468 lines
15 KiB
C
468 lines
15 KiB
C
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// Copyright (c) 1997
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// Utrecht University (The Netherlands),
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// ETH Zurich (Switzerland),
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// INRIA Sophia-Antipolis (France),
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// Max-Planck-Institute Saarbruecken (Germany),
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// and Tel-Aviv University (Israel). All rights reserved.
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//
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// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public License as
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// published by the Free Software Foundation; either version 3 of the License,
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// 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: LGPL-3.0+
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//
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//
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// Author(s) : Wieger Wesselink <wieger@cs.ruu.nl>
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/*!
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\file Polygon_2_algorithms.h
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*/
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#ifndef CGAL_POLYGON_2_ALGORITHMS_H
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#define CGAL_POLYGON_2_ALGORITHMS_H
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#include <CGAL/config.h>
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#include <CGAL/enum.h>
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#include <CGAL/Bbox_2.h>
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#include <CGAL/Polygon_2/polygon_assertions.h>
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///
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namespace CGAL {
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//-----------------------------------------------------------------------//
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// algorithms for sequences of 2D points
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//-----------------------------------------------------------------------//
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/// \addtogroup PkgPolygon2Functions
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/// @{
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/// Returns an iterator to the leftmost point from the range
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/// `[first,last)`. In case of a tie, the point
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/// with the smallest `y`-coordinate is taken.
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///
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/// \tparam Traits is a model of the concept `PolygonTraits_2`.
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/// Only the members `Less_xy_2` and
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/// `less_xy_2_object()` are used.
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/// \tparam ForwardIterator must have `Traits::Point_2` as value type.
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///
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///
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/// \sa `CGAL::right_vertex_2()`
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/// \sa `CGAL::top_vertex_2()`
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/// \sa `CGAL::bottom_vertex_2()`
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/// \sa `CGAL::Polygon_2`
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template <class ForwardIterator, class PolygonTraits>
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ForwardIterator left_vertex_2(ForwardIterator first,
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ForwardIterator last,
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const PolygonTraits& traits);
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/// Returns an iterator to the rightmost point from the range
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/// `[first,last)`. In case of a tie, the point
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/// with the largest `y`-coordinate is taken.
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///
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/// \tparam Traits is a model of the concept
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/// `PolygonTraits_2`.
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/// In fact, only the members `Less_xy_2` and
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/// `less_xy_2_object()` are used.
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/// \tparam ForwardIterator must have`Traits::Point_2` as value type.
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///
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///
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/// \sa `CGAL::left_vertex_2()`
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/// \sa `CGAL::top_vertex_2()`
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/// \sa `CGAL::bottom_vertex_2()`
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/// \sa `CGAL::Polygon_2`
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template <class ForwardIterator, class PolygonTraits>
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ForwardIterator right_vertex_2(ForwardIterator first,
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ForwardIterator last,
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const PolygonTraits& traits);
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/// Returns an iterator to the topmost point from the range
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/// `[first,last)`. In case of a tie, the point
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/// with the largest `x`-coordinate is taken.
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///
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/// \tparam Traits is a model of the concept
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/// `PolygonTraits_2`.
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/// Only the members `Less_yx_2` and
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/// `less_yx_2_object()` are used.
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/// \tparam ForwardIterator must have `Traits::Point_2` as value type.
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///
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/// \sa `CGAL::left_vertex_2()`
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/// \sa `CGAL::right_vertex_2()`
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/// \sa `CGAL::bottom_vertex_2()`
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/// \sa `CGAL::Polygon_2`
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template <class ForwardIterator, class PolygonTraits>
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ForwardIterator top_vertex_2(ForwardIterator first,
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ForwardIterator last,
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const PolygonTraits& traits);
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/// Returns an iterator to the bottommost point from the range
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/// `[first,last)`. In case of a tie, the point
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/// with the smallest `x`-coordinate is taken.
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///
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/// \tparam Traits is a model of the concept
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/// `PolygonTraits_2`.
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/// Only the members `Less_yx_2` and
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/// `less_yx_2_object()` are used.
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/// \tparam ForwardIterator must have `Traits::Point_2` as value type.
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///
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/// \sa `CGAL::left_vertex_2()`
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/// \sa `CGAL::right_vertex_2()`
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/// \sa `CGAL::top_vertex_2()`
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/// \sa `CGAL::Polygon_2`
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/// \sa `PolygonTraits_2`
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template <class ForwardIterator, class PolygonTraits>
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ForwardIterator bottom_vertex_2(ForwardIterator first,
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ForwardIterator last,
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const PolygonTraits& traits);
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/// Computes the signed area of the polygon defined by the range of points
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/// `[first,last)`. The area is returned in the parameter
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/// `result`. The sign is positive for counterclockwise polygons, negative for
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/// clockwise polygons. If the polygon is not simple, the area is not well defined.
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/// The functionality is also available by the `polygon_area_2()` function, which
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/// returns the area instead of taking it as a parameter.
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///
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/// \tparam Traits is a model of the concept
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/// `PolygonTraits_2`.
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/// Only the following members of this traits class are used:
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/// - `Compute_area_2` : Computes the signed area of the
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/// oriented triangle defined by 3 `Point_2` passed as arguments.
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/// - `FT`
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/// - `compute_area_2_object()`
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/// \tparam ForwardIterator must have `Traits::Point_2` as value type.
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///
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/// \sa `CGAL::polygon_area_2()`
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/// \sa `PolygonTraits_2`
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/// \sa `CGAL::orientation_2()`
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/// \sa `CGAL::Polygon_2`
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template <class ForwardIterator, class PolygonTraits>
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void
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area_2( ForwardIterator first, ForwardIterator last,
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typename PolygonTraits::FT &result,
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const PolygonTraits& traits)
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{
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typedef typename PolygonTraits::FT FT;
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result = FT(0);
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// check if the polygon is empty
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if (first == last) return;
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ForwardIterator second = first; ++second;
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// check if the polygon has only one point
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if (second == last) return;
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typename PolygonTraits::Compute_area_2 compute_area_2 =
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traits.compute_area_2_object();
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ForwardIterator third = second;
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while (++third != last) {
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result = result + compute_area_2(*first, *second, *third);
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second = third;
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}
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}
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/// Computes the signed area of the polygon defined by the range of points
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/// `[first,last)`.
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/// The sign is positive for counterclockwise polygons, negative for
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/// clockwise polygons. If the polygon is not simple, the area is not well defined.
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///
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/// \tparam Traits is a model of the concept `PolygonTraits_2`. Only the following members of this traits class are used:
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/// - `Compute_area_2` : Computes the signed area of the
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/// oriented triangle defined by 3 `Point_2` passed as arguments.
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/// - `FT`
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/// - `compute_area_2_object`
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/// \tparam ForwardIterator must have `Traits::Point_2` as value type.
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///
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///
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/// \sa `PolygonTraits_2 `
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/// \sa `CGAL::orientation_2()`
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/// \sa `CGAL::Polygon_2 `
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template <class ForwardIterator, class PolygonTraits>
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typename PolygonTraits::FT
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polygon_area_2( ForwardIterator first, ForwardIterator last,
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const PolygonTraits& traits)
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{
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typedef typename PolygonTraits::FT FT;
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FT result = FT(0);
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// check if the polygon is empty
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if (first == last) return result;
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ForwardIterator second = first; ++second;
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// check if the polygon has only one point
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if (second == last) return result;
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typename PolygonTraits::Compute_area_2 compute_area_2 =
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traits.compute_area_2_object();
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ForwardIterator third = second;
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while (++third != last) {
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result = result + compute_area_2(*first, *second, *third);
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second = third;
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}
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return result;
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}
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/// Checks if the polygon is convex.
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///
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/// \tparam Traits is a model of the concept
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/// `PolygonTraits_2`.
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/// Only the following members of this traits class are used:
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/// - `Less_xy_2`
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/// - `Orientation_2`
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/// - `less_xy_2_object`
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/// - `orientation_2_object`
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/// \tparam ForwardIterator must have `PolygonTraits::Point_2` as value type.
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///
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/// \sa `PolygonTraits_2 `
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/// \sa `CGAL::Polygon_2 `
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template <class ForwardIterator, class PolygonTraits>
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bool is_convex_2(ForwardIterator first,
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ForwardIterator last,
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const PolygonTraits& traits);
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/// Checks if the polygon defined by the
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/// iterator range `[first,last)` is simple, that is, if the edges
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/// do not intersect, except consecutive edges in their common vertex.
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///
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/// \tparam Traits is a model of the concept
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/// `PolygonTraits_2`.
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/// Only the following members of this traits class are used:
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/// - `Point_2`
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/// - `Less_xy_2`
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/// - `Orientation_2`
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/// - `less_xy_2_object()`
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/// - `orientation_2_object()`
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/// \tparam ForwardIterator must have `PolygonTraits::Point_2` as value type.
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///
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/// ### Implementation##
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///
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/// The simplicity test is implemented by means of a plane sweep algorithm.
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/// The algorithm is quite robust when used with inexact number types.
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/// The running time is `O(n log n)`, where n is the number of vertices of the
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/// polygon.
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///
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/// \sa `PolygonTraits_2`
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/// \sa `CGAL::Polygon_2`
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template <class ForwardIterator, class PolygonTraits>
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bool is_simple_2(ForwardIterator first,
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ForwardIterator last,
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const PolygonTraits& traits);
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// In the following two functions we would like to use Traits::Point_2
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// instead of Point, but this is not allowed by g++ 2.7.2.
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///
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/// Computes on which side of a polygon a point lies.
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/// \tparam Traits is a model of the concept
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/// `PolygonTraits_2`.
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/// Only the following members of this traits class are used:
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/// - `Less_xy_2`
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/// - `Compare_x_2`
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/// - `Compare_y_2`
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/// - `Orientation_2`
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/// - `less_xy_2_object()`
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/// - `compare_x_2_object()`
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/// - `compare_y_2_object()`
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/// - `orientation_2_object()`
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/// \tparam ForwardIterator must have `PolygonTraits::Point_2` as value type.
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///
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/// \sa `PolygonTraits_2`
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/// \sa `CGAL::bounded_side_2()`
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/// \sa `CGAL::is_simple_2()`
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/// \sa `CGAL::Polygon_2`
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/// \sa `Oriented_side`
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template <class ForwardIterator, class Point, class Traits>
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Oriented_side oriented_side_2(ForwardIterator first,
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ForwardIterator last,
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const Point& point,
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const Traits& traits);
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/// Computes if a point lies inside a polygon.
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/// The polygon is defined by the sequence of points `[first,last)`.
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/// Being inside is defined by the odd-even rule. If we take a ray starting at the
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/// point and extending to infinity (in any direction), we count the number of
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/// intersections. If this number is odd, the point is inside, otherwise it is
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/// outside. If the point is on a polygon edge, a special value is returned. A
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/// simple polygon divides the plane in an unbounded and a bounded region.
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/// According to the definition points in the bounded region are inside the polygon.
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///
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///
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/// \tparam Traits is a model of the concept
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/// `PolygonTraits_2`.
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/// Only the following members of this traits class are used:
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/// - `Compare_x_2`
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/// - `Compare_y_2`
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/// - `Orientation_2`
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/// - `compare_x_2_object()`
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/// - `compare_y_2_object()`
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/// - `orientation_2_object()`
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/// \tparam ForwardIterator must have `Traits::Point_2` as value type.
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///
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/// ### Implementation ###
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///
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/// The running time is linear in the number of vertices of the polygon.
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/// A horizontal ray is taken to count the number of intersections.
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/// Special care is taken that the result is correct even if there are degeneracies
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/// (if the ray passes through a vertex).
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///
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///
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/// \sa `PolygonTraits_2`
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/// \sa `CGAL::oriented_side_2()`
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/// \sa `CGAL::Polygon_2 `
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/// \sa `CGAL::Bounded_side`
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template <class ForwardIterator, class Point, class PolygonTraits>
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Bounded_side bounded_side_2(ForwardIterator first,
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ForwardIterator last,
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const Point& point,
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const PolygonTraits& traits);
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/// Computes if a polygon is clockwise or counterclockwise oriented.
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/// \pre `is_simple_2(first, last, traits);`
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///
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/// \tparam Traits is a model of the concept
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/// `PolygonTraits_2`.
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/// Only the following members of this traits class are used:
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/// - `Less_xy_2`
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/// - `less_xy_2_object()`
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/// - `orientation_2_object()`
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/// \tparam ForwardIterator must have`Traits::Point_2` as value type.
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///
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///
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///
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/// \sa `PolygonTraits_2`
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/// \sa `CGAL::is_simple_2()`
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/// \sa `CGAL::Polygon_2`
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/// \sa `CGAL::Orientation_2`
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template <class ForwardIterator, class Traits>
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Orientation orientation_2(ForwardIterator first,
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ForwardIterator last,
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const Traits& traits);
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/// @}
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//-----------------------------------------------------------------------//
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// implementation
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//-----------------------------------------------------------------------//
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template <class ForwardIterator>
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inline
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ForwardIterator left_vertex_2(ForwardIterator first,
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ForwardIterator last)
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{
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|
|
typedef typename Kernel_traits<
|
||
|
|
typename std::iterator_traits<ForwardIterator>::value_type>::Kernel K;
|
||
|
|
return left_vertex_2(first, last, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class ForwardIterator>
|
||
|
|
inline
|
||
|
|
ForwardIterator right_vertex_2(ForwardIterator first,
|
||
|
|
ForwardIterator last)
|
||
|
|
{
|
||
|
|
typedef typename Kernel_traits<
|
||
|
|
typename std::iterator_traits<ForwardIterator>::value_type>::Kernel K;
|
||
|
|
return right_vertex_2(first, last, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class ForwardIterator>
|
||
|
|
inline
|
||
|
|
ForwardIterator top_vertex_2(ForwardIterator first,
|
||
|
|
ForwardIterator last)
|
||
|
|
{
|
||
|
|
typedef typename Kernel_traits<
|
||
|
|
typename std::iterator_traits<ForwardIterator>::value_type>::Kernel K;
|
||
|
|
return top_vertex_2(first, last, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class ForwardIterator>
|
||
|
|
inline
|
||
|
|
ForwardIterator bottom_vertex_2(ForwardIterator first,
|
||
|
|
ForwardIterator last)
|
||
|
|
{
|
||
|
|
typedef typename Kernel_traits<
|
||
|
|
typename std::iterator_traits<ForwardIterator>::value_type>::Kernel K;
|
||
|
|
return bottom_vertex_2(first, last, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class ForwardIterator, class Numbertype>
|
||
|
|
inline
|
||
|
|
void area_2(ForwardIterator first,
|
||
|
|
ForwardIterator last,
|
||
|
|
Numbertype& result)
|
||
|
|
{
|
||
|
|
typedef typename Kernel_traits<
|
||
|
|
typename std::iterator_traits<ForwardIterator>::value_type>::Kernel K;
|
||
|
|
area_2(first, last, result, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
template <class ForwardIterator>
|
||
|
|
inline
|
||
|
|
bool is_convex_2(ForwardIterator first,
|
||
|
|
ForwardIterator last)
|
||
|
|
{
|
||
|
|
typedef typename Kernel_traits<
|
||
|
|
typename std::iterator_traits<ForwardIterator>::value_type>::Kernel K;
|
||
|
|
return is_convex_2(first, last, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
template <class ForwardIterator>
|
||
|
|
inline
|
||
|
|
bool is_simple_2(ForwardIterator first,
|
||
|
|
ForwardIterator last)
|
||
|
|
{
|
||
|
|
typedef typename Kernel_traits<
|
||
|
|
typename std::iterator_traits<ForwardIterator>::value_type>::Kernel K;
|
||
|
|
return is_simple_2(first, last, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
template <class ForwardIterator>
|
||
|
|
inline
|
||
|
|
Oriented_side oriented_side_2(
|
||
|
|
ForwardIterator first,
|
||
|
|
ForwardIterator last,
|
||
|
|
const typename std::iterator_traits<ForwardIterator>::value_type& point)
|
||
|
|
{
|
||
|
|
typedef typename Kernel_traits<
|
||
|
|
typename std::iterator_traits<ForwardIterator>::value_type>::Kernel K;
|
||
|
|
return oriented_side_2(first, last, point, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
template <class ForwardIterator>
|
||
|
|
inline
|
||
|
|
Bounded_side bounded_side_2(
|
||
|
|
ForwardIterator first,
|
||
|
|
ForwardIterator last,
|
||
|
|
const typename std::iterator_traits<ForwardIterator>::value_type& point)
|
||
|
|
{
|
||
|
|
typedef typename Kernel_traits<
|
||
|
|
typename std::iterator_traits<ForwardIterator>::value_type>::Kernel K;
|
||
|
|
return bounded_side_2(first, last, point, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
template <class ForwardIterator>
|
||
|
|
inline
|
||
|
|
Orientation orientation_2(ForwardIterator first,
|
||
|
|
ForwardIterator last)
|
||
|
|
{
|
||
|
|
typedef typename Kernel_traits<
|
||
|
|
typename std::iterator_traits<ForwardIterator>::value_type>::Kernel K;
|
||
|
|
return orientation_2(first, last, K());
|
||
|
|
}
|
||
|
|
|
||
|
|
} //namespace CGAL
|
||
|
|
|
||
|
|
#include <CGAL/Polygon_2/Polygon_2_algorithms_impl.h>
|
||
|
|
|
||
|
|
#endif // CGAL_POLYGON_2_ALGORITHMS_H
|