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// Copyright (c) 2002
// Utrecht University (The Netherlands),
// ETH Zurich (Switzerland),
// INRIA Sophia-Antipolis (France),
// Max-Planck-Institute Saarbruecken (Germany),
// and Tel-Aviv University (Israel). All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Kernel_d/include/CGAL/Kernel_d/intersection_objectsHd.h $
// $Id: include/CGAL/Kernel_d/intersection_objectsHd.h b26b07a1242 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : ?
#ifndef CGAL_INTERSECTION_OBJECTSHD_H
#define CGAL_INTERSECTION_OBJECTSHD_H
#include <CGAL/basic.h>
namespace CGAL {
/*{\Manpage{Line_line_intersectionHd}{R}{intersecting two lines}}*/
template <class R>
class Line_line_intersectionHd {
typedef typename R::RT RT;
typedef typename R::FT FT;
typedef typename R::LA LA;
typedef typename R::Point_d Point_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;
RT D;
RT s1w = s1.homogeneous(d);
RT t1w = t1.homogeneous(d);
RT s2w = s2.homogeneous(d);
RT t2w = t2.homogeneous(d);
RT g1w = s1w*t1w;
RT g2w = s2w*t2w;
RT t12w = t1w*t2w;
/* init $d \times 2$ - matrix |M| and $d$ - vector |b| */
for (i = 0; i < d; i++) {
M(i,0) = g2w * (t1.homogeneous(i) * s1w - s1.homogeneous(i) * t1w);
M(i,1) = g1w * (s2.homogeneous(i) * t2w - t2.homogeneous(i) * s2w);
b[i] = t12w * (s2.homogeneous(i) * s1w - s1.homogeneous(i) * s2w);
}
if (LA::linear_solver(M,b,lambda,D,S,c)) {
if (S.column_dimension()>0) return LINE;
l1 = R::make_FT(lambda[0],D);
l2 = R::make_FT(lambda[1],D);
p = s1 + l1 * (t1 - s1);
return POINT;
}
return NO_INTERSECTION;
}
};
/*{\Manpage {Line_hyperplane_intersectionHd}{R}
{intersecting a line and a hyperplane}}*/
template <class R>
class Line_hyperplane_intersectionHd {
typedef typename R::RT RT;
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;
RT S(0),T(0);
for (i=0; i<=d; ++i) {
S += h[i]*s.homogeneous(i);
T += h[i]*t.homogeneous(i);
}
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
RT D = S * t.homogeneous(d) - T * s.homogeneous(d);
if (CGAL_NTS is_zero(D)) return NO_INTERSECTION;
typename LA::Vector homog(d + 1);
for (i = 0; i < d; ++i)
homog[i] = S * t.homogeneous(i) - T * s.homogeneous(i);
homog[d] = D;
p = Point_d(d,homog.begin(),homog.end());
lambda = R::make_FT(S * t.homogeneous(d), D);
return POINT;
}
};
} //namespace CGAL
#include <CGAL/Kernel_d/intersection_objects_d.h>
#endif //CGAL_INTERSECTION_OBJECTSHD_H
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