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// Copyright (c) 2006 Tel-Aviv University (Israel). // All rights reserved. // // This file is part of CGAL (www.cgal.org). // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Minkowski_sum_2/include/CGAL/Minkowski_sum_2/Offset_conv_2.h $ // $Id: include/CGAL/Minkowski_sum_2/Offset_conv_2.h b26b07a1242 $ // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial // // Author(s) : Ron Wein #ifndef CGAL_OFFSET_CONV_H #define CGAL_OFFSET_CONV_H #include #include #include namespace CGAL { /*! \class * A class for computing the offset of a given polygon by a given radius * by constructing a single convolution cycle and computing its interior. */ template class Offset_by_convolution_2 : private Base_ { private: typedef Base_ Base; public: typedef typename Base::Basic_kernel Kernel; typedef typename Base::Basic_NT NT; typedef typename Base::Polygon_2 Polygon_2; typedef typename Base::Polygon_with_holes_2 Polygon_with_holes_2; typedef typename Base::Offset_polygon_2 Offset_polygon_2; private: typedef typename Base::Labeled_traits_2 Labeled_traits_2; typedef typename Base::Labeled_curve_2 Labeled_curve_2; typedef std::list Curves_list; typedef Union_of_curve_cycles_2 Union_2; using Base::_offset_polygon; public: /*! Constructor. */ Offset_by_convolution_2 (const Base_& base) : Base (base) {} /*! * Compute the offset of a simple polygon by a given radius. * Note that as the input polygon may not be convex, its offset may not be * simply connected. The result is therefore represented as the outer * boundary of the Minkowski sum (which is always a simple offset polygon) * and a container of offset polygons, representing the holes in this "outer" * polygon. * \param pgn The polygon. * \param r The offset radius. * \param off_bound Output: The outer boundary of the offset polygon. * \param off_holes Output: An output iterator for the holes in the offset. * \pre The polygon is simple. * \return A past-the-end iterator for the holes container. */ template OutputIterator operator() (const Polygon_2& pgn, const NT& r, Offset_polygon_2& off_bound, OutputIterator off_holes) const { CGAL_precondition (pgn.is_simple()); // Compute the curves that form the single convolution cycle for the // given polygon. Curves_list cycle; _offset_polygon (pgn, CGAL::COUNTERCLOCKWISE, r, 1, // The ID of the single cycle. std::back_inserter (cycle)); // Compute the union of the cycles that represent the offset polygon. Union_2 unite; off_holes = unite (cycle.begin(), cycle.end(), off_bound, off_holes); return (off_holes); } /*! * Compute the offset of a polygon with holes by a given radius. * The result is represented as the outer boundary of the Minkowski sum * (which is always a simple offset polygon) and a container of offset * polygons, representing the holes in this "outer" polygon. * \param pwh The polygon with holes. * \param r The offset radius. * \param off_bound Output: The outer boundary of the offset polygon. * \param off_holes Output: An output iterator for the holes in the offset. * \pre The polygon is bounded (has an outer boundary). * \return A past-the-end iterator for the holes container. */ template OutputIterator operator() (const Polygon_with_holes_2& pwh, const NT& r, Offset_polygon_2& off_bound, OutputIterator off_holes) const { CGAL_precondition (! pwh.is_unbounded()); // Compute the curves that form the convolution cycle for the polygon // that forms the outer boundary. Curves_list cycle; unsigned int cycle_id = 1; _offset_polygon (pwh.outer_boundary(), CGAL::COUNTERCLOCKWISE, r, cycle_id, std::back_inserter (cycle)); // Go over the polygon holes and compute the convolution cycle for each // hole. Note that in this case we traverse the holes in clockwise // orientation. typename Polygon_with_holes_2::Hole_const_iterator hoit; for (hoit = pwh.holes_begin(); hoit != pwh.holes_end(); ++hoit) { cycle_id++; _offset_polygon (*hoit, CGAL::CLOCKWISE, r, cycle_id, std::back_inserter (cycle)); } // Compute the union of the cycles that represent the offset polygon. Union_2 unite; off_holes = unite (cycle.begin(), cycle.end(), off_bound, off_holes); return (off_holes); } /*! * Compute the inset of a simple polygon by a given radius. * Note that as the input polygon may not be convex, its offset may not be * simply connected. The result is therefore represented as a sequence of * polygons (which may also be empty). * \param pgn The polygon. * \param r The inset radius. * \param oi Output: An output iterator for the inset polygons. * \pre The polygon is simple. * \return A past-the-end iterator for the polygons container. */ template OutputIterator inset (const Polygon_2& pgn, const NT& r, OutputIterator oi) const { CGAL_precondition (pgn.is_simple()); // Compute the curves that form the single convolution cycle for the // given polygon. Note that we traverse the polygon in clockwise direction, // as we treat it as a hole in the unbounded plane. Curves_list cycle; _offset_polygon (pgn, CGAL::CLOCKWISE, r, 1, // The ID of the single cycle. std::back_inserter (cycle)); // Compute the union of the cycles that represent the offset polygon. Union_2 unite; oi = unite.inverse (cycle.begin(), cycle.end(), oi); return (oi); } }; } //namespace CGAL #endif