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// Copyright (c) 2002 Utrecht University (The Netherlands),
// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
// and Tel-Aviv University (Israel). 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 Lesser General Public License as
// published by the Free Software Foundation; version 2.1 of the License.
// See the file LICENSE.LGPL distributed with CGAL.
//
// 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: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.5-branch/Kernel_d/include/CGAL/Kernel_d/intersection_objectsCd.h $
// $Id: intersection_objectsCd.h 41666 2008-01-17 21:59:23Z spion $
//
//
// Author(s) : ?
#ifndef CGAL_INTERSECTION_OBJECTSCD_H
#define CGAL_INTERSECTION_OBJECTSCD_H
#include <CGAL/basic.h>
#include <CGAL/Kernel_d/debug.h>
CGAL_BEGIN_NAMESPACE
/*{\Manpage{Line_line_intersectionCd}{R}{intersecting two lines}}*/
template <class R>
class Line_line_intersectionCd {
typedef typename R::FT FT;
typedef typename R::LA LA;
typedef typename R::Point_d Point_d;
typedef typename R::Line_d Line_d;
public:
enum Intersection_result { NO_INTERSECTION, POINT, LINE };
Intersection_result operator()(
const Point_d& s1, const Point_d& t1,
const Point_d& s2, const Point_d& t2,
Point_d& p, FT& l1, FT& l2)
/*{\Mfunop returns |NO_INTERSECTION| if the lines which are represented by |s1t1|
and |s2t2| don't intersect, returns |POINT| if they intersect in a
unique point, and returns LINE if they are identical. In the |POINT|
case the point of intersection is assigned to |p|. Then |p = s1 + l1
* t1-s1| and |p = s2 + l2 * t2-s2|. \precond none of the point pairs
is degenerate.}*/
{
int d = s1.dimension(),i;
CGAL_assertion_msg(d==s2.dimension(),
"intersection: dimensions disagree!");
typename LA::Matrix M(d,2),S;
typename LA::Vector b(d), lambda(2), c;
FT D;
/* init $d \times 2$ - matrix |M| and $d$ - vector |b| */
for (i = 0; i < d; i++) {
M(i,0) = t1.cartesian(i) - s1.cartesian(i);
M(i,1) = s2.cartesian(i) - t2.cartesian(i);
b[i] = s2.cartesian(i) - s1.cartesian(i);
}
if (LA::linear_solver(M,b,lambda,D,S,c)) {
if ( S.column_dimension()>0 ) return LINE;
l1 = lambda[0]; l2 = lambda[1];
p = s1 + l1 * (t1 - s1);
#ifdef CGAL_CHECK_EXACTNESS
Line_d L1(s1,t1), L2(s2,t2);
CGAL_assertion(L1.has_on(p)&&L2.has_on(p));
#endif
return POINT;
}
return NO_INTERSECTION;
}
};
/*{\Manpage {Line_hyperplane_intersectionCd}{R}
{intersecting a line and a hyperplane}}*/
template <class R>
class Line_hyperplane_intersectionCd {
typedef typename R::FT FT;
typedef typename R::LA LA;
typedef typename R::Point_d Point_d;
typedef typename R::Hyperplane_d Hyperplane_d;
public:
enum Intersection_result { NO_INTERSECTION, POINT, LINE };
Intersection_result operator()(const Point_d& s, const Point_d& t,
const Hyperplane_d& h, Point_d& p, FT& lambda)
/*{\Mfunop returns |NO_INTERSECTION| if the line represented by |s1t1| and the
hyperplane |h| don't intersect, returns |POINT| if they intersect in a
unique point, and returns LINE if the line is part of the
hyperplane. In the |POINT| case the point of intersection is assigned
to |p|. Then |p = s1 + lambda * t1-s1|. \precond the point pair is
not degenerate.}*/
{
CGAL_assertion_msg((h.dimension()==s.dimension() &&
h.dimension()==t.dimension()),
"Line_hyperplane_intersection_d: dimensions do not agree.");
int d = h.dimension(),i;
FT S = h.value_at(s), T = h.value_at(t);
bool s_contained = CGAL_NTS is_zero(S),
t_contained = CGAL_NTS is_zero(T);
if (s_contained && t_contained) { p = s; return LINE; }
if (s_contained) { p = s; return POINT; }
if (t_contained) { p = t; return POINT; }
// now the simple cases are done
FT D = S - T;
if ( CGAL_NTS is_zero(D) ) return NO_INTERSECTION;
typename LA::Vector v(d);
for (i = 0; i < d; ++i)
v[i] = (S * t.cartesian(i) - T * s.cartesian(i))/D;
p = Point_d(d,v.begin(),v.end()); lambda = S/D;
#ifdef CGAL_CHECK_EXACTNESS
Line_d l(s,t);
CGAL_assertion(h.has_on(p)&&l.has_on(p));
#endif
return POINT;
}
};
CGAL_END_NAMESPACE
#include <CGAL/Kernel_d/intersection_objects_d.h>
#endif //CGAL_INTERSECTION_OBJECTSCD_H
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