116 lines
3.6 KiB
C
116 lines
3.6 KiB
C
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// Copyright (c) 1997-2002 Max-Planck-Institute Saarbruecken (Germany).
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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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//
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// $URL: https://github.com/CGAL/cgal/blob/v5.1/Nef_S2/include/CGAL/Nef_S2/Sphere_direction.h $
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// $Id: Sphere_direction.h 0779373 2020-03-26T13:31:46+01:00 Sébastien Loriot
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// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
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//
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//
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// Author(s) : Michael Seel <seel@mpi-sb.mpg.de>
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#ifndef CGAL_SPHERE_DIRECTION_H
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#define CGAL_SPHERE_DIRECTION_H
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#include <CGAL/license/Nef_S2.h>
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#include <CGAL/basic.h>
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#include <CGAL/Kernel/global_functions_3.h>
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namespace CGAL {
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/*{\Manpage{Sphere_direction}{R}{Directions on the unit sphere}{c}}*/
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template <class R_> class Sphere_direction : public R_::Plane_3 {
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/*{\Mdefinition An object |\Mvar| of type |\Mname| is a direction
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on the surface of the unit sphere. Such directions can be used to
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describe walks that are part of great circles.}*/
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public:
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/*{\Mtypes 5}*/
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typedef R_ R;
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/*{\Mtypemember representation class.}*/
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typedef typename R::RT RT;
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/*{\Mtypemember ring type.}*/
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typedef typename R_::Point_3 Point_3;
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typedef typename R_::Plane_3 Plane_3;
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typedef typename R_::Plane_3 Base;
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typedef Sphere_direction<R_> Self;
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/*{\Mcreation 5}*/
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Sphere_direction() : Base() {}
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/*{\Mcreate creates some direction.}*/
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Sphere_direction(const Sphere_circle<R>& c)
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/*{\Mcreate creates the direction corresponding to the circle |c|.}*/
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: Base(c) {}
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Sphere_direction(const Sphere_point<R>& p, const Sphere_point<R>&q)
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: Base(Point_3(0,0,0),p,q)
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/*{\Mcreate creates a direction that describes the orientation of
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the great circle through $p$ and $q$ (oriented such that the segment
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$pq$ is the shorter one of the two possible ones. \precond $p$ and $q$
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are not opposite on $S_2$.}*/
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{ CGAL_assertion(p!=q.opposite());
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Point_3 p1(0,0,0), p4 = CGAL::ORIGIN + ((Base*) this)->orthogonal_vector();
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if ( CGAL::orientation(p1,p,q,p4) != CGAL::POSITIVE )
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*this = Sphere_direction(opposite());
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}
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Sphere_direction(const typename R::Plane_3& h)
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/*{\Xcreate creates the direction corresponding to the plane |h|.
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\precond |h| contains the origin.}*/
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: Base(h) { CGAL_assertion(h.d() == 0); }
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/*{\Moperations 4 2}*/
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Sphere_direction<R> opposite() const
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/*{\Mop returns the opposite of |\Mvar|.}*/
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{ return Base::opposite(); }
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Plane_3 plane() const { return Base(*this); }
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/*{\Xop returns the plane supporting |\Mvar|.}*/
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}; // Sphere_direction<R>
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/* We have:
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1) all directions fixed at p
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2) d1==d3 possible
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return true iff d1,d2,d3 are stricly ccw ordered around p
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Note: Sphere_directions are Plane_3
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we therefore compare the normal vectors of the planes
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that underly the directions d1,d2,d3 in the plane
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through 0 and orthogonal to the vector p-0
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*/
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template <typename R>
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bool strictly_ordered_ccw_at(const Sphere_point<R>& p,
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const Sphere_direction<R>& d1,
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const Sphere_direction<R>& d2,
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const Sphere_direction<R>& d3)
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{ CGAL_assertion(d1.has_on(p) && d2.has_on(p) && d3.has_on(p));
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typename R::Point_3 p0(0,0,0);
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typename R::Point_3 p1(CGAL::ORIGIN + d1.orthogonal_vector());
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typename R::Point_3 p2(CGAL::ORIGIN + d2.orthogonal_vector());
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typename R::Point_3 p3(CGAL::ORIGIN + d3.orthogonal_vector());
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if ( d1 == d3 ) return false;
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if ( CGAL::orientation(p0,p,p1,p3) == CGAL::POSITIVE ) {
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return CGAL::orientation(p0,p,p1,p2) == CGAL::POSITIVE &&
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CGAL::orientation(p0,p,p3,p2) == CGAL::NEGATIVE;
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} else {
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return CGAL::orientation(p0,p,p1,p2) == CGAL::POSITIVE ||
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CGAL::orientation(p0,p,p3,p2) == CGAL::NEGATIVE;
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}
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}
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} //namespace CGAL
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#endif //CGAL_SPHERE_DIRECTION_H
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