1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
|
// 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_objectsCd.h $
// $Id: include/CGAL/Kernel_d/intersection_objectsCd.h b26b07a1242 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : ?
#ifndef CGAL_INTERSECTION_OBJECTSCD_H
#define CGAL_INTERSECTION_OBJECTSCD_H
#include <CGAL/basic.h>
#include <CGAL/Kernel_d/debug.h>
namespace CGAL {
/*{\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;
}
};
} //namespace CGAL
#include <CGAL/Kernel_d/intersection_objects_d.h>
#endif //CGAL_INTERSECTION_OBJECTSCD_H
|
