691 lines
19 KiB
C
691 lines
19 KiB
C
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// Copyright (c) 2013 Technical University Braunschweig (Germany).
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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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// You can redistribute it and/or modify it under the terms of the GNU
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// General Public License as published by the Free Software Foundation,
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// either version 3 of the License, or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: GPL-3.0+
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//
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//
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// Author(s): Francisc Bungiu <fbungiu@gmail.com>
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// Michael Hemmer <michael.hemmer@cgal.org>
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// Ning Xu <longyin0904@gmail.com>
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#ifndef CGAL_SIMPLE_POLYGON_VISIBILITY_2_H
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#define CGAL_SIMPLE_POLYGON_VISIBILITY_2_H
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#include <CGAL/license/Visibility_2.h>
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#include <CGAL/tags.h>
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#include <CGAL/enum.h>
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#include <CGAL/Visibility_2/visibility_utils.h>
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#include <CGAL/Arrangement_2.h>
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#include <CGAL/Kernel/global_functions_2.h>
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#include <CGAL/Arr_walk_along_line_point_location.h>
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#include <CGAL/assertions.h>
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#include <stack>
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// TODO:
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// * fix handle needles = O(nlogn)
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namespace CGAL {
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template<class Arrangement_2_, class RegularizationCategory = CGAL::Tag_true>
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class Simple_polygon_visibility_2 {
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public:
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typedef Arrangement_2_ Arrangement_2;
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typedef typename Arrangement_2::Traits_2 Traits_2;
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typedef typename Arrangement_2::Geometry_traits_2 Geometry_traits_2;
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typedef typename Geometry_traits_2::Kernel K;
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typedef typename K::Intersect_2 Intersect_2;
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typedef typename Arrangement_2::Vertex_const_handle Vertex_const_handle;
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typedef typename Arrangement_2::Halfedge_const_handle
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Halfedge_const_handle;
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typedef typename Arrangement_2::Halfedge_handle Halfedge_handle;
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typedef typename Arrangement_2::Ccb_halfedge_const_circulator
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Ccb_halfedge_const_circulator;
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typedef typename Arrangement_2::Face_const_handle Face_const_handle;
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typedef typename Arrangement_2::Face_handle Face_handle;
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typedef typename Arrangement_2::Halfedge_around_vertex_const_circulator
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Halfedge_around_vertex_const_circulator;
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typedef typename Geometry_traits_2::Point_2 Point_2;
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typedef typename Geometry_traits_2::Ray_2 Ray_2;
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typedef typename Geometry_traits_2::Segment_2 Segment_2;
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typedef typename Geometry_traits_2::Line_2 Line_2;
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typedef typename Geometry_traits_2::Object_2 Object_2;
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typedef RegularizationCategory Regularization_category;
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typedef CGAL::Tag_false Supports_general_polygon_category;
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typedef CGAL::Tag_true Supports_simple_polygon_category;
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Simple_polygon_visibility_2() : p_arr(NULL), traits(NULL) {}
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/*! Constructor given an arrangement and the Regularization tag. */
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Simple_polygon_visibility_2(const Arrangement_2& arr):
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p_arr(&arr) {
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traits = p_arr->geometry_traits();
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point_location.attach(arr);
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query_pt_is_vertex = false;
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query_pt_is_on_halfedge = false;
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inserted_artificial_starting_vertex = false;
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}
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std::string name() const { return std::string("S_visibility_2"); }
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/*! Method to check if the visibility object is attached or not to
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an arrangement*/
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bool is_attached() const {
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return (p_arr != NULL);
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}
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/*! Attaches the visibility object to the 'arr' arrangement */
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void attach(const Arrangement_2& arr) {
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if(p_arr != &arr){
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detach();
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p_arr = &arr;
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traits = p_arr->geometry_traits();
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point_location.attach(arr);
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}
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}
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/*! Detaches the visibility object from the arrangement it is
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attached to*/
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void detach() {
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point_location.detach();
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p_arr = NULL;
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traits = NULL;
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vertices.clear();
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query_pt_is_vertex = false;
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query_pt_is_on_halfedge = false;
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inserted_artificial_starting_vertex = false;
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}
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/*! Getter method for the input arrangement*/
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const Arrangement_2& arrangement_2() const {
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return *p_arr;
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}
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/*! Computes the visibility object from the query point 'q' in the face
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'face' and constructs the output in 'out_arr'*/
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template <typename VARR>
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typename VARR::Face_handle
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compute_visibility(const Point_2& q,
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const Face_const_handle face,
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VARR& out_arr) const
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{
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CGAL_precondition(!face->is_unbounded());
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out_arr.clear();
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query_pt_is_vertex = false;
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query_pt_is_on_halfedge = false;
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inserted_artificial_starting_vertex = false;
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// Now retrieve the circulator to first visible vertex from triangulation
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Ccb_halfedge_const_circulator circ = find_visible_start(face, q);
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Ccb_halfedge_const_circulator curr = circ;
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do {
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vertices.push_back(curr->source()->point());
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} while(++curr != circ);
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vertices.push_back(vertices[0]);
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visibility_region_impl(q);
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return output(q, out_arr);
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}
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/*! Computes the visibility region of the query point 'q' located on the
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halfedge 'he' and constructs the output in 'out_arr'*/
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template <typename VARR>
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typename VARR::Face_handle
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compute_visibility(
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const Point_2& q,
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const Halfedge_const_handle he,
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VARR& out_arr ) const
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{
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out_arr.clear();
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query_pt_is_vertex = false;
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query_pt_is_on_halfedge = false;
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bool query_on_target = false;
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if (q != he->source()->point()) {
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if (q != he->target()->point()) {
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vertices.push_back(he->target()->point());
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query_pt_is_on_halfedge = true;
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}
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else {
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query_pt_is_vertex = true;
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query_on_target = true;
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}
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} else {
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vertices.push_back( he->target()->point() );
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query_pt_is_vertex = true;
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}
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Ccb_halfedge_const_circulator circ = he;
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++circ;
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Ccb_halfedge_const_circulator curr = circ;
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do {
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const Point_2& curr_vertex = curr->target()->point();
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vertices.push_back(curr_vertex);
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} while (++curr != circ);
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if ( query_on_target ) {
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vertices.push_back( vertices[0] );
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}
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visibility_region_impl(q);
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return output(q, out_arr);
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}
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private:
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typedef Arr_walk_along_line_point_location<Arrangement_2> Arr_point_location;
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typedef typename Arr_point_location::result_type Location_result;
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typedef std::vector<Point_2> Vertex_container;
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typedef typename Vertex_container::size_type Size_type;
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const Arrangement_2 *p_arr;
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const Geometry_traits_2 *traits;
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mutable Arr_point_location point_location;
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/*! Stack of visibile points; manipulated when going through the sequence
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of input vertices; contains the vertices of the visibility region after
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the run of the algorithm*/
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mutable std::stack<Point_2> stack;
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/*! Sequence of input vertices*/
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mutable Vertex_container vertices;
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/*! State of visibility region algorithm*/
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mutable enum {LEFT, RIGHT, SCANA, SCANB, SCANC, SCAND, FINISH} upcase;
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mutable bool query_pt_is_vertex;
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mutable bool query_pt_is_on_halfedge;
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mutable bool inserted_artificial_starting_vertex;
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template <typename VARR>
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typename VARR::Face_handle
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output(const Point_2& q, VARR& out_arr) const {
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if(inserted_artificial_starting_vertex)
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stack.pop();
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std::vector<Point_2> points;
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while(!stack.empty()) {
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const Point_2& top = stack.top();
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if (top != q || query_pt_is_vertex) {
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points.push_back(top);
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}
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stack.pop();
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}
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if(inserted_artificial_starting_vertex) {
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points.back() = points[0];
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inserted_artificial_starting_vertex = false;
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}
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// Quick fix for now. Can be done faster
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bool is_degenerate = false;
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for(typename std::vector<Point_2>::size_type i = 0; i < points.size()-2;i++){
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if(CGAL::orientation(points[i],points[i+1],points[i+2]) == CGAL::COLLINEAR){
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is_degenerate = true;
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break;
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}
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}
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if(is_degenerate){
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//std::cout << is_degenerate << std::endl;
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std::vector<Segment_2> segments;
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for(typename std::vector<Point_2>::size_type i = 0;i < points.size() - 1; ++i)
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{
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segments.push_back(Segment_2(points[i], points[i+1]));
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}
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CGAL::insert(out_arr, segments.begin(), segments.end());
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}else{
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points.pop_back();
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//std::cout << " ordanary " << std::endl;
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typename VARR::Vertex_handle v_last, v_first;
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v_last = v_first =
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out_arr.insert_in_face_interior(points[0],out_arr.unbounded_face());
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for(unsigned int i = 0; i < points.size()-1; i++){
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if(points[i] < points[(i+1)]){
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v_last = out_arr.insert_from_left_vertex (
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Segment_2(points[i], points[i+1]), v_last
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)->target();
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} else {
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v_last = out_arr.insert_from_right_vertex(
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Segment_2(points[i], points[i+1]), v_last
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)->target();
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}
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}
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out_arr.insert_at_vertices(
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Segment_2(points.front(), points.back()),
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v_last, v_first
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);
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}
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CGAL_postcondition(out_arr.number_of_isolated_vertices() == 0);
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CGAL_postcondition(stack.empty());
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Visibility_2::conditional_regularize(out_arr, Regularization_category());
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vertices.clear();
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if (out_arr.faces_begin()->is_unbounded()) {
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return ++out_arr.faces_begin();
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}
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else {
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return out_arr.faces_begin();
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}
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}
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/*! Finds a visible vertex from the query point 'q' in 'face'
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to start the algorithm from*/
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Ccb_halfedge_const_circulator find_visible_start(Face_const_handle face,
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const Point_2 &q) const
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{
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Location_result result = point_location.ray_shoot_up(q);
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if(const Halfedge_const_handle* e =
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boost::get<Halfedge_const_handle>(&(result)))
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{
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CGAL_assertion((*e)->face() == face);
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Point_2 p(q.x(),
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traits->compute_y_at_x_2_object()(
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Line_2((*e)->source()->point(),
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(*e)->target()->point()) ,
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q.x()));
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vertices.push_back(p);
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inserted_artificial_starting_vertex = true;
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return (*e)->next()->ccb();
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}
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else if (const Vertex_const_handle* v =
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boost::get<Vertex_const_handle>(&(result)))
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{
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Halfedge_around_vertex_const_circulator cir =
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(*v)->incident_halfedges();
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while(face != cir->face()) {
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++cir;
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}
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return cir->next()->ccb();
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}
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else
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{
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CGAL_assertion_msg(false, "Should not be reachable.");
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return Ccb_halfedge_const_circulator();
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}
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}
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/*! Main method of the algorithm - initializes the stack and variables
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and calles the corresponding methods acc. to the algorithm's state;
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'q' - query point;
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'i' - current vertex' index
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'w' - endpoint of ray shot from query point */
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void visibility_region_impl(const Point_2& q) const {
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Size_type i = 0;
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Point_2 w;
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Orientation o = traits->orientation_2_object()(q, vertices[0], vertices[1]);
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if ( o != RIGHT_TURN ) {
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upcase = LEFT;
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i = 1;
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w = vertices[1];
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stack.push(vertices[0]);
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stack.push(vertices[1]);
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}
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else {
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upcase = SCANA;
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i = 1;
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w = vertices[1];
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stack.push(vertices[0]);
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}
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Ray_2 ray_origin( q, vertices[0] );
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do {
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switch(upcase) {
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case LEFT:
|
||
|
|
left(i, w, q);
|
||
|
|
break;
|
||
|
|
case RIGHT:
|
||
|
|
right(i, w, q);
|
||
|
|
break;
|
||
|
|
case SCANA:
|
||
|
|
scana(i, w, q);
|
||
|
|
break;
|
||
|
|
case SCANB:
|
||
|
|
scanb(i, w);
|
||
|
|
break;
|
||
|
|
case SCANC:
|
||
|
|
scanc(i, w);
|
||
|
|
break;
|
||
|
|
case SCAND:
|
||
|
|
scand(i, w);
|
||
|
|
break;
|
||
|
|
case FINISH:
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
if ( upcase == LEFT ) {
|
||
|
|
Point_2 s_t = stack.top();
|
||
|
|
stack.pop();
|
||
|
|
if (traits->orientation_2_object()(q, vertices[0], stack.top() )
|
||
|
|
== RIGHT_TURN
|
||
|
|
&&
|
||
|
|
traits->orientation_2_object()(q, vertices[0], s_t)
|
||
|
|
== LEFT_TURN )
|
||
|
|
{
|
||
|
|
Segment_2 seg( stack.top(), s_t );
|
||
|
|
if (Object_2 result = Intersect_2()(seg, ray_origin) )
|
||
|
|
{
|
||
|
|
const Point_2 * ipoint = object_cast<Point_2>(&result);
|
||
|
|
CGAL_assertion( ipoint != NULL );
|
||
|
|
s_t = *ipoint;
|
||
|
|
upcase = SCANB;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
stack.push( s_t );
|
||
|
|
}
|
||
|
|
} while(upcase != FINISH);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Method that handles the left turns in the vertex algorithm */
|
||
|
|
void left(Size_type& i, Point_2& w, const Point_2& q) const {
|
||
|
|
if (i >= vertices.size() - 1) {
|
||
|
|
upcase = FINISH;
|
||
|
|
}
|
||
|
|
else {
|
||
|
|
Point_2 s_t = stack.top();
|
||
|
|
stack.pop();
|
||
|
|
Point_2 s_t_prev = stack.top();
|
||
|
|
stack.push( s_t );
|
||
|
|
Orientation orient1 = traits->orientation_2_object()(
|
||
|
|
q,
|
||
|
|
vertices[i],
|
||
|
|
vertices[i+1] );
|
||
|
|
|
||
|
|
if ( orient1 != RIGHT_TURN ) {
|
||
|
|
// Case L2
|
||
|
|
upcase = LEFT;
|
||
|
|
stack.push( vertices[i+1] );
|
||
|
|
w = vertices[i+1];
|
||
|
|
i++;
|
||
|
|
} else {
|
||
|
|
Orientation orient2 = traits->orientation_2_object()(
|
||
|
|
s_t_prev,
|
||
|
|
vertices[i],
|
||
|
|
vertices[i+1] );
|
||
|
|
|
||
|
|
if ( orient2 == RIGHT_TURN ) {
|
||
|
|
// Case L3
|
||
|
|
upcase = SCANA;
|
||
|
|
w = vertices[i+1];
|
||
|
|
i++;
|
||
|
|
} else {
|
||
|
|
// Case L4
|
||
|
|
upcase = RIGHT;
|
||
|
|
w = vertices[i];
|
||
|
|
i++;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Scans the stack such that all vertices that were pushed before to the
|
||
|
|
stack and are now not visible anymore. */
|
||
|
|
void right(Size_type& i, Point_2& w, const Point_2& q) const {
|
||
|
|
Point_2 s_j;
|
||
|
|
Point_2 s_j_prev;
|
||
|
|
Point_2 u;
|
||
|
|
int mode = 0;
|
||
|
|
Orientation orient1, orient2;
|
||
|
|
|
||
|
|
s_j_prev = stack.top();
|
||
|
|
orient2 = traits->orientation_2_object()( q, s_j_prev, vertices[i] );
|
||
|
|
|
||
|
|
while ( stack.size() > 1 ) {
|
||
|
|
s_j = s_j_prev;
|
||
|
|
orient1 = orient2;
|
||
|
|
stack.pop();
|
||
|
|
s_j_prev = stack.top();
|
||
|
|
|
||
|
|
orient2 = traits->orientation_2_object()( q, s_j_prev, vertices[i]);
|
||
|
|
if ( orient1 != LEFT_TURN && orient2 != RIGHT_TURN ) {
|
||
|
|
mode = 1;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
|
||
|
|
Segment_2 seg2( vertices[i-1], vertices[i] );
|
||
|
|
Segment_2 seg( s_j_prev, s_j );
|
||
|
|
if ( vertices[i-1] != s_j )
|
||
|
|
{
|
||
|
|
Object_2 result = Intersect_2()( seg, seg2 );
|
||
|
|
if(result) {
|
||
|
|
const Point_2 * ipoint = object_cast<Point_2>(&result);
|
||
|
|
CGAL_assertion( ipoint != NULL );
|
||
|
|
u = *ipoint;
|
||
|
|
mode = 2;
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
CGAL_assertion( mode != 0 );
|
||
|
|
if ( mode == 1 ) {
|
||
|
|
orient1 = traits->orientation_2_object()(q, vertices[i], vertices[i+1] );
|
||
|
|
|
||
|
|
orient2 = traits->orientation_2_object()(vertices[i-1],
|
||
|
|
vertices[i],
|
||
|
|
vertices[i+1] );
|
||
|
|
|
||
|
|
if ( orient1 == RIGHT_TURN ) {
|
||
|
|
// Case R1
|
||
|
|
// Since the next action is RIGHT, we do not compute the intersection
|
||
|
|
// of (s_j,s_j_prev) and the ray (query_pt, vertices[i]),
|
||
|
|
// thus, (s_j,s_j_prev) is not shortcutted, but it is harmless
|
||
|
|
upcase = RIGHT;
|
||
|
|
stack.push( s_j );
|
||
|
|
w = vertices[i];
|
||
|
|
i++;
|
||
|
|
} else if ( orient2 == RIGHT_TURN ) {
|
||
|
|
// Case R2
|
||
|
|
Ray_2 ray( q, vertices[i] );
|
||
|
|
Segment_2 seg( s_j_prev, s_j );
|
||
|
|
|
||
|
|
Object_2 result = Intersect_2()( seg, ray );
|
||
|
|
const Point_2 * ipoint = object_cast<Point_2>(&result);
|
||
|
|
|
||
|
|
CGAL_assertion( ipoint != NULL );
|
||
|
|
|
||
|
|
u = *ipoint;
|
||
|
|
if ( stack.top() != u ) {
|
||
|
|
stack.push( u );
|
||
|
|
}
|
||
|
|
upcase = LEFT;
|
||
|
|
stack.push( vertices[i] );
|
||
|
|
stack.push( vertices[i+1] );
|
||
|
|
w = vertices[i+1];
|
||
|
|
i++;
|
||
|
|
} else {
|
||
|
|
// Case R3
|
||
|
|
Ray_2 ray( q, vertices[i] );
|
||
|
|
Segment_2 seg( s_j_prev, s_j );
|
||
|
|
|
||
|
|
Object_2 result = Intersect_2()( seg, ray );
|
||
|
|
const Point_2 * ipoint = object_cast<Point_2>(&result);
|
||
|
|
|
||
|
|
CGAL_assertion( ipoint != NULL );
|
||
|
|
|
||
|
|
u = *ipoint;
|
||
|
|
if ( stack.top() != u ) {
|
||
|
|
stack.push( u );
|
||
|
|
}
|
||
|
|
upcase = SCANC;
|
||
|
|
w = vertices[i];
|
||
|
|
i++;
|
||
|
|
}
|
||
|
|
} else if ( mode == 2 ) {
|
||
|
|
// Case R4
|
||
|
|
upcase = SCAND;
|
||
|
|
w = u;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Scans the vertices starting from index 'i' for the first visible vertex
|
||
|
|
out of the back hidden window */
|
||
|
|
void scana(Size_type& i, Point_2& w, const Point_2& q) const {
|
||
|
|
// Scan v_i, v_i+1, ..., v_n for the first edge to intersect (z, s_t)
|
||
|
|
Point_2 u;
|
||
|
|
Size_type k = scan_edges( i, q, stack.top(), u, true );
|
||
|
|
|
||
|
|
Orientation orient1 =
|
||
|
|
traits->orientation_2_object()(q, vertices[k], vertices[k+1] );
|
||
|
|
|
||
|
|
if ( orient1 == RIGHT_TURN ) {
|
||
|
|
bool fwd = traits->
|
||
|
|
collinear_are_ordered_along_line_2_object()(q, stack.top(), u );
|
||
|
|
|
||
|
|
if ( !fwd ) {
|
||
|
|
// Case A1
|
||
|
|
upcase = RIGHT;
|
||
|
|
i = k+1;
|
||
|
|
w = u;
|
||
|
|
} else {
|
||
|
|
// Case A2
|
||
|
|
upcase = SCAND;
|
||
|
|
i = k+1;
|
||
|
|
w = u;
|
||
|
|
}
|
||
|
|
} else {
|
||
|
|
// Case A3
|
||
|
|
upcase = LEFT;
|
||
|
|
i = k+1;
|
||
|
|
stack.push( u );
|
||
|
|
if ( u != vertices[k+1] ) {
|
||
|
|
stack.push( vertices[k+1] );
|
||
|
|
}
|
||
|
|
w = vertices[k+1];
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Find the first edge interecting the segment (v_0, s_t) */
|
||
|
|
void scanb(Size_type& i, Point_2& w) const {
|
||
|
|
if ( i == vertices.size() - 1 ) {
|
||
|
|
upcase = FINISH;
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
Point_2 u;
|
||
|
|
Size_type k = scan_edges( i, stack.top(), vertices[0], u, false );
|
||
|
|
if ( (k+1 == vertices.size()-1) && (vertices[0] == u) ) {
|
||
|
|
// Case B1
|
||
|
|
upcase = FINISH;
|
||
|
|
stack.push( vertices[0] );
|
||
|
|
} else {
|
||
|
|
// Case B2
|
||
|
|
upcase = RIGHT;
|
||
|
|
i = k+1;
|
||
|
|
w = u;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Finds the exit from a general front hidden window by finding the first
|
||
|
|
vertex to the right of the ray defined by the query_point and w*/
|
||
|
|
void scanc(Size_type& i, Point_2& w) const {
|
||
|
|
Point_2 u;
|
||
|
|
Size_type k = scan_edges( i, stack.top(), w, u, false );
|
||
|
|
upcase = RIGHT;
|
||
|
|
i = k+1;
|
||
|
|
w = u;
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! find the first edge intersecting the given window (s_t, w) */
|
||
|
|
void scand(Size_type& i, Point_2& w) const {
|
||
|
|
Point_2 u;
|
||
|
|
Size_type k = scan_edges( i, stack.top(), w, u, false );
|
||
|
|
upcase = LEFT;
|
||
|
|
i = k+1;
|
||
|
|
stack.push( u );
|
||
|
|
if ( u != vertices[k+1] ) {
|
||
|
|
stack.push( vertices[k+1] );
|
||
|
|
}
|
||
|
|
w = vertices[k+1];
|
||
|
|
}
|
||
|
|
|
||
|
|
/*! Scan edges v_i,v_{i+1},...,v_n, until find an edge intersecting given ray
|
||
|
|
or given segment. is_ray = true -> ray, false -> segment.
|
||
|
|
The intersection point is returned by u */
|
||
|
|
Size_type scan_edges( Size_type i,
|
||
|
|
const Point_2& ray_begin,
|
||
|
|
const Point_2& ray_end,
|
||
|
|
Point_2& u,
|
||
|
|
bool is_ray ) const
|
||
|
|
{
|
||
|
|
Orientation old_orient = RIGHT_TURN;
|
||
|
|
Ray_2 ray( ray_begin, ray_end );
|
||
|
|
Segment_2 s2( ray_begin, ray_end );
|
||
|
|
Size_type k;
|
||
|
|
Object_2 result;
|
||
|
|
for ( k = i; k+1 < vertices.size(); k++ ) {
|
||
|
|
Orientation curr_orient = traits->orientation_2_object()(
|
||
|
|
ray_begin,
|
||
|
|
ray_end,
|
||
|
|
vertices[k+1] );
|
||
|
|
if ( curr_orient != old_orient ) {
|
||
|
|
// Orientation switch, an intersection may occur
|
||
|
|
Segment_2 seg( vertices[k], vertices[k+1] );
|
||
|
|
if ( is_ray ) {
|
||
|
|
result = Intersect_2()( seg, ray );
|
||
|
|
if(result)
|
||
|
|
break;
|
||
|
|
} else {
|
||
|
|
result = Intersect_2()( seg, s2 );
|
||
|
|
if(result)
|
||
|
|
break;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
old_orient = curr_orient;
|
||
|
|
}
|
||
|
|
CGAL_assertion( k+1<vertices.size() );
|
||
|
|
const Point_2 * ipoint = object_cast<Point_2>( &result );
|
||
|
|
if ( ipoint ) {
|
||
|
|
u = *ipoint;
|
||
|
|
} else {
|
||
|
|
u = vertices[k+1];
|
||
|
|
}
|
||
|
|
return k;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
} // namespace CGAL
|
||
|
|
#endif
|