125 lines
3.9 KiB
C
125 lines
3.9 KiB
C
|
// Copyright (c) 1997-2002 Max-Planck-Institute Saarbruecken (Germany).
|
||
|
|
// All rights reserved.
|
||
|
|
//
|
||
|
|
// This file is part of CGAL (www.cgal.org).
|
||
|
|
// You can redistribute it and/or modify it under the terms of the GNU
|
||
|
|
// General Public License as published by the Free Software Foundation,
|
||
|
|
// either version 3 of the License, or (at your option) any later version.
|
||
|
|
//
|
||
|
|
// Licensees holding a valid commercial license may use this file in
|
||
|
|
// accordance with the commercial license agreement provided with the software.
|
||
|
|
//
|
||
|
|
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
|
||
|
|
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
|
||
|
|
//
|
||
|
|
// $URL$
|
||
|
|
// $Id$
|
||
|
|
// SPDX-License-Identifier: GPL-3.0+
|
||
|
|
//
|
||
|
|
//
|
||
|
|
// Author(s) : Michael Seel <seel@mpi-sb.mpg.de>
|
||
|
|
|
||
|
|
#ifndef CGAL_SPHERE_DIRECTION_H
|
||
|
|
#define CGAL_SPHERE_DIRECTION_H
|
||
|
|
|
||
|
|
#include <CGAL/license/Nef_S2.h>
|
||
|
|
|
||
|
|
|
||
|
|
#include <CGAL/basic.h>
|
||
|
|
#include <CGAL/Kernel/global_functions_3.h>
|
||
|
|
|
||
|
|
namespace CGAL {
|
||
|
|
|
||
|
|
/*{\Manpage{Sphere_direction}{R}{Directions on the unit sphere}{c}}*/
|
||
|
|
|
||
|
|
template <class R_> class Sphere_direction : public R_::Plane_3 {
|
||
|
|
|
||
|
|
/*{\Mdefinition An object |\Mvar| of type |\Mname| is a direction
|
||
|
|
on the surface of the unit sphere. Such directions can be used to
|
||
|
|
describe walks that are part of great circles.}*/
|
||
|
|
|
||
|
|
public:
|
||
|
|
|
||
|
|
/*{\Mtypes 5}*/
|
||
|
|
typedef R_ R;
|
||
|
|
/*{\Mtypemember representation class.}*/
|
||
|
|
typedef typename R::RT RT;
|
||
|
|
/*{\Mtypemember ring type.}*/
|
||
|
|
|
||
|
|
typedef typename R_::Point_3 Point_3;
|
||
|
|
typedef typename R_::Plane_3 Plane_3;
|
||
|
|
typedef typename R_::Plane_3 Base;
|
||
|
|
typedef Sphere_direction<R_> Self;
|
||
|
|
|
||
|
|
/*{\Mcreation 5}*/
|
||
|
|
Sphere_direction() : Base() {}
|
||
|
|
/*{\Mcreate creates some direction.}*/
|
||
|
|
|
||
|
|
Sphere_direction(const Sphere_circle<R>& c)
|
||
|
|
/*{\Mcreate creates the direction corresponding to the circle |c|.}*/
|
||
|
|
: Base(c) {}
|
||
|
|
|
||
|
|
Sphere_direction(const Sphere_point<R>& p, const Sphere_point<R>&q)
|
||
|
|
: Base(Point_3(0,0,0),p,q)
|
||
|
|
/*{\Mcreate creates a direction that describes the orientation of
|
||
|
|
the great circle through $p$ and $q$ (oriented such that the segment
|
||
|
|
$pq$ is the shorter one of the two possible ones. \precond $p$ and $q$
|
||
|
|
are not opposite on $S_2$.}*/
|
||
|
|
{ CGAL_assertion(p!=q.opposite());
|
||
|
|
Point_3 p1(0,0,0), p4 = CGAL::ORIGIN + ((Base*) this)->orthogonal_vector();
|
||
|
|
if ( CGAL::orientation(p1,p,q,p4) != CGAL::POSITIVE )
|
||
|
|
*this = Sphere_direction(opposite());
|
||
|
|
}
|
||
|
|
|
||
|
|
Sphere_direction(const typename R::Plane_3& h)
|
||
|
|
/*{\Xcreate creates the direction corresponding to the plane |h|.
|
||
|
|
\precond |h| contains the origin.}*/
|
||
|
|
: Base(h) { CGAL_assertion(h.d() == 0); }
|
||
|
|
|
||
|
|
/*{\Moperations 4 2}*/
|
||
|
|
|
||
|
|
Sphere_direction<R> opposite() const
|
||
|
|
/*{\Mop returns the opposite of |\Mvar|.}*/
|
||
|
|
{ return Base::opposite(); }
|
||
|
|
|
||
|
|
Plane_3 plane() const { return Base(*this); }
|
||
|
|
/*{\Xop returns the plane supporting |\Mvar|.}*/
|
||
|
|
|
||
|
|
}; // Sphere_direction<R>
|
||
|
|
|
||
|
|
|
||
|
|
/* We have:
|
||
|
|
1) all directions fixed at p
|
||
|
|
2) d1==d3 possible
|
||
|
|
return true iff d1,d2,d3 are stricly ccw ordered around p
|
||
|
|
Note: Sphere_directions are Plane_3
|
||
|
|
we therefore compare the normal vectors of the planes
|
||
|
|
that underly the directions d1,d2,d3 in the plane
|
||
|
|
through 0 and orthogonal to the vector p-0
|
||
|
|
*/
|
||
|
|
|
||
|
|
template <typename R>
|
||
|
|
bool strictly_ordered_ccw_at(const Sphere_point<R>& p,
|
||
|
|
const Sphere_direction<R>& d1,
|
||
|
|
const Sphere_direction<R>& d2,
|
||
|
|
const Sphere_direction<R>& d3)
|
||
|
|
{ CGAL_assertion(d1.has_on(p) && d2.has_on(p) && d3.has_on(p));
|
||
|
|
typename R::Point_3 p0(0,0,0);
|
||
|
|
typename R::Point_3 p1(CGAL::ORIGIN + d1.orthogonal_vector());
|
||
|
|
typename R::Point_3 p2(CGAL::ORIGIN + d2.orthogonal_vector());
|
||
|
|
typename R::Point_3 p3(CGAL::ORIGIN + d3.orthogonal_vector());
|
||
|
|
|
||
|
|
if ( d1 == d3 ) return false;
|
||
|
|
if ( CGAL::orientation(p0,p,p1,p3) == CGAL::POSITIVE ) {
|
||
|
|
return CGAL::orientation(p0,p,p1,p2) == CGAL::POSITIVE &&
|
||
|
|
CGAL::orientation(p0,p,p3,p2) == CGAL::NEGATIVE;
|
||
|
|
} else {
|
||
|
|
return CGAL::orientation(p0,p,p1,p2) == CGAL::POSITIVE ||
|
||
|
|
CGAL::orientation(p0,p,p3,p2) == CGAL::NEGATIVE;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
|
||
|
|
} //namespace CGAL
|
||
|
|
#endif //CGAL_SPHERE_DIRECTION_H
|