1035 lines
34 KiB
C
1035 lines
34 KiB
C
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// Copyright (c) 1997-2010, 2017 INRIA Sophia-Antipolis (France).
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// 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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// Author(s) : Mariette Yvinec, Sebastien Loriot, Mael Rouxel-Labbé
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#ifndef CGAL_INTERNAL_PROJECTION_TRAITS_3_H
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#define CGAL_INTERNAL_PROJECTION_TRAITS_3_H
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#include <CGAL/assertions.h>
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#include <CGAL/Point_3.h>
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#include <CGAL/Segment_3.h>
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#include <CGAL/Triangle_3.h>
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#include <CGAL/Kernel/global_functions_2.h>
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namespace CGAL {
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namespace internal {
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//project Point_3 along coordinate dim
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template <class R,int dim>
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struct Projector;
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//project onto yz
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template <class R>
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struct Projector<R,0>
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{
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typedef typename R::Less_y_3 Less_x_2;
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typedef typename R::Less_z_3 Less_y_2;
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typedef typename R::Compare_y_3 Compare_x_2;
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typedef typename R::Compare_z_3 Compare_y_2;
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typedef typename R::Equal_y_3 Equal_x_2;
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typedef typename R::Equal_z_3 Equal_y_2;
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static typename R::FT x(const typename R::Point_3& p) {return p.y();}
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static typename R::FT y(const typename R::Point_3& p) {return p.z();}
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static typename R::FT x(const typename R::Vector_3& p) {return p.y();}
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static typename R::FT y(const typename R::Vector_3& p) {return p.z();}
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static const int x_index=1;
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static const int y_index=2;
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};
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//project onto xz
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template <class R>
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struct Projector<R,1>
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{
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typedef typename R::Less_x_3 Less_x_2;
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typedef typename R::Less_z_3 Less_y_2;
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typedef typename R::Compare_x_3 Compare_x_2;
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typedef typename R::Compare_z_3 Compare_y_2;
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typedef typename R::Equal_x_3 Equal_x_2;
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typedef typename R::Equal_z_3 Equal_y_2;
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static typename R::FT x(const typename R::Point_3& p) {return p.x();}
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static typename R::FT y(const typename R::Point_3& p) {return p.z();}
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static typename R::FT x(const typename R::Vector_3& p) {return p.x();}
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static typename R::FT y(const typename R::Vector_3& p) {return p.z();}
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static const int x_index=0;
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static const int y_index=2;
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};
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//project onto xy
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template <class R>
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struct Projector<R,2>
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{
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typedef typename R::Less_x_3 Less_x_2;
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typedef typename R::Less_y_3 Less_y_2;
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typedef typename R::Compare_x_3 Compare_x_2;
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typedef typename R::Compare_y_3 Compare_y_2;
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typedef typename R::Equal_x_3 Equal_x_2;
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typedef typename R::Equal_y_3 Equal_y_2;
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static typename R::FT x(const typename R::Point_3& p) {return p.x();}
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static typename R::FT y(const typename R::Point_3& p) {return p.y();}
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static typename R::FT x(const typename R::Vector_3& p) {return p.x();}
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static typename R::FT y(const typename R::Vector_3& p) {return p.y();}
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static const int x_index=0;
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static const int y_index=1;
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};
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template <class R,int dim>
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class Orientation_projected_3
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{
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public:
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typedef typename R::Point_3 Point;
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typename R::FT x(const Point &p) const { return Projector<R,dim>::x(p); }
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typename R::FT y(const Point &p) const { return Projector<R,dim>::y(p); }
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typename R::Point_2 project(const Point& p) const
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{
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return typename R::Point_2(x(p),y(p));
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}
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CGAL::Orientation operator()(const Point& p,
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const Point& q,
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const Point& r) const
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{
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return CGAL::orientation(project(p), project(q), project(r));
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}
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};
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template <class R,int dim>
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class Side_of_oriented_circle_projected_3
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{
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public:
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typedef typename R::Point_3 Point;
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typename R::FT x(const Point &p) const { return Projector<R,dim>::x(p); }
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typename R::FT y(const Point &p) const { return Projector<R,dim>::y(p); }
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typename R::Point_2 project(const Point& p) const
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{
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return typename R::Point_2(x(p),y(p));
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}
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CGAL::Oriented_side operator() (const Point &p,
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const Point &q,
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const Point &r,
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const Point &s) const
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{
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return CGAL::side_of_oriented_circle(project(p),project(q),project(r),project(s) );
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}
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};
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template <class R,int dim>
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class Side_of_bounded_circle_projected_3
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{
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public:
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typedef typename R::Point_3 Point;
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typename R::FT x(const Point &p) const { return Projector<R,dim>::x(p); }
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typename R::FT y(const Point &p) const { return Projector<R,dim>::y(p); }
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typename R::Point_2 project(const Point& p) const
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{
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return typename R::Point_2(x(p),y(p));
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}
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CGAL::Bounded_side operator() (const Point &p,
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const Point &q,
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const Point &r,
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const Point &s) const
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{
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return CGAL::side_of_bounded_circle(project(p),project(q),project(r),project(s) );
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}
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CGAL::Bounded_side operator() (const Point &p,
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const Point &q,
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const Point &r) const
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{
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return CGAL::side_of_bounded_circle(project(p),project(q),project(r));
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}
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};
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template <class R,int dim>
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class Compare_distance_projected_3
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{
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public:
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typedef typename R::Point_3 Point_3;
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typedef typename R::Point_2 Point_2;
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typedef typename R::FT RT;
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typename R::FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
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typename R::FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
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Point_2 project(const Point_3& p) const
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{
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return Point_2(x(p),y(p));
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}
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Comparison_result operator()(const Point_3& p,const Point_3& q,const Point_3& r) const
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{
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Point_2 p2 = project(p);
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Point_2 q2 = project(q);
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Point_2 r2 = project(r);
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return compare_distance_to_point(p2,q2,r2);
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}
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};
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template <class R,int dim>
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class Collinear_are_ordered_along_line_projected_3
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{
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public:
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typedef typename R::Point_3 Point_3;
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typedef typename R::Point_2 Point_2;
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typedef typename R::FT FT;
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FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
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FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
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Point_2 project(const Point_3& p) const
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{
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return Point_2(x(p),y(p));
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}
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bool operator()(const Point_3& p,const Point_3& q,const Point_3& r) const
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{
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Point_2 p2 = project(p);
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Point_2 q2 = project(q);
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Point_2 r2 = project(r);
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return collinear_are_ordered_along_line(p2,q2,r2);
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}
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};
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template <class R, int dim>
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class Less_signed_distance_to_line_projected_3
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{
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public:
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typedef typename R::Point_3 Point_3;
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typedef typename R::Point_2 Point_2;
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typedef typename R::FT RT;
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typename R::FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
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typename R::FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
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typedef bool result_type;
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Point_2 project(const Point_3& p) const
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{
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return Point_2(x(p),y(p));
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}
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result_type operator()(const Point_3& p,
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const Point_3& q,
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const Point_3& r,
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const Point_3& s) const
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{
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return typename R::Less_signed_distance_to_line_2()
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( project(p), project(q), project(r), project(s) );
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}
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};
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template <class R,int dim>
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class Squared_distance_projected_3
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{
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public:
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typedef typename R::Point_3 Point_3;
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typedef typename R::Point_2 Point_2;
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typedef typename R::Line_3 Line_3;
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typedef typename R::Line_2 Line_2;
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typedef typename R::FT RT;
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typename R::FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
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typename R::FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
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Point_2 project(const Point_3& p) const
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{
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return Point_2(x(p),y(p));
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}
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RT operator()(const Point_3& p, const Point_3& q) const
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{
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Point_2 p2(project(p));
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Point_2 q2(project(q));
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return squared_distance(p2, q2);
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}
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RT operator()(const Line_3& l, const Point_3& p) const
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{
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Point_2 p2(project(p));
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Line_2 l2(project(l.point(0)), project(l.point(1)));
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return squared_distance(p2, l2);
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}
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};
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template <class R,int dim>
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class Intersect_projected_3
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{
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public:
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typedef typename R::Point_3 Point_3;
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typedef typename R::Segment_3 Segment_3;
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typedef typename R::Point_2 Point_2;
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typedef typename R::Vector_2 Vector_2;
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typedef typename R::Segment_2 Segment_2;
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typedef typename R::FT FT;
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typename R::FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
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typename R::FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
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Point_2 project(const Point_3& p) const
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{
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return Point_2(x(p),y(p));
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}
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FT alpha(const Point_2& p, const Point_2& source, const Point_2& target) const
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{
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FT dx = target.x() - source.x();
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FT dy = target.y() - source.y();
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return (CGAL::abs(dx)>CGAL::abs(dy)) ? ( p.x()-source.x() ) / dx : (p.y()-source.y() ) / dy;
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}
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Object operator()(const Segment_3& s1, const Segment_3& s2) const
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{
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Point_2 s1_source = project(s1.source());
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Point_2 s1_target = project(s1.target());
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Point_2 s2_source = project(s2.source());
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Point_2 s2_target = project(s2.target());
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Segment_2 s1_2(s1_source, s1_target);
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Segment_2 s2_2(s2_source, s2_target);
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CGAL_precondition(!s1_2.is_degenerate());
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CGAL_precondition(!s2_2.is_degenerate());
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//compute intersection points in projected plane
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//We know that none of the segment is degenerate
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Object o = intersection(s1_2,s2_2);
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const Point_2* pi=CGAL::object_cast<Point_2>(&o);
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if (pi==NULL) { //case of segment or empty
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const Segment_2* si=CGAL::object_cast<Segment_2>(&o);
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if (si==NULL) return Object();
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FT src[3],tgt[3];
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//the third coordinate is the midpoint between the points on s1 and s2
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FT z1 = s1.source()[dim] + ( alpha(si->source(), s1_source, s1_target) * ( s1.target()[dim] - s1.source()[dim] ));
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FT z2 = s2.source()[dim] + ( alpha(si->source(), s2_source, s2_target) * ( s2.target()[dim] - s2.source()[dim] ));
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src[dim] = (z1+z2) / FT(2);
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z1 = s1.source()[dim] + ( alpha(si->target(), s1_source, s1_target) * ( s1.target()[dim] - s1.source()[dim] ));
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z2 = s2.source()[dim] + ( alpha(si->target(), s2_source, s2_target) * ( s2.target()[dim] - s2.source()[dim] ));
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tgt[dim] = (z1+z2) / FT(2);
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src[Projector<R,dim>::x_index] = si->source().x();
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src[Projector<R,dim>::y_index] = si->source().y();
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tgt[Projector<R,dim>::x_index] = si->target().x();
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tgt[Projector<R,dim>::y_index] = si->target().y();
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return make_object( Segment_3( Point_3(src[0],src[1],src[2]),Point_3(tgt[0],tgt[1],tgt[2]) ) );
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}
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FT coords[3];
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//compute the third coordinate of the projected intersection point onto 3D segments
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FT z1 = s1.source()[dim] + ( alpha(*pi, s1_source, s1_target) * ( s1.target()[dim] - s1.source()[dim] ));
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FT z2 = s2.source()[dim] + ( alpha(*pi, s2_source, s2_target) * ( s2.target()[dim] - s2.source()[dim] ));
|
||
|
|
|
||
|
|
coords[dim] = (z1+z2) / FT(2);
|
||
|
|
coords[Projector<R,dim>::x_index] = pi->x();
|
||
|
|
coords[Projector<R,dim>::y_index] = pi->y();
|
||
|
|
|
||
|
|
Point_3 res(coords[0],coords[1],coords[2]);
|
||
|
|
CGAL_assertion(x(res)==pi->x() && y(res)==pi->y());
|
||
|
|
return make_object(res);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R, int dim>
|
||
|
|
class Circumcenter_center_projected
|
||
|
|
{
|
||
|
|
typedef typename R::Point_3 Point_3;
|
||
|
|
typedef typename R::Point_2 Point_2;
|
||
|
|
|
||
|
|
typename R::FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
typename R::FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
Point_2 project(const Point_3& p) const
|
||
|
|
{
|
||
|
|
return Point_2(x(p),y(p));
|
||
|
|
}
|
||
|
|
|
||
|
|
Point_3 embed (const Point_2& p) const
|
||
|
|
{
|
||
|
|
typename R::FT coords[3];
|
||
|
|
coords[Projector<R,dim>::x_index]=p.x();
|
||
|
|
coords[Projector<R,dim>::y_index]=p.y();
|
||
|
|
coords[dim]=typename R::FT(0);
|
||
|
|
return Point_3(coords[0],coords[1],coords[2]);
|
||
|
|
}
|
||
|
|
|
||
|
|
public:
|
||
|
|
Point_3 operator() (const Point_3& p1,const Point_3& p2) const
|
||
|
|
{
|
||
|
|
return embed( CGAL::circumcenter(project(p1),project(p2)) );
|
||
|
|
}
|
||
|
|
|
||
|
|
Point_3 operator() (const Point_3& p1,const Point_3& p2,const Point_3& p3) const
|
||
|
|
{
|
||
|
|
return embed( CGAL::circumcenter(project(p1),project(p2),project(p3)) );
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R, int dim>
|
||
|
|
class Compute_area_projected
|
||
|
|
{
|
||
|
|
typedef typename R::Point_3 Point_3;
|
||
|
|
typedef typename R::Point_2 Point_2;
|
||
|
|
|
||
|
|
typename R::FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
typename R::FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
Point_2 project(const Point_3& p) const
|
||
|
|
{
|
||
|
|
return Point_2(x(p),y(p));
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
public:
|
||
|
|
typename R::FT operator() (const Point_3& p1,const Point_3& p2,const Point_3& p3) const
|
||
|
|
{
|
||
|
|
return R().compute_area_2_object() ( project(p1),project(p2),project(p3) );
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R, int dim>
|
||
|
|
class Compute_squared_radius_projected
|
||
|
|
{
|
||
|
|
typedef typename R::Point_3 Point_3;
|
||
|
|
typedef typename R::Point_2 Point_2;
|
||
|
|
|
||
|
|
typename R::FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
typename R::FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
Point_2 project(const Point_3& p) const
|
||
|
|
{
|
||
|
|
return Point_2(x(p),y(p));
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
public:
|
||
|
|
typename R::FT operator() (const Point_3& p1,const Point_3& p2,const Point_3& p3) const
|
||
|
|
{
|
||
|
|
return R().compute_squared_radius_2_object() ( project(p1),project(p2),project(p3) );
|
||
|
|
}
|
||
|
|
typename R::FT operator() (const Point_3& p1,const Point_3& p2) const
|
||
|
|
{
|
||
|
|
return R().compute_squared_radius_2_object() ( project(p1),project(p2) );
|
||
|
|
}
|
||
|
|
|
||
|
|
typename R::FT operator() (const Point_3& p1) const
|
||
|
|
{
|
||
|
|
return R().compute_squared_radius_2_object() ( project(p1) );
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R,int dim>
|
||
|
|
class Compute_scalar_product_projected_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef typename R::Vector_3 Vector_3;
|
||
|
|
typedef typename R::FT FT;
|
||
|
|
FT x(const Vector_3 &v) const { return Projector<R,dim>::x(v); }
|
||
|
|
FT y(const Vector_3 &v) const { return Projector<R,dim>::y(v); }
|
||
|
|
|
||
|
|
FT operator()(const Vector_3& v1, const Vector_3& v2) const
|
||
|
|
{
|
||
|
|
return x(v1)*x(v2) + y(v1)*y(v2);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R,int dim>
|
||
|
|
class Compute_squared_length_projected_3
|
||
|
|
{
|
||
|
|
typedef typename R::Vector_3 Vector_3;
|
||
|
|
typedef typename R::FT FT;
|
||
|
|
|
||
|
|
typedef FT result_type;
|
||
|
|
|
||
|
|
FT x(const Vector_3 &v) const { return Projector<R,dim>::x(v); }
|
||
|
|
FT y(const Vector_3 &v) const { return Projector<R,dim>::y(v); }
|
||
|
|
|
||
|
|
public:
|
||
|
|
FT operator()(const Vector_3& v) const
|
||
|
|
{
|
||
|
|
return CGAL::square(x(v)) + CGAL::square(y(v));
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R, int dim>
|
||
|
|
struct Angle_projected_3{
|
||
|
|
typedef typename R::Point_3 Point_3;
|
||
|
|
typedef typename R::Point_2 Point_2;
|
||
|
|
|
||
|
|
typename R::FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
typename R::FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
Point_2 project(const Point_3& p) const
|
||
|
|
{
|
||
|
|
return Point_2(x(p),y(p));
|
||
|
|
}
|
||
|
|
|
||
|
|
CGAL::Angle operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
|
||
|
|
{
|
||
|
|
return CGAL::angle(project(p), project(q), project(r));
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
// weighted functors
|
||
|
|
template <class R, int dim>
|
||
|
|
class Compare_power_distance_projected_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef typename R::Point_2 Point_2;
|
||
|
|
typedef typename R::Weighted_point_2 Weighted_point_2;
|
||
|
|
typedef typename R::Point_3 Point_3;
|
||
|
|
typedef typename R::Weighted_point_3 Weighted_point_3;
|
||
|
|
typedef typename R::FT FT;
|
||
|
|
|
||
|
|
FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
Point_2 project(const Point_3& p) const
|
||
|
|
{
|
||
|
|
return Point_2(x(p), y(p));
|
||
|
|
}
|
||
|
|
|
||
|
|
Weighted_point_2 project(const Weighted_point_3& wp) const
|
||
|
|
{
|
||
|
|
Point_3 p = R().construct_point_3_object()(wp);
|
||
|
|
return Weighted_point_2(Point_2(x(p), y(p)), wp.weight());
|
||
|
|
}
|
||
|
|
|
||
|
|
Comparison_result operator()(const Point_3& p,
|
||
|
|
const Weighted_point_3& wq, const Weighted_point_3& wr) const
|
||
|
|
{
|
||
|
|
Point_2 p2 = project(p);
|
||
|
|
Weighted_point_2 wq2 = project(wq);
|
||
|
|
Weighted_point_2 wr2 = project(wr);
|
||
|
|
return CGAL::compare_power_distance(p2, wq2, wr2);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R, int dim>
|
||
|
|
class Compute_power_product_projected_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef typename R::Point_2 Point_2;
|
||
|
|
typedef typename R::Weighted_point_2 Weighted_point_2;
|
||
|
|
typedef typename R::Point_3 Point_3;
|
||
|
|
typedef typename R::Weighted_point_3 Weighted_point_3;
|
||
|
|
typedef typename R::FT FT;
|
||
|
|
|
||
|
|
FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
Weighted_point_2 project(const Weighted_point_3& wp) const
|
||
|
|
{
|
||
|
|
Point_3 p = R().construct_point_3_object()(wp);
|
||
|
|
return Weighted_point_2(Point_2(x(p), y(p)), wp.weight());
|
||
|
|
}
|
||
|
|
|
||
|
|
FT operator()(const Weighted_point_3& wp, const Weighted_point_3& wq) const
|
||
|
|
{
|
||
|
|
Weighted_point_2 wp2(project(wp));
|
||
|
|
Weighted_point_2 wq2(project(wq));
|
||
|
|
return CGAL::power_product(wp2, wq2);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R, int dim>
|
||
|
|
class Compute_squared_radius_smallest_orthogonal_circle_projected_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef typename R::Point_2 Point_2;
|
||
|
|
typedef typename R::Weighted_point_2 Weighted_point_2;
|
||
|
|
typedef typename R::Point_3 Point_3;
|
||
|
|
typedef typename R::Weighted_point_3 Weighted_point_3;
|
||
|
|
typedef typename R::FT FT;
|
||
|
|
|
||
|
|
FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
Weighted_point_2 project(const Weighted_point_3& wp) const
|
||
|
|
{
|
||
|
|
Point_3 p = R().construct_point_3_object()(wp);
|
||
|
|
return Weighted_point_2(Point_2(x(p), y(p)), wp.weight());
|
||
|
|
}
|
||
|
|
|
||
|
|
FT operator()(const Weighted_point_3& wp1, const Weighted_point_3& wp2, const Weighted_point_3& wp3) const
|
||
|
|
{
|
||
|
|
return CGAL::squared_radius_smallest_orthogonal_circle( project(wp1), project(wp2), project(wp3) );
|
||
|
|
}
|
||
|
|
|
||
|
|
FT operator()(const Weighted_point_3& wp1, const Weighted_point_3& wp2) const
|
||
|
|
{
|
||
|
|
return CGAL::squared_radius_smallest_orthogonal_circle( project(wp1), project(wp2) );
|
||
|
|
}
|
||
|
|
|
||
|
|
FT operator()(const Weighted_point_3& wp1) const
|
||
|
|
{
|
||
|
|
return CGAL::squared_radius_smallest_orthogonal_circle( project(wp1) );
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R, int dim>
|
||
|
|
class Construct_radical_axis_projected_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef typename R::Line_2 Line_2;
|
||
|
|
typedef typename R::Line_3 Line_3;
|
||
|
|
typedef typename R::Point_2 Point_2;
|
||
|
|
typedef typename R::Weighted_point_2 Weighted_point_2;
|
||
|
|
typedef typename R::Point_3 Point_3;
|
||
|
|
typedef typename R::Weighted_point_3 Weighted_point_3;
|
||
|
|
typedef typename R::FT FT;
|
||
|
|
|
||
|
|
FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
Weighted_point_2 project(const Weighted_point_3& wp) const
|
||
|
|
{
|
||
|
|
Point_3 p = R().construct_point_3_object()(wp);
|
||
|
|
return Weighted_point_2(Point_2(x(p), y(p)), wp.weight());
|
||
|
|
}
|
||
|
|
|
||
|
|
Line_3 embed (const Line_2& l) const
|
||
|
|
{
|
||
|
|
Point_2 p0 = l.point(0);
|
||
|
|
Point_2 p1 = l.point(1);
|
||
|
|
|
||
|
|
FT coords_p0[3];
|
||
|
|
coords_p0[Projector<R,dim>::x_index] = p0.x();
|
||
|
|
coords_p0[Projector<R,dim>::y_index] = p0.y();
|
||
|
|
coords_p0[dim] = FT(0);
|
||
|
|
|
||
|
|
FT coords_p1[3];
|
||
|
|
coords_p1[Projector<R,dim>::x_index] = p1.x();
|
||
|
|
coords_p1[Projector<R,dim>::y_index] = p1.y();
|
||
|
|
coords_p1[dim] = FT(0);
|
||
|
|
|
||
|
|
return Line_3(Point_3(coords_p0[0], coords_p0[1], coords_p0[2]),
|
||
|
|
Point_3(coords_p1[0], coords_p1[1], coords_p1[2]));
|
||
|
|
}
|
||
|
|
|
||
|
|
public:
|
||
|
|
Line_3 operator() (const Weighted_point_3& wp1, const Weighted_point_3& wp2) const
|
||
|
|
{
|
||
|
|
return embed( CGAL::radical_axis(project(wp1), project(wp2)) );
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R, int dim>
|
||
|
|
class Construct_weighted_circumcenter_projected_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef typename R::Point_2 Point_2;
|
||
|
|
typedef typename R::Weighted_point_2 Weighted_point_2;
|
||
|
|
typedef typename R::Point_3 Point_3;
|
||
|
|
typedef typename R::Weighted_point_3 Weighted_point_3;
|
||
|
|
typedef typename R::FT FT;
|
||
|
|
|
||
|
|
FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
Weighted_point_2 project(const Weighted_point_3& wp) const
|
||
|
|
{
|
||
|
|
Point_3 p = R().construct_point_3_object()(wp);
|
||
|
|
return Weighted_point_2(Point_2(x(p), y(p)), wp.weight());
|
||
|
|
}
|
||
|
|
|
||
|
|
Point_3 embed (const Point_2& p) const
|
||
|
|
{
|
||
|
|
FT coords[3];
|
||
|
|
coords[Projector<R,dim>::x_index] = p.x();
|
||
|
|
coords[Projector<R,dim>::y_index] = p.y();
|
||
|
|
coords[dim] = FT(0);
|
||
|
|
|
||
|
|
return Point_3(coords[0], coords[1], coords[2]);
|
||
|
|
}
|
||
|
|
|
||
|
|
public:
|
||
|
|
Point_3 operator()(const Weighted_point_3& wp1,
|
||
|
|
const Weighted_point_3& wp2,
|
||
|
|
const Weighted_point_3& wp3) const
|
||
|
|
{
|
||
|
|
return embed( CGAL::weighted_circumcenter(project(wp1), project(wp2), project(wp3)) );
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R, int dim>
|
||
|
|
class Power_side_of_bounded_power_circle_projected_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef typename R::Point_2 Point_2;
|
||
|
|
typedef typename R::Weighted_point_2 Weighted_point_2;
|
||
|
|
typedef typename R::Point_3 Point_3;
|
||
|
|
typedef typename R::Weighted_point_3 Weighted_point_3;
|
||
|
|
typedef typename R::FT FT;
|
||
|
|
|
||
|
|
FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
Weighted_point_2 project(const Weighted_point_3& wp) const
|
||
|
|
{
|
||
|
|
Point_3 p = R().construct_point_3_object()(wp);
|
||
|
|
return Weighted_point_2(Point_2(x(p), y(p)), wp.weight());
|
||
|
|
}
|
||
|
|
|
||
|
|
CGAL::Bounded_side operator()(const Weighted_point_3 &wp,
|
||
|
|
const Weighted_point_3 &wq,
|
||
|
|
const Weighted_point_3 &wr,
|
||
|
|
const Weighted_point_3 &ws) const
|
||
|
|
{
|
||
|
|
return CGAL::power_side_of_bounded_power_circle(project(wp), project(wq),
|
||
|
|
project(wr), project(ws));
|
||
|
|
}
|
||
|
|
|
||
|
|
CGAL::Bounded_side operator()(const Weighted_point_3 &wp,
|
||
|
|
const Weighted_point_3 &wq,
|
||
|
|
const Weighted_point_3 &wr) const
|
||
|
|
{
|
||
|
|
return CGAL::power_side_of_bounded_power_circle(project(wp), project(wq), project(wr));
|
||
|
|
}
|
||
|
|
|
||
|
|
CGAL::Bounded_side operator()(const Weighted_point_3 &wp,
|
||
|
|
const Weighted_point_3 &wq) const
|
||
|
|
{
|
||
|
|
return CGAL::power_side_of_bounded_power_circle(project(wp), project(wq));
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template <class R, int dim>
|
||
|
|
class Power_side_of_oriented_power_circle_projected_3
|
||
|
|
{
|
||
|
|
public:
|
||
|
|
typedef typename R::Point_2 Point_2;
|
||
|
|
typedef typename R::Weighted_point_2 Weighted_point_2;
|
||
|
|
typedef typename R::Point_3 Point_3;
|
||
|
|
typedef typename R::Weighted_point_3 Weighted_point_3;
|
||
|
|
typedef typename R::FT FT;
|
||
|
|
|
||
|
|
FT x(const Point_3 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
FT y(const Point_3 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
Weighted_point_2 project(const Weighted_point_3& wp) const
|
||
|
|
{
|
||
|
|
Point_3 p = R().construct_point_3_object()(wp);
|
||
|
|
return Weighted_point_2(Point_2(x(p), y(p)), wp.weight());
|
||
|
|
}
|
||
|
|
|
||
|
|
CGAL::Oriented_side operator()(const Weighted_point_3 &wp,
|
||
|
|
const Weighted_point_3 &wq,
|
||
|
|
const Weighted_point_3 &wr,
|
||
|
|
const Weighted_point_3 &ws) const
|
||
|
|
{
|
||
|
|
return CGAL::power_side_of_oriented_power_circle(project(wp), project(wq),
|
||
|
|
project(wr), project(ws));
|
||
|
|
}
|
||
|
|
|
||
|
|
CGAL::Oriented_side operator()(const Weighted_point_3 &wp,
|
||
|
|
const Weighted_point_3 &wq,
|
||
|
|
const Weighted_point_3 &wr) const
|
||
|
|
{
|
||
|
|
return CGAL::power_side_of_oriented_power_circle(project(wp), project(wq), project(wr));
|
||
|
|
}
|
||
|
|
|
||
|
|
CGAL::Oriented_side operator()(const Weighted_point_3 &wp,
|
||
|
|
const Weighted_point_3 &wq) const
|
||
|
|
{
|
||
|
|
return CGAL::power_side_of_oriented_power_circle(project(wp), project(wq));
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
template < class R, int dim >
|
||
|
|
class Projection_traits_3 {
|
||
|
|
public:
|
||
|
|
typedef Projection_traits_3<R,dim> Traits;
|
||
|
|
typedef R Rp;
|
||
|
|
typedef typename R::FT FT;
|
||
|
|
typedef typename Rp::Point_3 Point_2;
|
||
|
|
typedef typename Rp::Weighted_point_3 Weighted_point_2;
|
||
|
|
typedef typename Rp::Segment_3 Segment_2;
|
||
|
|
typedef typename Rp::Vector_3 Vector_2;
|
||
|
|
typedef typename Rp::Triangle_3 Triangle_2;
|
||
|
|
typedef typename Rp::Line_3 Line_2;
|
||
|
|
typedef typename Rp::Ray_3 Ray_2;
|
||
|
|
|
||
|
|
typedef typename Projector<R,dim>::Less_x_2 Less_x_2;
|
||
|
|
typedef typename Projector<R,dim>::Less_y_2 Less_y_2;
|
||
|
|
typedef typename Projector<R,dim>::Compare_x_2 Compare_x_2;
|
||
|
|
typedef typename Projector<R,dim>::Compare_y_2 Compare_y_2;
|
||
|
|
typedef Orientation_projected_3<Rp,dim> Orientation_2;
|
||
|
|
typedef Angle_projected_3<Rp,dim> Angle_2;
|
||
|
|
typedef Side_of_oriented_circle_projected_3<Rp,dim> Side_of_oriented_circle_2;
|
||
|
|
typedef Less_signed_distance_to_line_projected_3<Rp,dim> Less_signed_distance_to_line_2;
|
||
|
|
typedef Side_of_bounded_circle_projected_3<Rp,dim> Side_of_bounded_circle_2;
|
||
|
|
typedef Compare_distance_projected_3<Rp,dim> Compare_distance_2;
|
||
|
|
typedef Collinear_are_ordered_along_line_projected_3<Rp,dim> Collinear_are_ordered_along_line_2;
|
||
|
|
typedef Squared_distance_projected_3<Rp,dim> Compute_squared_distance_2;
|
||
|
|
typedef Intersect_projected_3<Rp,dim> Intersect_2;
|
||
|
|
typedef Compute_squared_radius_projected<Rp,dim> Compute_squared_radius_2;
|
||
|
|
typedef Compute_scalar_product_projected_3<Rp,dim> Compute_scalar_product_2;
|
||
|
|
typedef Compute_squared_length_projected_3<Rp,dim> Compute_squared_length_2;
|
||
|
|
|
||
|
|
typedef Compare_power_distance_projected_3<Rp,dim> Compare_power_distance_2;
|
||
|
|
typedef Compute_power_product_projected_3<Rp,dim> Compute_power_product_2;
|
||
|
|
typedef Compute_squared_radius_smallest_orthogonal_circle_projected_3<Rp,dim>
|
||
|
|
Compute_squared_radius_smallest_orthogonal_circle_2;
|
||
|
|
typedef Construct_radical_axis_projected_3<Rp,dim> Construct_radical_axis_2;
|
||
|
|
typedef Construct_weighted_circumcenter_projected_3<Rp,dim> Construct_weighted_circumcenter_2;
|
||
|
|
typedef Power_side_of_bounded_power_circle_projected_3<Rp,dim> Power_side_of_bounded_power_circle_2;
|
||
|
|
typedef Power_side_of_oriented_power_circle_projected_3<Rp, dim> Power_side_of_oriented_power_circle_2;
|
||
|
|
|
||
|
|
typedef typename Rp::Construct_point_3 Construct_point_2;
|
||
|
|
typedef typename Rp::Construct_weighted_point_3 Construct_weighted_point_2;
|
||
|
|
typedef typename Rp::Construct_segment_3 Construct_segment_2;
|
||
|
|
typedef typename Rp::Construct_translated_point_3 Construct_translated_point_2;
|
||
|
|
typedef typename Rp::Construct_midpoint_3 Construct_midpoint_2;
|
||
|
|
typedef typename Rp::Construct_vector_3 Construct_vector_2;
|
||
|
|
typedef typename Rp::Construct_scaled_vector_3 Construct_scaled_vector_2;
|
||
|
|
typedef typename Rp::Construct_triangle_3 Construct_triangle_2;
|
||
|
|
typedef typename Rp::Construct_line_3 Construct_line_2;
|
||
|
|
typedef typename Rp::Construct_bbox_3 Construct_bbox_2;
|
||
|
|
|
||
|
|
struct Less_xy_2 {
|
||
|
|
typedef bool result_type;
|
||
|
|
bool operator()(const Point_2& p, const Point_2& q) const
|
||
|
|
{
|
||
|
|
Compare_x_2 cx;
|
||
|
|
Comparison_result crx = cx(p,q);
|
||
|
|
if(crx == SMALLER){ return true;}
|
||
|
|
if(crx == LARGER){return false;}
|
||
|
|
Less_y_2 ly;
|
||
|
|
return ly(p,q);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
struct Less_yx_2 {
|
||
|
|
typedef bool result_type;
|
||
|
|
bool operator()(const Point_2& p, const Point_2& q) const
|
||
|
|
{
|
||
|
|
Compare_y_2 cy;
|
||
|
|
Comparison_result cry = cy(p,q);
|
||
|
|
if(cry == SMALLER){ return true;}
|
||
|
|
if(cry == LARGER){return false;}
|
||
|
|
Less_x_2 lx;
|
||
|
|
return lx(p,q);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
struct Equal_2 {
|
||
|
|
typedef bool result_type;
|
||
|
|
bool operator()(const Point_2& p, const Point_2& q) const
|
||
|
|
{
|
||
|
|
|
||
|
|
Equal_x_2 eqx;
|
||
|
|
Equal_y_2 eqy;
|
||
|
|
return eqx(p,q) & eqy(p,q);
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
struct Left_turn_2 {
|
||
|
|
typedef bool result_type;
|
||
|
|
bool operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
|
||
|
|
{
|
||
|
|
|
||
|
|
Orientation_2 ori;
|
||
|
|
return ori(p,q,r) == LEFT_TURN;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
struct Collinear_2 {
|
||
|
|
typedef bool result_type;
|
||
|
|
bool operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
|
||
|
|
{
|
||
|
|
Orientation_2 ori;
|
||
|
|
return ori(p,q,r) == COLLINEAR;
|
||
|
|
}
|
||
|
|
};
|
||
|
|
|
||
|
|
//for natural_neighbor_coordinates_2
|
||
|
|
typedef typename Projector<R,dim>::Equal_x_2 Equal_x_2;
|
||
|
|
typedef typename Projector<R,dim>::Equal_y_2 Equal_y_2;
|
||
|
|
typedef Circumcenter_center_projected<Rp,dim> Construct_circumcenter_2;
|
||
|
|
typedef Compute_area_projected<Rp,dim> Compute_area_2;
|
||
|
|
Construct_circumcenter_2 construct_circumcenter_2_object () const {return Construct_circumcenter_2();}
|
||
|
|
Compute_area_2 compute_area_2_object () const {return Compute_area_2();}
|
||
|
|
|
||
|
|
|
||
|
|
// for compatibility with previous versions
|
||
|
|
typedef Point_2 Point;
|
||
|
|
typedef Segment_2 Segment;
|
||
|
|
typedef Triangle_2 Triangle;
|
||
|
|
|
||
|
|
Projection_traits_3(){}
|
||
|
|
Projection_traits_3(
|
||
|
|
const Projection_traits_3&){}
|
||
|
|
Projection_traits_3 &operator=(
|
||
|
|
const Projection_traits_3&){return *this;}
|
||
|
|
|
||
|
|
typename Rp::FT x(const Point_2 &p) const { return Projector<R,dim>::x(p); }
|
||
|
|
typename Rp::FT y(const Point_2 &p) const { return Projector<R,dim>::y(p); }
|
||
|
|
|
||
|
|
|
||
|
|
Equal_2
|
||
|
|
equal_2_object() const
|
||
|
|
{ return Equal_2();}
|
||
|
|
|
||
|
|
Left_turn_2
|
||
|
|
left_turn_2_object() const
|
||
|
|
{ return Left_turn_2();}
|
||
|
|
|
||
|
|
Less_x_2
|
||
|
|
less_x_2_object() const
|
||
|
|
{ return Less_x_2();}
|
||
|
|
|
||
|
|
Less_xy_2
|
||
|
|
less_xy_2_object() const
|
||
|
|
{ return Less_xy_2();}
|
||
|
|
|
||
|
|
Less_yx_2
|
||
|
|
less_yx_2_object() const
|
||
|
|
{ return Less_yx_2();}
|
||
|
|
|
||
|
|
Less_signed_distance_to_line_2
|
||
|
|
less_signed_distance_to_line_2_object() const
|
||
|
|
{return Less_signed_distance_to_line_2();}
|
||
|
|
|
||
|
|
Less_y_2
|
||
|
|
less_y_2_object() const
|
||
|
|
{ return Less_y_2();}
|
||
|
|
Compare_x_2
|
||
|
|
compare_x_2_object() const
|
||
|
|
{ return Compare_x_2();}
|
||
|
|
Angle_2
|
||
|
|
angle_2_object() const {
|
||
|
|
return Angle_2();
|
||
|
|
}
|
||
|
|
|
||
|
|
Compare_y_2
|
||
|
|
compare_y_2_object() const
|
||
|
|
{ return Compare_y_2();}
|
||
|
|
|
||
|
|
Orientation_2
|
||
|
|
orientation_2_object() const
|
||
|
|
{ return Orientation_2();}
|
||
|
|
|
||
|
|
Side_of_oriented_circle_2
|
||
|
|
side_of_oriented_circle_2_object() const
|
||
|
|
{return Side_of_oriented_circle_2();}
|
||
|
|
|
||
|
|
Side_of_bounded_circle_2
|
||
|
|
side_of_bounded_circle_2_object() const
|
||
|
|
{return Side_of_bounded_circle_2();}
|
||
|
|
|
||
|
|
Compare_distance_2
|
||
|
|
compare_distance_2_object() const
|
||
|
|
{
|
||
|
|
return Compare_distance_2();
|
||
|
|
}
|
||
|
|
|
||
|
|
Compute_squared_distance_2
|
||
|
|
compute_squared_distance_2_object () const
|
||
|
|
{
|
||
|
|
return Compute_squared_distance_2();
|
||
|
|
}
|
||
|
|
|
||
|
|
Compute_squared_radius_2
|
||
|
|
compute_squared_radius_2_object () const
|
||
|
|
{
|
||
|
|
return Compute_squared_radius_2();
|
||
|
|
}
|
||
|
|
|
||
|
|
Intersect_2
|
||
|
|
intersect_2_object () const
|
||
|
|
{
|
||
|
|
return Intersect_2();
|
||
|
|
}
|
||
|
|
|
||
|
|
Construct_point_2 construct_point_2_object() const
|
||
|
|
{ return Construct_point_2();}
|
||
|
|
|
||
|
|
Construct_weighted_point_2 construct_weighted_point_2_object() const
|
||
|
|
{ return Construct_weighted_point_2();}
|
||
|
|
|
||
|
|
Construct_segment_2 construct_segment_2_object() const
|
||
|
|
{return Construct_segment_2();}
|
||
|
|
|
||
|
|
Construct_translated_point_2 construct_translated_point_2_object() const
|
||
|
|
{return Construct_translated_point_2();}
|
||
|
|
|
||
|
|
Construct_midpoint_2 construct_midpoint_2_object() const
|
||
|
|
{return Construct_midpoint_2();}
|
||
|
|
|
||
|
|
Construct_vector_2 construct_vector_2_object() const
|
||
|
|
{return Construct_vector_2();}
|
||
|
|
|
||
|
|
Construct_scaled_vector_2 construct_scaled_vector_2_object() const
|
||
|
|
{return Construct_scaled_vector_2();}
|
||
|
|
|
||
|
|
Construct_triangle_2 construct_triangle_2_object() const
|
||
|
|
{return Construct_triangle_2();}
|
||
|
|
|
||
|
|
Construct_line_2 construct_line_2_object() const
|
||
|
|
{return Construct_line_2();}
|
||
|
|
|
||
|
|
Construct_bbox_2 construct_bbox_2_object() const
|
||
|
|
{return Construct_bbox_2();}
|
||
|
|
|
||
|
|
Compute_scalar_product_2 compute_scalar_product_2_object() const
|
||
|
|
{return Compute_scalar_product_2();}
|
||
|
|
|
||
|
|
Collinear_2 collinear_2_object() const
|
||
|
|
{return Collinear_2();}
|
||
|
|
|
||
|
|
Collinear_are_ordered_along_line_2 collinear_are_ordered_along_line_2_object() const
|
||
|
|
{return Collinear_are_ordered_along_line_2();}
|
||
|
|
|
||
|
|
Compute_squared_length_2 compute_squared_length_2_object() const
|
||
|
|
{return Compute_squared_length_2();}
|
||
|
|
|
||
|
|
Compare_power_distance_2 compare_power_distance_2_object() const
|
||
|
|
{return Compare_power_distance_2();}
|
||
|
|
|
||
|
|
Compute_power_product_2 compute_power_product_2_object() const
|
||
|
|
{return Compute_power_product_2();}
|
||
|
|
|
||
|
|
Compute_squared_radius_smallest_orthogonal_circle_2
|
||
|
|
compute_squared_radius_smallest_orthogonal_circle_2_object() const
|
||
|
|
{return Compute_squared_radius_smallest_orthogonal_circle_2();}
|
||
|
|
|
||
|
|
Construct_radical_axis_2 construct_radical_axis_2_object() const
|
||
|
|
{return Construct_radical_axis_2();}
|
||
|
|
|
||
|
|
Construct_weighted_circumcenter_2 construct_weighted_circumcenter_2_object() const
|
||
|
|
{return Construct_weighted_circumcenter_2();}
|
||
|
|
|
||
|
|
Power_side_of_bounded_power_circle_2 power_side_of_bounded_power_circle_2_object() const
|
||
|
|
{return Power_side_of_bounded_power_circle_2();}
|
||
|
|
|
||
|
|
Power_side_of_oriented_power_circle_2 power_side_of_oriented_power_circle_2_object() const
|
||
|
|
{return Power_side_of_oriented_power_circle_2();}
|
||
|
|
};
|
||
|
|
|
||
|
|
|
||
|
|
} } //namespace CGAL::internal
|
||
|
|
|
||
|
|
#endif // CGAL_INTERNAL_PROJECTION_TRAITS_3_H
|