mirror of https://github.com/CGAL/cgal
Removed old traits class (moved to branch INRIA/Periodic_2g_hyperbolic_triangulation_2-IIordanov)
This commit is contained in:
Iordan Iordanov
parent
71327aad01
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e9abcec1df
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// Copyright (c) 2010-2018 INRIA Sophia Antipolis, INRIA Nancy (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).
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// You can redistribute it and/or modify it under the terms of the GNU
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// General Public License as published by the Free Software Foundation,
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// either version 3 of the License, or (at your option) any later version.
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//
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// Licensees holding a valid commercial license may use this file in
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// accordance with the commercial license agreement provided with the software.
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//
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// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
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// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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//
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// $URL$
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// $Id$
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// SPDX-License-Identifier: GPL-3.0+
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//
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// Author(s) : Mikhail Bogdanov
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// Monique Teillaud <Monique.Teillaud@inria.fr>
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#ifndef CGAL_HYPERBOLIC_DELAUNAY_TRIANGULATION_OLD_TRAITS_2_H
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#define CGAL_HYPERBOLIC_DELAUNAY_TRIANGULATION_OLD_TRAITS_2_H
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#include <CGAL/license/Hyperbolic_triangulation_2.h>
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//#include <CGAL/Regular_triangulation_filtered_traits_2.h>
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#include <CGAL/predicates_on_points_2.h>
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#include <CGAL/basic_constructions_2.h>
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#include <CGAL/distance_predicates_2.h>
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#include <CGAL/determinant.h>
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#include "boost/tuple/tuple.hpp"
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#include "boost/variant.hpp"
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namespace CGAL {
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template < class R >
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class Hyperbolic_Delaunay_triangulation_old_traits_2
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: public R
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{
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public:
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typedef typename R::FT FT;
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typedef typename R::Point_2 Point_2;
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typedef Point_2 Hyperbolic_point_2;
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typedef Hyperbolic_point_2 Hyperbolic_Voronoi_point_2;
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typedef typename R::Circle_2 Circle_2;
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typedef typename R::Triangle_2 Hyperbolic_triangle_2;
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typedef boost::tuple<Circle_2, Point_2, Point_2> Arc_2;
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typedef typename R::Segment_2 Euclidean_segment_2; //only used internally here
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typedef boost::variant<Arc_2, Euclidean_segment_2> Hyperbolic_segment_2;
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typedef typename R::Compare_x_2 Compare_x_2;
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typedef typename R::Compare_y_2 Compare_y_2;
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typedef typename R::Orientation_2 Orientation_2;
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typedef typename R::Side_of_oriented_circle_2 Side_of_oriented_circle_2;
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// only kept for demo to please T2graphicsitems
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typedef Euclidean_segment_2 Line_segment_2;
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typedef Hyperbolic_segment_2 Segment_2;
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// the following types are only used internally in this traits class,
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// so they need not be documented, and they don't need _object()
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typedef typename R::Collinear_2 Euclidean_collinear_2;
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typedef typename R::Construct_bisector_2 Construct_Euclidean_bisector_2;
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typedef typename R::Construct_midpoint_2 Construct_Euclidean_midpoint_2;
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typedef typename R::Compute_squared_distance_2 Compute_squared_Euclidean_distance_2;
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typedef typename R::Line_2 Euclidean_line_2;
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typedef typename R::Vector_2 Vector_2;
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// used by Is_hyperbolic
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typedef typename R::Vector_3 Vector_3;
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typedef typename R::Point_3 Point_3;
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// MT useless?
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// typedef Hyperbolic_Delaunay_triangulation_traits_2<R> Self;
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// typedef typename R::RT RT;
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// typedef R Kernel;
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// typedef R Rep;
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// typedef typename R::Triangle_2 Triangle_2;
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// typedef typename R::Line_2 Line_2;
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// typedef typename R::Ray_2 Ray_2; // why would we need Eucldean rays??
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// typedef typename R::Iso_rectangle_2 Iso_rectangle_2;
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// typedef typename R::Angle_2 Angle_2;
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// typedef typename R::Less_x_2 Less_x_2;
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// typedef typename R::Less_y_2 Less_y_2;
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// typedef typename R::Compare_distance_2 Compare_distance_2;
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// typedef typename R::Construct_triangle_2 Construct_triangle_2;
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// typedef typename R::Construct_direction_2 Construct_direction_2;
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public:
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class Side_of_oriented_hyperbolic_segment_2 {};
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class Construct_hyperbolic_segment_2
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{
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//typedef typename CGAL::Regular_triangulation_filtered_traits_2<R> Regular_geometric_traits_2;
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typedef R Regular_geometric_traits_2;
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typedef typename Regular_geometric_traits_2::Construct_weighted_circumcenter_2 Construct_weighted_circumcenter_2;
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typedef typename Regular_geometric_traits_2::Weighted_point_2 Weighted_point_2;
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typedef typename Regular_geometric_traits_2::Bare_point Bare_point;
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public:
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Construct_hyperbolic_segment_2()
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{
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}
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Hyperbolic_segment_2 operator()(const Point_2& p, const Point_2& q) const
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{
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Origin o;
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if(Euclidean_collinear_2()(p, q, Point_2(o))){
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return Euclidean_segment_2(p, q);
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}
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Weighted_point_2 wp(p);
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Weighted_point_2 wq(q);
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Weighted_point_2 wo(Point_2(o), FT(1)); // Poincaré circle
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Bare_point center = Construct_weighted_circumcenter_2()(wp, wo, wq);
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FT radius = Compute_squared_Euclidean_distance_2()(p, center);
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Circle_2 circle( center, radius);
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// uncomment!!!
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//assert(circle.has_on_boundary(p) && circle.has_on_boundary(q));
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if(Orientation_2()(p, q, center) == LEFT_TURN) {
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return Arc_2(circle, p, q);
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}
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return Arc_2(circle, q, p);
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}
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};
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Construct_hyperbolic_segment_2
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construct_hyperbolic_segment_2_object() const
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{ return Construct_hyperbolic_segment_2(); }
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// wrong names kept for demo
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typedef Construct_hyperbolic_segment_2 Construct_segment_2;
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Construct_segment_2
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construct_segment_2_object() const
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{ return Construct_hyperbolic_segment_2(); }
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class Construct_circumcenter_2
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{
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public:
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// TODO: improve this function
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Point_2 operator()(Point_2 p, Point_2 q, Point_2 r)
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{
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CGAL_triangulation_assertion_code(Origin oo; Point_2 poo(oo); Circle_2 co(poo,FT(1)));
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CGAL_triangulation_assertion(co.bounded_side(p) == ON_BOUNDED_SIDE);
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CGAL_triangulation_assertion(co.bounded_side(q) == ON_BOUNDED_SIDE);
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CGAL_triangulation_assertion(co.bounded_side(r) == ON_BOUNDED_SIDE);
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Circle_2 circle(p, q, r);
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// circle must be inside the unit one
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CGAL_triangulation_assertion(do_intersect(co, circle) == false);
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Origin o;
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Point_2 po = Point_2(o);
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if(circle.center() == po)
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{ return po; }
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FT x0 = circle.center().x(), y0 = circle.center().y();
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// a*alphaˆ2 + b*alpha + c = 0;
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FT a = x0*x0 + y0*y0;
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FT b = a - circle.squared_radius() + FT(1); // Poincare disc has radius 1
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FT D = b*b - 4*a;
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FT alpha = (b - CGAL::sqrt(to_double(D)))/(2*a);
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Point_2 center(x0*alpha, y0*alpha);
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if(!circle.has_on_bounded_side(center))
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{ std::cout << "Center does not belong to the pencil of spheres!!!" << std::endl;} ;
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return center;
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}
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};
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Construct_circumcenter_2
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construct_circumcenter_2_object()
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{ return Construct_circumcenter_2(); }
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Hyperbolic_Delaunay_triangulation_old_traits_2()
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{}
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Hyperbolic_Delaunay_triangulation_old_traits_2(const Hyperbolic_Delaunay_triangulation_old_traits_2 & other)
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{}
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Hyperbolic_Delaunay_triangulation_old_traits_2 &operator=
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(const Hyperbolic_Delaunay_triangulation_old_traits_2 &)
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{
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return *this;
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}
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Compare_x_2
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compare_x_2_object() const
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{ return Compare_x_2();}
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Compare_y_2
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compare_y_2_object() const
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{ return Compare_y_2();}
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Orientation_2
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orientation_2_object() const
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{ return Orientation_2();}
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Side_of_oriented_circle_2
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side_of_oriented_circle_2_object() const
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{ return Side_of_oriented_circle_2(); }
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Construct_circumcenter_2
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construct_circumcenter_2_object() const
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{ return Construct_circumcenter_2(); }
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class Construct_hyperbolic_bisector_2
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{
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public:
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Construct_hyperbolic_bisector_2()
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{}
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Hyperbolic_segment_2 operator()(Point_2 p, Point_2 q) const
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{
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// If two points are almost of the same distance to the origin, then
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// the bisector is supported by the circle of huge radius etc.
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// This circle is computed inexactly.
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// At present time, in this case the bisector is supported by the line.
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Compute_squared_Euclidean_distance_2 dist = Compute_squared_Euclidean_distance_2();
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Origin o;
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Point_2 po = Point_2(o);
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FT dif = dist(po, p) - dist(po, q);
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FT eps = 0.0000000001;
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// Bisector is straight in euclidean sense
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if(dif > -eps && dif < eps){
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// ideally
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//if(Compare_distance_2()(origin, p, q) == EQUAL){
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// TODO: calling R::Construct_bisector
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Euclidean_line_2 l = Construct_Euclidean_bisector_2()(p, q);
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// compute the ending points
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std::pair<Point_2, Point_2> points = find_intersection(l);
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// TODO: improve
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Vector_2 v(points.first, points.second);
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if(v*l.to_vector() > 0){
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return Euclidean_segment_2(points.first, points.second);
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}
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return Euclidean_segment_2(points.second, points.first);
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}
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Circle_2 c = construct_supporting_circle_of_bisector(p, q);
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// compute the ending points
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std::pair<Point_2, Point_2> points = find_intersection(c);
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if(Orientation_2()(points.first, points.second, c.center()) == LEFT_TURN) {
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return Arc_2(c, points.first, points.second);
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}
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return Arc_2(c, points.second, points.first);
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}
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private:
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// The cirle belongs to the pencil with limit points p and q
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Circle_2 construct_supporting_circle_of_bisector(Point_2 p, Point_2 q) const
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{
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// p, q are zero-circles
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// (x, y, xˆ2 + yˆ2 - rˆ2) = alpha*(xp, yp, xpˆ2 + ypˆ2) + (1-alpha)*(xq, yq, xqˆ2 + yqˆ2)
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// xˆ2 + yˆ2 - rˆ2 = Rˆ2, where R - is a radius of the given unit circle
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FT op = p.x()*p.x() + p.y()*p.y();
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FT oq = q.x()*q.x() + q.y()*q.y();
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FT alpha = (FT(1) - oq) / (op - oq); // Poincare disc has radius 1
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FT x = alpha*p.x() + (1-alpha)*q.x();
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FT y = alpha*p.y() + (1-alpha)*q.y();
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FT radius = x*x + y*y - FT(1);
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//improve
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Euclidean_line_2 l = Construct_Euclidean_bisector_2()(p, q);
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Point_2 middle = Construct_Euclidean_midpoint_2()(p, q);
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Point_2 temp = middle + l.to_vector();
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if(Orientation_2()(middle, temp, Point_2(x, y)) == ON_POSITIVE_SIDE){
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return Circle_2(Point_2(x, y), radius, CLOCKWISE);
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}
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return Circle_2(Point_2(x, y), radius, COUNTERCLOCKWISE);
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}
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// Find intersection of an input circle orthogonal to the Poincare disk
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// and the circle representing this disk
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// TODO: sqrt(to_double()?)
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std::pair<Point_2, Point_2> find_intersection(Circle_2& circle) const
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{
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FT x = circle.center().x(), y = circle.center().y();
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// axˆ2 + 2bˆx + c = 0;
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FT a = x*x + y*y;
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/* FT b = -_unit_circle.squared_radius() * x; */
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/* FT c = _unit_circle.squared_radius()*_unit_circle.squared_radius() - _unit_circle.squared_radius()*y*y; */
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FT b = -x;
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FT c = 1-y*y;
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assert(b*b - a*c > 0);
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FT D = CGAL::sqrt(to_double(b*b - a*c));
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FT x1 = (-b - D)/a;
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FT x2 = (-b + D)/a;
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FT y1 = (FT(1) - x1*x)/y;
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FT y2 = (FT(1) - x2*x)/y;
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return std::make_pair(Point_2(x1, y1), Point_2(x2, y2));
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}
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// Find intersection of an input line orthogonal to the Poincare disk
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// and the circle representing this disk
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// TODO: sqrt(to_double()?)
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std::pair<Point_2, Point_2> find_intersection(Euclidean_line_2& l) const
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{
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typedef typename R::Vector_2 Vector_2;
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Vector_2 v = l.to_vector();
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// normalize the vector
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FT squared_coeff = FT(1)/v.squared_length();
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FT coeff = CGAL::sqrt(to_double(squared_coeff));
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Point_2 p1(coeff*v.x(), coeff*v.y());
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Point_2 p2(-p1.x(), -p1.y());
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return std::make_pair(p1, p2);
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}
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};
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Construct_hyperbolic_bisector_2
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construct_hyperbolic_bisector_2_object() const
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{ return Construct_hyperbolic_bisector_2(); }
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Construct_Euclidean_bisector_2
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construct_Euclidean_bisector_2_object() const
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{ return Construct_Euclidean_bisector_2(); }
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class Construct_ray_2
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{
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public:
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Construct_ray_2()
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{}
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Hyperbolic_segment_2 operator()(Point_2 p, Hyperbolic_segment_2 l) const
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{
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if(Euclidean_segment_2* s = boost::get<Euclidean_segment_2>(&l)){
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return operator()(p, *s);
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}
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if(Arc_2* arc = boost::get<Arc_2>(&l)){
|
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if(get<0>(*arc).orientation() == CLOCKWISE){
|
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get<1>(*arc) = p;
|
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return *arc;
|
|
||||||
}
|
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||||||
get<2>(*arc) = p;
|
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return *arc;
|
|
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}
|
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||||||
assert(false);
|
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||||||
return Hyperbolic_segment_2();
|
|
||||||
}
|
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||||||
|
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||||||
Hyperbolic_segment_2 operator()(Point_2 p, Euclidean_segment_2 s) const
|
|
||||||
{
|
|
||||||
return Euclidean_segment_2(p, s.target());
|
|
||||||
}
|
|
||||||
|
|
||||||
};
|
|
||||||
|
|
||||||
Construct_ray_2
|
|
||||||
construct_ray_2_object() const
|
|
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{ return Construct_ray_2(); }
|
|
||||||
|
|
||||||
// For details see the JoCG paper (5:56-85, 2014)
|
|
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class Is_Delaunay_hyperbolic
|
|
||||||
{
|
|
||||||
public:
|
|
||||||
|
|
||||||
bool operator() (const Point_2& p0, const Point_2& p1, const Point_2& p2) const
|
|
||||||
{
|
|
||||||
Vector_3 v0 = Vector_3(p0.x()*p0.x() + p0.y()*p0.y(),
|
|
||||||
p1.x()*p1.x() + p1.y()*p1.y(),
|
|
||||||
p2.x()*p2.x() + p2.y()*p2.y());
|
|
||||||
|
|
||||||
Vector_3 v1 = Vector_3(p0.x(), p1.x(), p2.x());
|
|
||||||
Vector_3 v2 = Vector_3(p0.y(), p1.y(), p2.y());
|
|
||||||
Vector_3 v3 = Vector_3(FT(1), FT(1), FT(1));
|
|
||||||
|
|
||||||
FT dt0 = determinant(v0, v1, v3);
|
|
||||||
FT dt1 = determinant(v0, v2, v3);
|
|
||||||
FT dt2 = determinant(v0 - v3, v1, v2);
|
|
||||||
|
|
||||||
return dt0*dt0 + dt1*dt1 - dt2*dt2 < 0;
|
|
||||||
}
|
|
||||||
|
|
||||||
bool operator() (const Point_2& p0, const Point_2& p1, const Point_2& p2, int& ind) const
|
|
||||||
{
|
|
||||||
if(this->operator()(p0, p1, p2) == false) {
|
|
||||||
ind = find_non_hyperbolic_edge(p0, p1, p2);
|
|
||||||
return false;
|
|
||||||
}
|
|
||||||
return true;
|
|
||||||
}
|
|
||||||
|
|
||||||
private:
|
|
||||||
|
|
||||||
// assume the face (p0, p1, p2) is non-hyperbolic
|
|
||||||
int find_non_hyperbolic_edge(const Point_2& p0, const Point_2& p1, const Point_2& p2) const
|
|
||||||
{
|
|
||||||
typedef typename R::Direction_2 Direction_2;
|
|
||||||
|
|
||||||
Vector_3 v0 = Vector_3(p0.x()*p0.x() + p0.y()*p0.y(),
|
|
||||||
p1.x()*p1.x() + p1.y()*p1.y(),
|
|
||||||
p2.x()*p2.x() + p2.y()*p2.y());
|
|
||||||
|
|
||||||
Vector_3 v1 = Vector_3(p0.x(), p1.x(), p2.x());
|
|
||||||
Vector_3 v2 = Vector_3(p0.y(), p1.y(), p2.y());
|
|
||||||
Vector_3 v3 = Vector_3(FT(1), FT(1), FT(1));
|
|
||||||
|
|
||||||
FT dt0 = determinant(v0, 2*v2, -v3);
|
|
||||||
FT dt1 = determinant(2*v1, v0, -v3);
|
|
||||||
FT dt2 = determinant(2*v1, 2*v2, -v3);
|
|
||||||
|
|
||||||
Direction_2 d0(p0.x()*dt2 - dt0, p0.y()*dt2 - dt1);
|
|
||||||
Direction_2 d1(p1.x()*dt2 - dt0, p1.y()*dt2 - dt1);
|
|
||||||
Direction_2 d2(p2.x()*dt2 - dt0, p2.y()*dt2 - dt1);
|
|
||||||
|
|
||||||
Direction_2 d(dt0, dt1);
|
|
||||||
|
|
||||||
if(d.counterclockwise_in_between(d0, d1)) {
|
|
||||||
return 2;
|
|
||||||
}
|
|
||||||
|
|
||||||
if(d.counterclockwise_in_between(d1, d2)) {
|
|
||||||
return 0;
|
|
||||||
}
|
|
||||||
|
|
||||||
return 1;
|
|
||||||
}
|
|
||||||
};
|
|
||||||
|
|
||||||
Is_Delaunay_hyperbolic
|
|
||||||
Is_Delaunay_hyperbolic_object() const
|
|
||||||
{ return Is_Delaunay_hyperbolic(); }
|
|
||||||
};
|
|
||||||
|
|
||||||
// Take out the code below to some separate file
|
|
||||||
|
|
||||||
#ifdef CGAL_EXACT_PREDICATES_EXACT_CONSTRUCTIONS_KERNEL_H
|
|
||||||
template <>
|
|
||||||
struct Triangulation_structural_filtering_traits< Hyperbolic_Delaunay_triangulation_old_traits_2<Epeck> > {
|
|
||||||
typedef Tag_true Use_structural_filtering_tag;
|
|
||||||
};
|
|
||||||
#endif // CGAL_EXACT_PREDICATES_EXACT_CONSTRUCTIONS_KERNEL_H
|
|
||||||
|
|
||||||
#ifdef CGAL_EXACT_PREDICATES_INEXACT_CONSTRUCTIONS_KERNEL_H
|
|
||||||
template <>
|
|
||||||
struct Triangulation_structural_filtering_traits< Hyperbolic_Delaunay_triangulation_old_traits_2<Epick> > {
|
|
||||||
typedef Tag_true Use_structural_filtering_tag;
|
|
||||||
};
|
|
||||||
#endif // CGAL_EXACT_PREDICATES_INEXACT_CONSTRUCTIONS_KERNEL_H
|
|
||||||
|
|
||||||
} //namespace CGAL
|
|
||||||
|
|
||||||
#endif // CGAL_HYPERBOLIC_DELAUNAY_TRIANGULATION_TRAITS_2_H
|
|
||||||
Loading…
Reference in New Issue