesDecomposition_, typename WithHolesDecomposition_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_by_decomposition_2
|
||
|
|
(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_2<Kernel_, Container_>& pgn2,
|
||
|
|
const NoHolesDecomposition_& decomp_no_holes,
|
||
|
|
const WithHolesDecomposition_& decomp_with_holes)
|
||
|
|
{
|
||
|
|
typename Minkowski_sum_by_decomposition_2<NoHolesDecomposition_,
|
||
|
|
WithHolesDecomposition_,
|
||
|
|
Container_>::Traits_2 traits;
|
||
|
|
return minkowski_sum_by_decomposition_2(pgn1, pgn2,
|
||
|
|
decomp_no_holes, decomp_with_holes,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Compute the Minkowski sum of a simple polygon and a polygon with holes
|
||
|
|
* by decomposing each polygon to convex sub-polygons and computing the union
|
||
|
|
* of the pairwise Minkowski sums of the sub-polygons. The result is also
|
||
|
|
* represented as a polygon with holes.
|
||
|
|
* \param[in] pgn1 The polygon with holes.
|
||
|
|
* \param[in] pgn2 The simple polygon.
|
||
|
|
* \param[in] decomposition A functor for decomposing polygons.
|
||
|
|
* \param[in] traits The traits.
|
||
|
|
* \return The resulting polygon with holes, representing the sum.
|
||
|
|
*/
|
||
|
|
template <typename Kernel_, typename Container_,
|
||
|
|
typename NoHoleDecomposition_, typename WithHolesDecomposition_>
|
||
|
|
Polygon_with_holes_2<Kernel_, Container_>
|
||
|
|
minkowski_sum_by_decomposition_2
|
||
|
|
(const Polygon_with_holes_2<Kernel_, Container_>& pgn1,
|
||
|
|
const Polygon_2<Kernel_, Container_>& pgn2,
|
||
|
|
const NoHoleDecomposition_& decomp_no_holes,
|
||
|
|
const WithHolesDecomposition_& decomp_with_holes,
|
||
|
|
const Gps_segment_traits_2<Kernel_, Container_>& traits)
|
||
|
|
{
|
||
|
|
return minkowski_sum_by_decomposition_2(pgn2, pgn1,
|
||
|
|
decomp_no_holes, decomp_with_holes,
|
||
|
|
traits);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*!@}*/
|
||
|
|
|
||
|
|
} //namespace CGAL
|
||
|
|
|
||
|
|
#endif
|