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// Copyright (c) 2003,2004,2006 INRIA Sophia-Antipolis (France).
// 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-3.5-branch/Apollonius_graph_2/include/CGAL/Apollonius_graph_2/Incircle_C2.h $
// $Id: Incircle_C2.h 44317 2008-07-22 12:29:01Z spion $
//
//
// Author(s) : Menelaos Karavelas <mkaravel@cse.nd.edu>
#ifndef CGAL_APOLLONIUS_GRAPH_2_INCIRCLE_C2_H
#define CGAL_APOLLONIUS_GRAPH_2_INCIRCLE_C2_H
#include <CGAL/Apollonius_graph_2/basic.h>
#include <CGAL/Apollonius_graph_2/Predicate_constructions_C2.h>
#include <CGAL/Apollonius_graph_2/Bounded_side_of_ccw_circle_C2.h>
CGAL_BEGIN_NAMESPACE
CGAL_APOLLONIUS_GRAPH_2_BEGIN_NAMESPACE
//--------------------------------------------------------------------
template< class K >
class Sign_of_distance_from_bitangent_line_2
{
public:
typedef Bitangent_line_2<K> Bitangent_line;
typedef typename K::Site_2 Site_2;
typedef Inverted_weighted_point_2<K> Inverted_weighted_point;
typedef typename K::FT FT;
typedef typename K::Sign Sign;
public:
inline Sign
operator()(const Bitangent_line& bl, const Site_2& q,
const Field_with_sqrt_tag&) const
{
#ifdef AG2_PROFILE_PREDICATES
ag2_predicate_profiler::distance_from_bitangent_counter++;
#endif
FT a = bl.a1() + bl.a2() * CGAL::sqrt(bl.delta());
FT b = bl.b1() + bl.b2() * CGAL::sqrt(bl.delta());
FT c = bl.c1() + bl.c2() * CGAL::sqrt(bl.delta());
FT r = a * q.x() + b * q.y() + c - q.weight() * bl.d();
return CGAL::sign(r);
}
inline Sign
operator()(const Bitangent_line& bl, const Site_2& q,
const Integral_domain_without_division_tag&) const
{
#ifdef AG2_PROFILE_PREDICATES
ag2_predicate_profiler::distance_from_bitangent_counter++;
#endif
FT A = bl.a1() * q.x() + bl.b1() * q.y() + bl.c1()
- q.weight() * bl.d();
FT B = bl.a2() * q.x() + bl.b2() * q.y() + bl.c2();
return sign_a_plus_b_x_sqrt_c(A, B, bl.delta());
}
};
//--------------------------------------------------------------------
template< class K >
class Sign_of_distance_from_CCW_circle_2
{
public:
typedef Bitangent_line_2<K> Bitangent_line;
typedef Inverted_weighted_point_2<K> Inverted_weighted_point;
typedef typename K::FT FT;
typedef typename K::Sign Sign;
public:
inline Sign
operator()(const Bitangent_line& bl,
const Inverted_weighted_point& v,
const Field_with_sqrt_tag&) const
{
FT a = bl.a1() + bl.a2() * CGAL::sqrt(bl.delta());
FT b = bl.b1() + bl.b2() * CGAL::sqrt(bl.delta());
FT c = bl.c1() + bl.c2() * CGAL::sqrt(bl.delta());
FT r = a * v.x() + b * v.y() + c * v.p() - v.weight() * bl.d();
return CGAL::sign(r);
}
inline Sign
operator()(const Bitangent_line& bl,
const Inverted_weighted_point& v,
const Integral_domain_without_division_tag&) const
{
FT A = bl.a1() * v.x() + bl.b1() * v.y() + bl.c1() * v.p()
- v.weight() * bl.d();
FT B = bl.a2() * v.x() + bl.b2() * v.y() + bl.c2() * v.p();
return sign_a_plus_b_x_sqrt_c(A, B, bl.delta());
}
};
template < class Weighted_point >
class Weighted_point_less_than
{
public:
inline
bool operator()(const Weighted_point& p1,
const Weighted_point& p2) const
{
if ( p1.x() == p2.x() ) {
return p1.y() < p2.y();
}
return p1.x() < p2.x();
}
};
template < class K, class MTag >
class Vertex_conflict_2
{
public:
typedef K Kernel;
typedef MTag Method_tag;
typedef typename K::Point_2 Point_2;
typedef typename K::Site_2 Site_2;
typedef Weighted_point_inverter_2<K> Weighted_point_inverter;
typedef Inverted_weighted_point_2<K> Inverted_weighted_point;
typedef Bitangent_line_2<K> Bitangent_line;
typedef Voronoi_radius_2<K> Voronoi_radius;
typedef typename K::FT FT;
typedef typename K::Orientation Orientation;
typedef typename K::Sign Sign;
typedef typename K::Bounded_side Bounded_side;
typedef Bounded_side_of_CCW_circle_2<K> Bounded_side_of_CCW_circle;
typedef Sign_of_distance_from_bitangent_line_2<K>
Sign_of_distance_from_bitangent_line;
typedef Sign_of_distance_from_CCW_circle_2<K>
Sign_of_distance_from_CCW_circle;
private:
inline Orientation
orientation(const Bitangent_line& l, const Point_2& p,
const Field_with_sqrt_tag&) const
{
FT A = l.a1() * p.x() + l.b1() * p.y() + l.c1();
FT B = l.a2() * p.x() + l.b2() * p.y() + l.c2();
FT P = A + B * CGAL::sqrt(l.delta());
return CGAL::sign(P);
}
inline Orientation
orientation(const Bitangent_line& l, const Point_2& p,
const Integral_domain_without_division_tag&) const
{
FT A = l.a1() * p.x() + l.b1() * p.y() + l.c1();
FT B = l.a2() * p.x() + l.b2() * p.y() + l.c2();
return sign_a_plus_b_x_sqrt_c(A, B, l.delta());
}
inline Orientation
orientation(const Bitangent_line& l,
const Inverted_weighted_point& u) const
{
FT A = l.a1() * u.x() / u.p() + l.b1() * u.y() / u.p() + l.c1();
FT B = l.a2() * u.x() / u.p() + l.b2() * u.y() / u.p() + l.c2();
FT P = A + B * CGAL::sqrt(l.delta());
return CGAL::sign(P);
}
public:
typedef Sign result_type;
typedef Site_2 argument_type;
inline
Sign operator()(const Site_2& p1, const Site_2& p2,
const Site_2& p3, const Site_2& q) const
{
#ifdef AG2_PROFILE_PREDICATES
ag2_predicate_profiler::incircle_counter++;
#endif
//
Method_tag tag;
Weighted_point_inverter inverter(p1);
Inverted_weighted_point u2 = inverter(p2);
Inverted_weighted_point u3 = inverter(p3);
Voronoi_radius vr_123(u2, u3);
Bounded_side bs = Bounded_side_of_CCW_circle()(vr_123, tag );
if ( bs != ON_UNBOUNDED_SIDE ) { return NEGATIVE; }
Inverted_weighted_point v = inverter(q);
Bitangent_line blinv_23(u2, u3);
Sign s = Sign_of_distance_from_CCW_circle()(blinv_23, v, tag);
return s;
}
inline
Sign operator()(const Site_2& p1, const Site_2& p2,
const Site_2& q) const
{
Method_tag tag;
//
Bitangent_line bl_21(p2, p1);
Sign s = Sign_of_distance_from_bitangent_line()(bl_21, q, tag);
if ( s != ZERO ) { return s; }
Bitangent_line bl1_perp = bl_21.perpendicular(p1.point());
Bitangent_line bl2_perp = bl_21.perpendicular(p2.point());
Orientation o1 = orientation(bl1_perp, q.point(), tag);
Orientation o2 = orientation(bl2_perp, q.point(), tag);
CGAL_assertion( o1 != COLLINEAR || o2 != COLLINEAR );
if ( o1 == o2 ) { return POSITIVE; }
return NEGATIVE;
}
};
//--------------------------------------------------------------------
CGAL_APOLLONIUS_GRAPH_2_END_NAMESPACE
CGAL_END_NAMESPACE
#endif // CGAL_APOLLONIUS_GRAPH_2_INCIRCLE_C2_H
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