mirror of https://github.com/CGAL/cgal
modified and moved the predicate Is_hyperbolic to the traits
This commit is contained in:
Mikhail Bogdanov
Aymeric PELLE
parent
221d624d73
commit
27a81e581d
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@ -424,111 +424,33 @@ private:
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Mark_face test(*this);
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mark_face(f, test);
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}
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class Is_hyperbolic
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{
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public:
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Is_hyperbolic()
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{
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}
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bool operator() (const Face_handle& f) const
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{
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typedef typename Gt::Vector_3 Vector_3;
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Point p0 = f->vertex(0)->point();
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Point p1 = f->vertex(1)->point();
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Point p2 = f->vertex(2)->point();
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Vector_3 v0 = Vector_3(p0.x()*p0.x() + p0.y()*p0.y(),
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p1.x()*p1.x() + p1.y()*p1.y(),
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p2.x()*p2.x() + p2.y()*p2.y());
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Vector_3 v1 = Vector_3(p0.x(), p1.x(), p2.x());
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Vector_3 v2 = Vector_3(p0.y(), p1.y(), p2.y());
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Vector_3 v3 = Vector_3(FT(1), FT(1), FT(1));
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FT dt0 = CGAL::determinant(v0, v1, v3);
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FT dt1 = CGAL::determinant(v0, v2, v3);
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FT dt2 = CGAL::determinant(v0 - v3, v1, v2);
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return dt0*dt0 + dt1*dt1 - dt2*dt2 < 0;
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}
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// assume the incident faces are "non-hyperbolic"
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bool operator() (const Edge& e) const
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{
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typedef typename Gt::Vector_2 Vector_2;
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typedef typename Gt::Vector_3 Vector_3;
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// endpoints of the edge
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Point p0 = e.first->vertex(cw(e.second))->point();
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Point p1 = e.first->vertex(ccw(e.second))->point();
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// vertices opposite to p0 and p1
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Point q0 = e.first->vertex(e.second)->point();
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Face_handle f = e.first->neighbor(e.second);
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int ind = f->index(e.first);
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Point q1 = f->vertex(ind);
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Vector_3 v0 = Vector_3(p0.x()*p0.x() + p0.y()*p0.y(),
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p1.x()*p1.x() + p1.y()*p1.y(),
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q0.x()*q0.x() + q0.y()*q0.y());
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Vector_3 v1 = Vector_3(2*p0.y(), 2*p1.y(), 2*q0.y());
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Vector_3 v2 = Vector_3(2*p0.x(), 2*p1.x(), 2*q0.x());
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Vector_3 v3 = Vector_3(FT(-1), FT(-1), FT(-1));
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FT dt0 = CGAL::determinant(v0, v1, v3);
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FT dt1 = CGAL::determinant(v2, v0, v3);
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FT m11 = p0.x() * (p1.x()*p1.x() + p1.y()*p1.y() - 2) - p1.x() * (p0.x()*p0.x() + p0.y()*p0.y() - 2);
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FT m12 = p0.y() * (p1.x()*p1.x() + p1.y()*p1.y() - 2) - p1.y() * (p0.x()*p0.x() + p0.y()*p0.y() - 2);
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Vector_3 v4 = Vector_3(p0.x()*p0.x() + p0.y()*p0.y(),
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p1.x()*p1.x() + p1.y()*p1.y(),
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q1.x()*q1.x() + q1.y()*q1.y());
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Vector_3 v5 = Vector_3(2*p0.y(), 2*p1.y(), 2*q1.y());
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Vector_3 v6 = Vector_3(2*p0.x(), 2*p1.x(), 2*q1.x());
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Vector_3 v7 = Vector_3(FT(-1), FT(-1), FT(-1));
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FT dt3 = CGAL::determinant(v4, v5, v7);
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FT dt4 = CGAL::determinant(v6, v4, v7);
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FT big_dt0 = CGAL::determinant(Vector_2(dt0, m11), Vector_2(dt1, m12));
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FT big_dt1 = CGAL::determinant(Vector_2(dt3, m11), Vector_2(dt4, m12));
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assert(big_dt0 == 0 || big_dt1 == 0);
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return (big_dt0 > 0 && big_dt1 > 0) || (big_dt0 < 0 && big_dt1 < 0);
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}
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private:
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Is_hyperbolic(const Is_hyperbolic&);
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Is_hyperbolic& operator= (const Is_hyperbolic&);
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};
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class Mark_face
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{
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public:
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typedef typename Gt::Circle_2 Circle_2;
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Mark_face(const Self& tr) :
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_tr(tr)
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{}
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Face_info operator ()(const Face_handle& f) const
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{
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typedef typename Gt::Is_hyperbolic Is_hyperbolic;
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Face_info info;
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if(_tr.has_infinite_vertex(f)) {
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return info;
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}
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if(Is_hyperbolic()(f) == false) {
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Point p0 = f->vertex(0)->point();
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Point p1 = f->vertex(1)->point();
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Point p2 = f->vertex(2)->point();
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int ind = 0;
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Is_hyperbolic is_hyperbolic = _tr.geom_traits().Is_hyperbolic_object();
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if(is_hyperbolic(p0, p1, p2, ind) == false) {
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info.set_finite_invisible(true);
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info.set_invisible_edge(find_invisible_edge(f));
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info.set_invisible_edge(ind);
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return info;
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}
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@ -537,46 +459,10 @@ private:
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}
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private:
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// assume that the circumscribing circle of a given face intersects
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// the circle at infinity
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unsigned char find_invisible_edge(const Face_handle& f) const
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{
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typedef Euclidean_geom_traits Egt;
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typedef typename Egt::Construct_circumcenter_2 Construct_circumcenter_2;
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typedef typename Egt::Direction_2 Direction_2;
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assert(!_tr.has_infinite_vertex(f));
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Point p0 = f->vertex(0)->point();
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Point p1 = f->vertex(1)->point();
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Point p2 = f->vertex(2)->point();
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_circle = Circle_2(p0, p1, p2);
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Point c = _circle.center();
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Direction_2 d0(p0.x()-c.x(), p0.y()-c.y());
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Direction_2 d1(p1.x()-c.x(), p1.y()-c.y());
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Direction_2 d2(p2.x()-c.x(), p2.y()-c.y());
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Direction_2 d(c.x(), c.y());
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if(d.counterclockwise_in_between(d0, d1)) {
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return 2;
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}
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if(d.counterclockwise_in_between(d1, d2)) {
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return 0;
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}
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return 1;
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}
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Mark_face(const Mark_face&);
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Mark_face& operator= (const Mark_face&);
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mutable Circle_2 _circle;
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const Self& _tr;
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};
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@ -35,407 +35,475 @@
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namespace CGAL {
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template < class R >
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class Triangulation_hyperbolic_traits_2 {
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template < class R >
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class Triangulation_hyperbolic_traits_2 {
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public:
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typedef Triangulation_hyperbolic_traits_2<R> Self;
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typedef R Triangulation_euclidean_traits_2;
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typedef R Rep;
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typedef typename R::RT RT;
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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::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;
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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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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_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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typedef typename R::Construct_bisector_2 Construct_bisector_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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typedef typename R::Angle_2 Angle_2;
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typedef typename R::Construct_midpoint_2 Construct_midpoint_2;
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typedef typename R::Compute_squared_distance_2 Compute_squared_distance_2;
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typedef typename R::Iso_rectangle_2 Iso_rectangle_2;
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typedef typename R::Circle_2 Circle_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 Line_segment_2;
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typedef boost::variant<Arc_2, Line_segment_2> Segment_2;
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typedef typename R::Line_2 Euclidean_line_2;
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private:
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// Poincaré disk
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const Circle_2 _unit_circle;
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public:
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const Circle_2& unit_circle() const
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{
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return _unit_circle;
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}
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Angle_2
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angle_2_object() const
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{ return Angle_2(); }
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Compute_squared_distance_2
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compute_squared_distance_2_object() const
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{ return Compute_squared_distance_2(); }
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class Construct_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 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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typedef Triangulation_hyperbolic_traits_2<R> Self;
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Construct_segment_2(const Circle_2& c) : _unit_circle(c)
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{
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}
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typedef R Triangulation_euclidean_traits_2;
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typedef R Rep;
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typedef typename R::RT RT;
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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::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;
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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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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_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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typedef typename R::Construct_bisector_2 Construct_bisector_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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typedef typename R::Angle_2 Angle_2;
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typedef typename R::Construct_midpoint_2 Construct_midpoint_2;
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typedef typename R::Compute_squared_distance_2 Compute_squared_distance_2;
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typedef typename R::Iso_rectangle_2 Iso_rectangle_2;
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typedef typename R::Circle_2 Circle_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 Line_segment_2;
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typedef boost::variant<Arc_2, Line_segment_2> Segment_2;
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typedef typename R::Line_2 Euclidean_line_2;
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Segment_2 operator()(const Point_2& p, const Point_2& q) const
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{
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typedef typename R::Collinear_2 Collinear_2;
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if(Collinear_2()(p, q, _unit_circle.center())){
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return Line_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(_unit_circle.center(), _unit_circle.squared_radius());
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Bare_point center = Construct_weighted_circumcenter_2()(wp, wo, wq);
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FT radius = Compute_squared_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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private:
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// Poincaré disk
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const Circle_2 _unit_circle;
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const Circle_2& _unit_circle;
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};
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Construct_segment_2
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construct_segment_2_object() const
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{
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return Construct_segment_2(_unit_circle);
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}
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class Construct_circumcenter_2
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{
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public:
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const Circle_2& unit_circle() const
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{
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return _unit_circle;
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}
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Angle_2
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angle_2_object() const
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{ return Angle_2(); }
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Compute_squared_distance_2
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compute_squared_distance_2_object() const
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{ return Compute_squared_distance_2(); }
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class Construct_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 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_segment_2(const Circle_2& c) : _unit_circle(c)
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{
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}
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Segment_2 operator()(const Point_2& p, const Point_2& q) const
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{
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typedef typename R::Collinear_2 Collinear_2;
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if(Collinear_2()(p, q, _unit_circle.center())){
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return Line_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(_unit_circle.center(), _unit_circle.squared_radius());
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Bare_point center = Construct_weighted_circumcenter_2()(wp, wo, wq);
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FT radius = Compute_squared_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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private:
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const Circle_2& _unit_circle;
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};
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Construct_segment_2
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construct_segment_2_object() const
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{
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return Construct_segment_2(_unit_circle);
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}
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class Construct_circumcenter_2
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{
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public:
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Construct_circumcenter_2(const Circle_2& c) : _unit_circle(c)
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{}
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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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assert(_unit_circle.bounded_side(p) == ON_BOUNDED_SIDE);
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assert(_unit_circle.bounded_side(q) == ON_BOUNDED_SIDE);
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assert(_unit_circle.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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assert(CGAL::do_intersect(_unit_circle, circle) == false);
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if(circle.center() <= _unit_circle.center() && circle.center() >= _unit_circle.center()){
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return _unit_circle.center();
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}
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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() + _unit_circle.squared_radius();
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FT c = _unit_circle.squared_radius();
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FT D = b*b - 4*a*c;
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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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private:
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const Circle_2 _unit_circle;
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};
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Construct_circumcenter_2
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construct_circumcenter_2_object()
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{
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Construct_circumcenter_2(_unit_circle);
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}
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Construct_midpoint_2
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construct_midpoint_2_object() const
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{ return Construct_midpoint_2(); }
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//for natural_neighbor_coordinates_2
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typedef typename R::FT FT;
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typedef typename R::Equal_x_2 Equal_x_2;
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typedef typename R::Compute_area_2 Compute_area_2;
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Compute_area_2 compute_area_2_object () const
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{
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return Compute_area_2();
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}
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// for compatibility with previous versions
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typedef Point_2 Point;
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typedef Segment_2 Segment;
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typedef Triangle_2 Triangle;
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typedef Ray_2 Ray;
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//typedef Line_2 Line;
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Triangulation_hyperbolic_traits_2() :
|
||||
_unit_circle(Point_2(0, 0), 1*1)
|
||||
Construct_circumcenter_2(const Circle_2& c) : _unit_circle(c)
|
||||
{}
|
||||
|
||||
Triangulation_hyperbolic_traits_2(FT r) :
|
||||
_unit_circle(Point_2(0, 0), r*r)
|
||||
{}
|
||||
|
||||
Triangulation_hyperbolic_traits_2(const Triangulation_hyperbolic_traits_2 & other) :
|
||||
_unit_circle(other._unit_circle)
|
||||
{}
|
||||
|
||||
Triangulation_hyperbolic_traits_2 &operator=
|
||||
(const Triangulation_hyperbolic_traits_2 &)
|
||||
{
|
||||
return *this;
|
||||
}
|
||||
|
||||
Less_x_2
|
||||
less_x_2_object() const
|
||||
{ return Less_x_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();}
|
||||
|
||||
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();}
|
||||
|
||||
Construct_circumcenter_2
|
||||
construct_circumcenter_2_object() const
|
||||
{
|
||||
return Construct_circumcenter_2(_unit_circle);
|
||||
}
|
||||
|
||||
class Construct_hyperbolic_bisector_2
|
||||
{
|
||||
public:
|
||||
Construct_hyperbolic_bisector_2(const Circle_2& unit_circle) :
|
||||
_unit_circle(unit_circle) {}
|
||||
// TODO: improve this function
|
||||
Point_2 operator()(Point_2 p, Point_2 q, Point_2 r)
|
||||
{
|
||||
assert(_unit_circle.bounded_side(p) == ON_BOUNDED_SIDE);
|
||||
assert(_unit_circle.bounded_side(q) == ON_BOUNDED_SIDE);
|
||||
assert(_unit_circle.bounded_side(r) == ON_BOUNDED_SIDE);
|
||||
|
||||
Segment_2 operator()(Point_2 p, Point_2 q) const
|
||||
{
|
||||
// If two points are almost of the same distance to the origin, then
|
||||
// the bisector is supported by the circle of huge radius etc.
|
||||
// This circle is computed inexactly.
|
||||
// At present time, in this case the bisector is supported by the line.
|
||||
Circle_2 circle(p, q, r);
|
||||
// circle must be inside the unit one
|
||||
assert(CGAL::do_intersect(_unit_circle, circle) == false);
|
||||
|
||||
if(circle.center() <= _unit_circle.center() && circle.center() >= _unit_circle.center()){
|
||||
return _unit_circle.center();
|
||||
}
|
||||
|
||||
FT x0 = circle.center().x(), y0 = circle.center().y();
|
||||
// a*alphaˆ2 + b*alpha + c = 0;
|
||||
FT a = x0*x0 + y0*y0;
|
||||
FT b = a - circle.squared_radius() + _unit_circle.squared_radius();
|
||||
FT c = _unit_circle.squared_radius();
|
||||
FT D = b*b - 4*a*c;
|
||||
|
||||
FT alpha = (b - CGAL::sqrt(to_double(D)))/(2*a);
|
||||
|
||||
Point_2 center(x0*alpha, y0*alpha);
|
||||
if(!circle.has_on_bounded_side(center))
|
||||
{ std::cout << "Center does not belong to the pencil of spheres!!!" << std::endl;} ;
|
||||
return center;
|
||||
}
|
||||
|
||||
private:
|
||||
const Circle_2 _unit_circle;
|
||||
};
|
||||
|
||||
Construct_circumcenter_2
|
||||
construct_circumcenter_2_object()
|
||||
{
|
||||
Construct_circumcenter_2(_unit_circle);
|
||||
}
|
||||
|
||||
Construct_midpoint_2
|
||||
construct_midpoint_2_object() const
|
||||
{ return Construct_midpoint_2(); }
|
||||
|
||||
//for natural_neighbor_coordinates_2
|
||||
typedef typename R::FT FT;
|
||||
typedef typename R::Equal_x_2 Equal_x_2;
|
||||
typedef typename R::Compute_area_2 Compute_area_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;
|
||||
typedef Ray_2 Ray;
|
||||
//typedef Line_2 Line;
|
||||
|
||||
Triangulation_hyperbolic_traits_2() :
|
||||
_unit_circle(Point_2(0, 0), 1*1)
|
||||
{}
|
||||
|
||||
Triangulation_hyperbolic_traits_2(FT r) :
|
||||
_unit_circle(Point_2(0, 0), r*r)
|
||||
{}
|
||||
|
||||
Triangulation_hyperbolic_traits_2(const Triangulation_hyperbolic_traits_2 & other) :
|
||||
_unit_circle(other._unit_circle)
|
||||
{}
|
||||
|
||||
Triangulation_hyperbolic_traits_2 &operator=
|
||||
(const Triangulation_hyperbolic_traits_2 &)
|
||||
{
|
||||
return *this;
|
||||
}
|
||||
|
||||
Less_x_2
|
||||
less_x_2_object() const
|
||||
{ return Less_x_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();}
|
||||
|
||||
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();}
|
||||
|
||||
Construct_circumcenter_2
|
||||
construct_circumcenter_2_object() const
|
||||
{
|
||||
return Construct_circumcenter_2(_unit_circle);
|
||||
}
|
||||
|
||||
class Construct_hyperbolic_bisector_2
|
||||
{
|
||||
public:
|
||||
Construct_hyperbolic_bisector_2(const Circle_2& unit_circle) :
|
||||
_unit_circle(unit_circle) {}
|
||||
|
||||
Segment_2 operator()(Point_2 p, Point_2 q) const
|
||||
{
|
||||
// If two points are almost of the same distance to the origin, then
|
||||
// the bisector is supported by the circle of huge radius etc.
|
||||
// This circle is computed inexactly.
|
||||
// At present time, in this case the bisector is supported by the line.
|
||||
|
||||
Compute_squared_distance_2 dist = Compute_squared_distance_2();
|
||||
Point origin = _unit_circle.center();
|
||||
FT dif = dist(origin, p) - dist(origin, q);
|
||||
FT eps = 0.0000000001;
|
||||
|
||||
// Bisector is straight in euclidean sense
|
||||
if(dif > -eps && dif < eps){
|
||||
|
||||
Compute_squared_distance_2 dist = Compute_squared_distance_2();
|
||||
Point origin = _unit_circle.center();
|
||||
FT dif = dist(origin, p) - dist(origin, q);
|
||||
FT eps = 0.0000000001;
|
||||
|
||||
// Bisector is straight in euclidean sense
|
||||
if(dif > -eps && dif < eps){
|
||||
|
||||
// ideally
|
||||
//if(Compare_distance_2()(_unit_circle.center(), p, q) == EQUAL){
|
||||
|
||||
// TODO: calling R::Construct_bisector
|
||||
Euclidean_line_2 l = Construct_bisector_2()(p, q);
|
||||
// compute the ending points
|
||||
std::pair<Point_2, Point_2> points = find_intersection(l);
|
||||
// TODO: improve
|
||||
Vector_2 v(points.first, points.second);
|
||||
if(v*l.to_vector() > 0){
|
||||
return Line_segment_2(points.first, points.second);
|
||||
}
|
||||
return Line_segment_2(points.second, points.first);
|
||||
}
|
||||
|
||||
Circle_2 c = construct_supporting_circle(p, q);
|
||||
// TODO: calling R::Construct_bisector
|
||||
Euclidean_line_2 l = Construct_bisector_2()(p, q);
|
||||
// compute the ending points
|
||||
std::pair<Point_2, Point_2> points = find_intersection(c);
|
||||
|
||||
if(Orientation_2()(points.first, points.second, c.center()) == LEFT_TURN) {
|
||||
return Arc_2(c, points.first, points.second);
|
||||
std::pair<Point_2, Point_2> points = find_intersection(l);
|
||||
// TODO: improve
|
||||
Vector_2 v(points.first, points.second);
|
||||
if(v*l.to_vector() > 0){
|
||||
return Line_segment_2(points.first, points.second);
|
||||
}
|
||||
return Arc_2(c, points.second, points.first);
|
||||
return Line_segment_2(points.second, points.first);
|
||||
}
|
||||
|
||||
private:
|
||||
// The cirle belongs to the pencil with limit points p and q
|
||||
Circle_2 construct_supporting_circle(Point_2 p, Point_2 q) const
|
||||
{
|
||||
// p, q are zero-circles
|
||||
// (x, y, xˆ2 + yˆ2 - rˆ2) = alpha*(xp, yp, xpˆ2 + ypˆ2) + (1-alpha)*(xq, yq, xqˆ2 + yqˆ2)
|
||||
// xˆ2 + yˆ2 - rˆ2 = Rˆ2, where R - is a radius of the given unit circle
|
||||
FT op = p.x()*p.x() + p.y()*p.y();
|
||||
FT oq = q.x()*q.x() + q.y()*q.y();
|
||||
FT alpha = (_unit_circle.squared_radius() - oq) / (op - oq);
|
||||
|
||||
FT x = alpha*p.x() + (1-alpha)*q.x();
|
||||
FT y = alpha*p.y() + (1-alpha)*q.y();
|
||||
FT radius = x*x + y*y - _unit_circle.squared_radius();
|
||||
|
||||
//improve
|
||||
typename R::Line_2 l = typename R::Construct_bisector_2()(p, q);
|
||||
Point_2 middle = Construct_midpoint_2()(p, q);
|
||||
Point_2 temp = middle + l.to_vector();
|
||||
if(Orientation_2()(middle, temp, Point_2(x, y)) == ON_POSITIVE_SIDE){
|
||||
return Circle_2(Point_2(x, y), radius, CLOCKWISE);
|
||||
}
|
||||
|
||||
return Circle_2(Point_2(x, y), radius, COUNTERCLOCKWISE);
|
||||
Circle_2 c = construct_supporting_circle(p, q);
|
||||
// compute the ending points
|
||||
std::pair<Point_2, Point_2> points = find_intersection(c);
|
||||
|
||||
if(Orientation_2()(points.first, points.second, c.center()) == LEFT_TURN) {
|
||||
return Arc_2(c, points.first, points.second);
|
||||
}
|
||||
|
||||
// Find intersection of an input circle orthogonal to the Poincaré disk
|
||||
// and the circle representing this disk
|
||||
|
||||
// TODO: sqrt(to_double()?)
|
||||
std::pair<Point_2, Point_2> find_intersection(Circle_2& circle) const
|
||||
{
|
||||
FT x = circle.center().x(), y = circle.center().y();
|
||||
|
||||
// axˆ2 + 2bˆx + c = 0;
|
||||
FT a = x*x + y*y;
|
||||
FT b = -_unit_circle.squared_radius() * x;
|
||||
FT c = _unit_circle.squared_radius()*_unit_circle.squared_radius() - _unit_circle.squared_radius()*y*y;
|
||||
assert(b*b - a*c > 0);
|
||||
FT D = CGAL::sqrt(to_double(b*b - a*c));
|
||||
|
||||
FT x1 = (-b - D)/a;
|
||||
FT x2 = (-b + D)/a;
|
||||
FT y1 = (_unit_circle.squared_radius() - x1*x)/y;
|
||||
FT y2 = (_unit_circle.squared_radius() - x2*x)/y;
|
||||
|
||||
return std::make_pair(Point_2(x1, y1), Point_2(x2, y2));
|
||||
}
|
||||
|
||||
// Find intersection of an input line orthogonal to the Poincaré disk
|
||||
// and the circle representing this disk
|
||||
|
||||
// TODO: sqrt(to_double()?)
|
||||
std::pair<Point_2, Point_2> find_intersection(Euclidean_line_2& l) const
|
||||
{
|
||||
typedef typename R::Vector_2 Vector_2;
|
||||
Vector_2 v = l.to_vector();
|
||||
|
||||
// normalize the vector
|
||||
FT squared_coeff = _unit_circle.squared_radius()/v.squared_length();
|
||||
FT coeff = CGAL::sqrt(to_double(squared_coeff));
|
||||
|
||||
Point_2 p1(coeff*v.x(), coeff*v.y());
|
||||
Point_2 p2(-p1.x(), -p1.y());
|
||||
return std::make_pair(p1, p2);
|
||||
}
|
||||
|
||||
private:
|
||||
const Circle_2 _unit_circle;
|
||||
};
|
||||
return Arc_2(c, points.second, points.first);
|
||||
}
|
||||
|
||||
Construct_hyperbolic_bisector_2
|
||||
construct_hyperbolic_bisector_2_object() const
|
||||
{ return Construct_hyperbolic_bisector_2(_unit_circle);}
|
||||
|
||||
Construct_bisector_2
|
||||
construct_bisector_2_object() const
|
||||
{return Construct_bisector_2();}
|
||||
|
||||
Compare_distance_2
|
||||
compare_distance_2_object() const
|
||||
{return Compare_distance_2();}
|
||||
|
||||
Construct_triangle_2 construct_triangle_2_object() const
|
||||
{return Construct_triangle_2();}
|
||||
|
||||
Construct_direction_2 construct_direction_2_object() const
|
||||
{return Construct_direction_2();}
|
||||
|
||||
class Construct_ray_2
|
||||
private:
|
||||
// The cirle belongs to the pencil with limit points p and q
|
||||
Circle_2 construct_supporting_circle(Point_2 p, Point_2 q) const
|
||||
{
|
||||
public:
|
||||
Construct_ray_2(Circle_2 c) :
|
||||
_unit_circle(c) {}
|
||||
// p, q are zero-circles
|
||||
// (x, y, xˆ2 + yˆ2 - rˆ2) = alpha*(xp, yp, xpˆ2 + ypˆ2) + (1-alpha)*(xq, yq, xqˆ2 + yqˆ2)
|
||||
// xˆ2 + yˆ2 - rˆ2 = Rˆ2, where R - is a radius of the given unit circle
|
||||
FT op = p.x()*p.x() + p.y()*p.y();
|
||||
FT oq = q.x()*q.x() + q.y()*q.y();
|
||||
FT alpha = (_unit_circle.squared_radius() - oq) / (op - oq);
|
||||
|
||||
Segment_2 operator()(Point_2 p, Segment_2 l) const
|
||||
{
|
||||
if(typename R::Segment_2* s = boost::get<typename R::Segment_2>(&l)){
|
||||
return operator()(p, *s);
|
||||
}
|
||||
if(Arc_2* arc = boost::get<Arc_2>(&l)){
|
||||
if(arc->get<0>().orientation() == CLOCKWISE){
|
||||
arc->get<1>() = p;
|
||||
return *arc;
|
||||
}
|
||||
arc->get<2>() = p;
|
||||
FT x = alpha*p.x() + (1-alpha)*q.x();
|
||||
FT y = alpha*p.y() + (1-alpha)*q.y();
|
||||
FT radius = x*x + y*y - _unit_circle.squared_radius();
|
||||
|
||||
//improve
|
||||
typename R::Line_2 l = typename R::Construct_bisector_2()(p, q);
|
||||
Point_2 middle = Construct_midpoint_2()(p, q);
|
||||
Point_2 temp = middle + l.to_vector();
|
||||
if(Orientation_2()(middle, temp, Point_2(x, y)) == ON_POSITIVE_SIDE){
|
||||
return Circle_2(Point_2(x, y), radius, CLOCKWISE);
|
||||
}
|
||||
|
||||
return Circle_2(Point_2(x, y), radius, COUNTERCLOCKWISE);
|
||||
}
|
||||
|
||||
// Find intersection of an input circle orthogonal to the Poincaré disk
|
||||
// and the circle representing this disk
|
||||
|
||||
// TODO: sqrt(to_double()?)
|
||||
std::pair<Point_2, Point_2> find_intersection(Circle_2& circle) const
|
||||
{
|
||||
FT x = circle.center().x(), y = circle.center().y();
|
||||
|
||||
// axˆ2 + 2bˆx + c = 0;
|
||||
FT a = x*x + y*y;
|
||||
FT b = -_unit_circle.squared_radius() * x;
|
||||
FT c = _unit_circle.squared_radius()*_unit_circle.squared_radius() - _unit_circle.squared_radius()*y*y;
|
||||
assert(b*b - a*c > 0);
|
||||
FT D = CGAL::sqrt(to_double(b*b - a*c));
|
||||
|
||||
FT x1 = (-b - D)/a;
|
||||
FT x2 = (-b + D)/a;
|
||||
FT y1 = (_unit_circle.squared_radius() - x1*x)/y;
|
||||
FT y2 = (_unit_circle.squared_radius() - x2*x)/y;
|
||||
|
||||
return std::make_pair(Point_2(x1, y1), Point_2(x2, y2));
|
||||
}
|
||||
|
||||
// Find intersection of an input line orthogonal to the Poincaré disk
|
||||
// and the circle representing this disk
|
||||
|
||||
// TODO: sqrt(to_double()?)
|
||||
std::pair<Point_2, Point_2> find_intersection(Euclidean_line_2& l) const
|
||||
{
|
||||
typedef typename R::Vector_2 Vector_2;
|
||||
Vector_2 v = l.to_vector();
|
||||
|
||||
// normalize the vector
|
||||
FT squared_coeff = _unit_circle.squared_radius()/v.squared_length();
|
||||
FT coeff = CGAL::sqrt(to_double(squared_coeff));
|
||||
|
||||
Point_2 p1(coeff*v.x(), coeff*v.y());
|
||||
Point_2 p2(-p1.x(), -p1.y());
|
||||
return std::make_pair(p1, p2);
|
||||
}
|
||||
|
||||
private:
|
||||
const Circle_2 _unit_circle;
|
||||
};
|
||||
|
||||
Construct_hyperbolic_bisector_2
|
||||
construct_hyperbolic_bisector_2_object() const
|
||||
{ return Construct_hyperbolic_bisector_2(_unit_circle);}
|
||||
|
||||
Construct_bisector_2
|
||||
construct_bisector_2_object() const
|
||||
{return Construct_bisector_2();}
|
||||
|
||||
Compare_distance_2
|
||||
compare_distance_2_object() const
|
||||
{return Compare_distance_2();}
|
||||
|
||||
Construct_triangle_2 construct_triangle_2_object() const
|
||||
{return Construct_triangle_2();}
|
||||
|
||||
Construct_direction_2 construct_direction_2_object() const
|
||||
{return Construct_direction_2();}
|
||||
|
||||
class Construct_ray_2
|
||||
{
|
||||
public:
|
||||
Construct_ray_2(Circle_2 c) :
|
||||
_unit_circle(c) {}
|
||||
|
||||
Segment_2 operator()(Point_2 p, Segment_2 l) const
|
||||
{
|
||||
if(typename R::Segment_2* s = boost::get<typename R::Segment_2>(&l)){
|
||||
return operator()(p, *s);
|
||||
}
|
||||
if(Arc_2* arc = boost::get<Arc_2>(&l)){
|
||||
if(arc->get<0>().orientation() == CLOCKWISE){
|
||||
arc->get<1>() = p;
|
||||
return *arc;
|
||||
}
|
||||
assert(false);
|
||||
return Segment_2();
|
||||
arc->get<2>() = p;
|
||||
return *arc;
|
||||
}
|
||||
|
||||
Segment_2 operator()(Point_2 p, typename R::Segment_2 s) const
|
||||
{
|
||||
return typename R::Segment_2(p, s.target());
|
||||
}
|
||||
|
||||
private:
|
||||
|
||||
const Circle_2 _unit_circle;
|
||||
};
|
||||
assert(false);
|
||||
return Segment_2();
|
||||
}
|
||||
|
||||
Construct_ray_2 construct_ray_2_object() const
|
||||
{return Construct_ray_2(_unit_circle);}
|
||||
Segment_2 operator()(Point_2 p, typename R::Segment_2 s) const
|
||||
{
|
||||
return typename R::Segment_2(p, s.target());
|
||||
}
|
||||
|
||||
private:
|
||||
|
||||
const Circle_2 _unit_circle;
|
||||
};
|
||||
|
||||
Construct_ray_2 construct_ray_2_object() const
|
||||
{return Construct_ray_2(_unit_circle);}
|
||||
|
||||
// For details see the rapport RR-8146
|
||||
class Is_hyperbolic
|
||||
{
|
||||
public:
|
||||
|
||||
bool operator() (const Point& p0, const Point& p1, const Point& 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 = CGAL::determinant(v0, v1, v3);
|
||||
FT dt1 = CGAL::determinant(v0, v2, v3);
|
||||
FT dt2 = CGAL::determinant(v0 - v3, v1, v2);
|
||||
|
||||
return dt0*dt0 + dt1*dt1 - dt2*dt2 < 0;
|
||||
}
|
||||
|
||||
bool operator() (const Point& p0, const Point& p1, const Point& 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& p0, const Point& p1, const Point& 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 = CGAL::determinant(v0, 2*v2, -v3);
|
||||
FT dt1 = CGAL::determinant(2*v1, v0, -v3);
|
||||
FT dt2 = CGAL::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_hyperbolic Is_hyperbolic_object() const
|
||||
{ return Is_hyperbolic(); }
|
||||
};
|
||||
|
||||
|
||||
// Take out the code below to some separate file
|
||||
|
||||
|
||||
#ifdef CGAL_EXACT_PREDICATES_EXACT_CONSTRUCTIONS_KERNEL_H
|
||||
template <>
|
||||
struct Triangulation_structural_filtering_traits< Triangulation_hyperbolic_traits_2<Epeck> > {
|
||||
typedef Tag_true Use_structural_filtering_tag;
|
||||
typedef Tag_true Use_structural_filtering_tag;
|
||||
};
|
||||
#endif // CGAL_EXACT_PREDICATES_EXACT_CONSTRUCTIONS_KERNEL_H
|
||||
|
||||
|
|
@ -445,7 +513,7 @@ struct Triangulation_structural_filtering_traits< Triangulation_hyperbolic_trait
|
|||
typedef Tag_true Use_structural_filtering_tag;
|
||||
};
|
||||
#endif // CGAL_EXACT_PREDICATES_INEXACT_CONSTRUCTIONS_KERNEL_H
|
||||
|
||||
|
||||
} //namespace CGAL
|
||||
|
||||
#endif // CGAL_TRIANGULATION_HYPERBOLIC_TRAITS_2_H
|
||||
|
|
|
|||
Loading…
Reference in New Issue