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
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
|
// Copyright (c) 2000
// 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); 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; 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: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/next/Intersections_2/include/CGAL/Ray_2_Ray_2_intersection.h $
// $Id: Ray_2_Ray_2_intersection.h 67093 2012-01-13 11:22:39Z lrineau $
//
//
// Author(s) : Geert-Jan Giezeman
#ifndef CGAL_RAY_2_RAY_2_INTERSECTION_H
#define CGAL_RAY_2_RAY_2_INTERSECTION_H
#include <CGAL/Ray_2.h>
#include <CGAL/Segment_2.h>
#include <CGAL/Point_2.h>
#include <CGAL/kernel_assertions.h>
#include <CGAL/number_utils.h>
#include <CGAL/Line_2.h>
#include <CGAL/Line_2_Line_2_intersection.h>
#include <CGAL/Object.h>
namespace CGAL {
namespace internal {
template <class K>
class Ray_2_Ray_2_pair {
public:
enum Intersection_results {NO_INTERSECTION, POINT, SEGMENT, RAY};
Ray_2_Ray_2_pair(typename K::Ray_2 const *ray1,
typename K::Ray_2 const *ray2)
: _ray1(ray1), _ray2(ray2), _known(false) {}
Intersection_results intersection_type() const;
typename K::Point_2 intersection_point() const;
typename K::Segment_2 intersection_segment() const;
typename K::Ray_2 intersection_ray() const;
protected:
typename K::Ray_2 const* _ray1;
typename K::Ray_2 const * _ray2;
mutable bool _known;
mutable Intersection_results _result;
mutable typename K::Point_2 _intersection_point, _other_point;
};
template <class K>
inline bool do_intersect(
const typename K::Ray_2 &p1,
const typename K::Ray_2 &p2,
const K&)
{
typedef Ray_2_Ray_2_pair<K> pair_t;
pair_t pair(&p1, &p2);
return pair.intersection_type() != pair_t::NO_INTERSECTION;
}
template <class K>
typename Ray_2_Ray_2_pair<K>::Intersection_results
Ray_2_Ray_2_pair<K>::intersection_type() const
{
if (_known)
return _result;
// The non const this pointer is used to cast away const.
_known = true;
// if (!do_overlap(_ray1->bbox(), _ray2->bbox()))
// return NO_INTERSECTION;
const typename K::Line_2 &l1 = _ray1->supporting_line();
const typename K::Line_2 &l2 = _ray2->supporting_line();
Line_2_Line_2_pair<K> linepair(&l1, &l2);
switch ( linepair.intersection_type()) {
case Line_2_Line_2_pair<K>::NO_INTERSECTION:
_result = NO_INTERSECTION;
return _result;
case Line_2_Line_2_pair<K>::POINT:
_intersection_point = linepair.intersection_point();
_result = (_ray1->collinear_has_on(_intersection_point)
&& _ray2->collinear_has_on(_intersection_point) )
? POINT : NO_INTERSECTION;
return _result;
case Line_2_Line_2_pair<K>::LINE:
{
typedef typename K::RT RT;
const typename K::Vector_2 &dir1 = _ray1->direction().to_vector();
const typename K::Vector_2 &dir2 = _ray2->direction().to_vector();
if (CGAL_NTS abs(dir1.x()) > CGAL_NTS abs(dir1.y())) {
typedef typename K::FT FT;
if (dir1.x() > FT(0)) {
if (dir2.x() > FT(0)) {
_intersection_point =
(_ray1->source().x() < _ray2->source().x())
? _ray2->source() : _ray1->source();
_result = RAY;
return _result;
} else {
if (_ray1->source().x() > _ray2->source().x()) {
_result = NO_INTERSECTION;
return _result;
}
if (_ray1->source().x() == _ray2->source().x()) {
_intersection_point = _ray1->source();
_result = POINT;
return _result;
}
_result = SEGMENT;
return _result;
}
} else {
if (dir2.x() < FT(0)) {
_intersection_point =
(_ray1->source().x() > _ray2->source().x())
? _ray2->source() : _ray1->source();
_result = RAY;
return _result;
} else {
if (_ray1->source().x() < _ray2->source().x()) {
_result = NO_INTERSECTION;
return _result;
}
if (_ray1->source().x() == _ray2->source().x()) {
_intersection_point = _ray1->source();
_result = POINT;
return _result;
}
_result = SEGMENT;
return _result;
}
}
} else {
typedef typename K::FT FT;
if (dir1.y() > FT(0)) {
if (dir2.y() > FT(0)) {
_intersection_point =
(_ray1->source().y() < _ray2->source().y())
? _ray2->source() : _ray1->source();
_result = RAY;
return _result;
} else {
if (_ray1->source().y() > _ray2->source().y()) {
_result = NO_INTERSECTION;
return _result;
}
if (_ray1->source().y() == _ray2->source().y()) {
_intersection_point = _ray1->source();
_result = POINT;
return _result;
}
_result = SEGMENT;
return _result;
}
} else {
if (dir2.y() < FT(0)) {
_intersection_point =
(_ray1->source().y() > _ray2->source().y())
? _ray2->source() : _ray1->source();
_result = RAY;
return _result;
} else {
if (_ray1->source().y() < _ray2->source().y()) {
_result = NO_INTERSECTION;
return _result;
}
if (_ray1->source().y() == _ray2->source().y()) {
_intersection_point = _ray1->source();
_result = POINT;
return _result;
}
_result = SEGMENT;
return _result;
}
}
}
}
default:
CGAL_kernel_assertion(false); // should not be reached:
return _result;
}
}
template <class K>
typename K::Point_2
Ray_2_Ray_2_pair<K>::intersection_point() const
{
if (!_known)
intersection_type();
CGAL_kernel_assertion(_result == POINT);
return _intersection_point;
}
template <class K>
typename K::Segment_2
Ray_2_Ray_2_pair<K>::intersection_segment() const
{
typedef typename K::Segment_2 Segment_2;
if (!_known)
intersection_type();
CGAL_kernel_assertion(_result == SEGMENT);
return Segment_2(_ray1->source(), _ray2->source());
}
template <class K>
typename K::Ray_2
Ray_2_Ray_2_pair<K>::intersection_ray() const
{
typedef typename K::Ray_2 Ray_2;
if (!_known)
intersection_type();
CGAL_kernel_assertion(_result == RAY);
return Ray_2(_intersection_point, _ray1->direction());
}
template <class K>
Object
intersection(const typename K::Ray_2 &ray1,
const typename K::Ray_2 &ray2,
const K&)
{
typedef Ray_2_Ray_2_pair<K> is_t;
is_t ispair(&ray1, &ray2);
switch (ispair.intersection_type()) {
case is_t::NO_INTERSECTION:
default:
return Object();
case is_t::POINT:
return make_object(ispair.intersection_point());
case is_t::SEGMENT:
return make_object(ispair.intersection_segment());
case is_t::RAY:
return make_object(ispair.intersection_ray());
}
}
} // namespace internal
template <class K>
inline
bool
do_intersect(const Ray_2<K> &ray1,
const Ray_2<K> &ray2)
{
typedef typename K::Do_intersect_2 Do_intersect;
return Do_intersect()(ray1, ray2);
}
template <class K>
Object
intersection(const Ray_2<K> &ray1,
const Ray_2<K> &ray2)
{
typedef typename K::Intersect_2 Intersect;
return Intersect()(ray1, ray2);
}
} //namespace CGAL
#endif
|
