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// Copyright (c) 2000 Max-Planck-Institute Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.2-branch/Partition_2/include/CGAL/partition_approx_convex_2.h $
// $Id: partition_approx_convex_2.h 28567 2006-02-16 14:30:13Z lsaboret $
//
//
// Author(s) : Susan Hert <hert@mpi-sb.mpg.de>
#ifndef CGAL_PARTITION_APPROX_CONVEX_H
#define CGAL_PARTITION_APPROX_CONVEX_H
#include <CGAL/Constrained_triangulation_2.h>
#include <CGAL/Triangulation_indirect_traits_2.h>
#include <CGAL/Turn_reverser.h>
#include <CGAL/Partitioned_polygon_2.h>
#include <CGAL/IO/Tee_for_output_iterator.h>
#include <CGAL/Partition_traits_2.h>
#include <CGAL/partition_is_valid_2.h>
#include <CGAL/partition_assertions.h>
#include <utility>
#include <iterator>
namespace CGAL {
template< class Point_2, class Traits >
bool partition_appx_cvx_is_edge_through_interior(const Point_2& before_s,
const Point_2& source,
const Point_2& after_s,
const Point_2& target,
const Traits& traits )
{
// determine if the edge goes through the interior of the polygon or not
typedef typename Traits::Left_turn_2 Left_turn_2;
Left_turn_2 left_turn = traits.left_turn_2_object();
Turn_reverser<Point_2, Left_turn_2> right_turn(left_turn);
if (right_turn(before_s, source, after_s)) // concave angle
{
if (right_turn(before_s, source, target) &&
right_turn(target, source, after_s))
return false;
}
else // left turn or straight
if (right_turn(before_s, source, target) ||
right_turn(target, source, after_s))
return false;
return true;
}
// e_circ is a circulator for the edges incident to the point referred to by
// v_ref, which is a circualtor around the vertices of the original polygon
template <class Edge_circulator, class Circulator, class Triangulation,
class Traits>
bool partition_appx_cvx_cuts_nonconvex_angle( Edge_circulator e_circ,
Circulator v_ref,
const Triangulation& triangles,
const Traits& traits)
{
typedef typename Triangulation::Segment Segment_2;
#ifdef CGAL_PARTITION_APPROX_CONVEX_DEBUG
Segment_2 edge = triangles.segment((*e_circ).first, (*e_circ).second);
std::cout << "edge: " << *edge.source() << " " << *edge.target()
<< std::endl;
#endif
typename Triangulation::Point next_ccw_pt_ref, prev_ccw_pt_ref;
// the next and previous edges in the ccw ordering of edges around v_ref
Edge_circulator next_e = e_circ; next_e++;
Edge_circulator prev_e = e_circ; prev_e--;
// find the first edge before this one that has been included in the
// partition polygon (and is thus marked as constrained in triangulation)
while (prev_e != e_circ && (triangles.is_infinite(*prev_e) ||
!(*prev_e).first->is_constrained((*prev_e).second)))
prev_e--;
Segment_2 next_edge = triangles.segment((*next_e).first,(*next_e).second);
Segment_2 prev_edge = triangles.segment((*prev_e).first,(*prev_e).second);
#ifdef CGAL_PARTITION_APPROX_CONVEX_DEBUG
std::cout << "next_edge: " << *next_edge.source() << " "
<< *next_edge.target() <<std::endl;
std::cout << "prev_edge: " << *prev_edge.source() << " "
<< *prev_edge.target() <<std::endl;
#endif
// find which endpoint is shared by the two edges
if (next_edge.source() == v_ref)
next_ccw_pt_ref = next_edge.target();
else
next_ccw_pt_ref = next_edge.source();
if (prev_edge.source() == v_ref)
prev_ccw_pt_ref = prev_edge.target();
else
prev_ccw_pt_ref = prev_edge.source();
#ifdef CGAL_PARTITION_APPROX_CONVEX_DEBUG
std::cout << "partition_appx_cvx_cuts_nonconvex_angle: next_ccw_pt "
<< *next_ccw_pt_ref << " v_ref " << *v_ref << " prev_ccw_pt_ref "
<< *prev_ccw_pt_ref << std::endl;
#endif
typedef typename Traits::Left_turn_2 Left_turn_2;
typedef typename Traits::Point_2 Point_2;
Left_turn_2 left_turn = traits.left_turn_2_object();
Turn_reverser<Point_2, Left_turn_2> right_turn(left_turn);
return right_turn(*next_ccw_pt_ref, *v_ref, *prev_ccw_pt_ref);
}
template<class InputIterator, class Traits, class OutputIterator>
OutputIterator partition_approx_convex_2(InputIterator first,
InputIterator beyond,
OutputIterator result,
const Traits& traits)
{
if (first == beyond) return result;
typedef Partitioned_polygon_2< Traits > P_Polygon_2;
typedef typename P_Polygon_2::iterator I;
typedef Circulator_from_iterator<I> Circulator;
typedef Triangulation_indirect_traits_2<Circulator, Traits> Gt;
typedef Constrained_triangulation_2<Gt> Constrained_tri_2;
typedef typename Constrained_tri_2::Edge_iterator Edge_iterator;
typedef typename Constrained_tri_2::Edge_circulator Edge_circulator;
typedef typename Constrained_tri_2::Vertex_iterator Tri_vertex_iterator;
typedef typename Constrained_tri_2::Vertex_handle Vertex_handle;
typedef typename Gt::Segment_2 Segment_2;
P_Polygon_2 polygon(first, beyond);
CGAL_partition_precondition(
orientation_2(polygon.begin(), polygon.end(), traits) == COUNTERCLOCKWISE);
Circulator first_c(polygon.begin(), polygon.end(), polygon.begin());
Circulator c(polygon.begin(), polygon.end());
Circulator next(polygon.begin(), polygon.end());
Constrained_tri_2 triangles;
do
{
next = c; next++;
triangles.insert(c, next);
} while (++c != first_c);
Segment_2 edge;
Circulator source, target, before_s, after_s;
#ifdef CGAL_PARTITION_APPROX_CONVEX_DEBUG
std::cout << "Inserting diagonals: " << std::endl;
#endif
Edge_circulator e_circ, first_e;
Tri_vertex_iterator v_it;
for (v_it = triangles.vertices_begin(); v_it != triangles.vertices_end();
v_it++)
{
first_e = triangles.incident_edges(Vertex_handle(v_it));
// find the constrained edge attached to this vertex that is first
// when going CW from the first edge returned above.
while (triangles.is_infinite(*first_e) ||
!(*first_e).first->is_constrained((*first_e).second))
{
first_e--;
}
e_circ = first_e;
do
{
if ((*e_circ).first->is_constrained((*e_circ).second))
{
edge = triangles.segment((*e_circ).first, (*e_circ).second);
#ifdef CGAL_PARTITION_APPROX_CONVEX_DEBUG
std::cout << "edge " << *edge.source() << " " << *edge.target()
<< " is constrained " << std::endl;
#endif
}
else
{
if (!triangles.is_infinite(*e_circ))
{
edge = triangles.segment((*e_circ).first, (*e_circ).second);
source = edge.source();
target = edge.target();
before_s = source; before_s--;
after_s = source; after_s++;
#ifdef CGAL_PARTITION_APPROX_CONVEX_DEBUG
std::cout << "considering " << *source << " " << *target
<< "...";
#endif
if (partition_appx_cvx_is_edge_through_interior(*before_s,
*source, *after_s, *target, traits))
{
if (partition_appx_cvx_cuts_nonconvex_angle(e_circ,
(*v_it).point(), triangles, traits))
{
#ifdef CGAL_PARTITION_APPROX_CONVEX_DEBUG
std::cout << "inserting" << std::endl;
#endif
polygon.insert_diagonal(source, target);
triangles.insert(source, target);
}
#ifdef CGAL_PARTITION_APPROX_CONVEX_DEBUG
else
std::cout << "doesn't cut reflex angle" << std::endl;
#endif
}
#ifdef CGAL_PARTITION_APPROX_CONVEX_DEBUG
else
std::cout << "not an edge through the interior"
<< std::endl;
#endif
}
#ifdef CGAL_PARTITION_APPROX_CONVEX_DEBUG
std::cout << "edge is infinite " << std::endl;
#endif
}
} while (++e_circ != first_e);
}
#if defined(CGAL_PARTITION_NO_POSTCONDITIONS) || \
defined(CGAL_NO_POSTCONDITIONS) || defined(NDEBUG)
OutputIterator res(result);
#else
typedef typename Traits::Polygon_2 Polygon_2;
Tee_for_output_iterator<OutputIterator, Polygon_2> res(result);
#endif // no postconditions
polygon.partition(res, 0);
CGAL_partition_postcondition(
convex_partition_is_valid_2(polygon.begin(), polygon.end(),
res.output_so_far_begin(),
res.output_so_far_end(), traits));
#if defined(CGAL_PARTITION_NO_POSTCONDITIONS) || \
defined(CGAL_NO_POSTCONDITIONS) || defined(NDEBUG)
return res;
#else
return res.to_output_iterator();
#endif // no postconditions
}
template <class InputIterator, class OutputIterator>
inline
OutputIterator partition_approx_convex_2(InputIterator first,
InputIterator beyond,
OutputIterator result)
{
typedef typename std::iterator_traits<InputIterator>::value_type Point_2;
typedef typename Kernel_traits<Point_2>::Kernel K;
return partition_approx_convex_2(first, beyond, result,
Partition_traits_2<K>());
}
}
#endif // CGAL_PARTITION_APPROX_CONVEX_H
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