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
|
// Copyright (c) 1999 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL 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-3.6-branch/Triangulation_3/include/CGAL/predicates/Regular_triangulation_ftC3.h $
// $Id: Regular_triangulation_ftC3.h 52320 2009-10-15 08:27:22Z sloriot $
//
//
// Author(s) : Sylvain Pion
#ifndef CGAL_REGULAR_TRIANGULATION_FTC3_H
#define CGAL_REGULAR_TRIANGULATION_FTC3_H
// This file contains the low level cartesian predicates
// used by the 3D regular triangulation.
CGAL_BEGIN_NAMESPACE
// return minus the sign of the 5x5 determinant [P,Q,R,S,T]
// where column [P] = transpose[px,py,pz,p^2 -wp,1]
template <class FT>
Oriented_side
power_testC3( const FT &px, const FT &py, const FT &pz, const FT &pwt,
const FT &qx, const FT &qy, const FT &qz, const FT &qwt,
const FT &rx, const FT &ry, const FT &rz, const FT &rwt,
const FT &sx, const FT &sy, const FT &sz, const FT &swt,
const FT &tx, const FT &ty, const FT &tz, const FT &twt)
{
// We translate the points so that T becomes the origin.
FT dpx = px - tx;
FT dpy = py - ty;
FT dpz = pz - tz;
FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) +
CGAL_NTS square(dpz) + (twt - pwt);
FT dqx = qx - tx;
FT dqy = qy - ty;
FT dqz = qz - tz;
FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) +
CGAL_NTS square(dqz) + (twt - qwt);
FT drx = rx - tx;
FT dry = ry - ty;
FT drz = rz - tz;
FT drt = CGAL_NTS square(drx) + CGAL_NTS square(dry) +
CGAL_NTS square(drz) + (twt - rwt);
FT dsx = sx - tx;
FT dsy = sy - ty;
FT dsz = sz - tz;
FT dst = CGAL_NTS square(dsx) + CGAL_NTS square(dsy) +
CGAL_NTS square(dsz) + (twt - swt);
return - sign_of_determinant(dpx, dpy, dpz, dpt,
dqx, dqy, dqz, dqt,
drx, dry, drz, drt,
dsx, dsy, dsz, dst);
}
template <class FT>
Oriented_side
power_testC3( const FT &px, const FT &py, const FT &pz, const FT &pwt,
const FT &qx, const FT &qy, const FT &qz, const FT &qwt,
const FT &rx, const FT &ry, const FT &rz, const FT &rwt,
const FT &tx, const FT &ty, const FT &tz, const FT &twt)
{
// Same translation as above.
FT dpx = px - tx;
FT dpy = py - ty;
FT dpz = pz - tz;
FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) +
CGAL_NTS square(dpz) + (twt - pwt);
FT dqx = qx - tx;
FT dqy = qy - ty;
FT dqz = qz - tz;
FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) +
CGAL_NTS square(dqz) + (twt - qwt);
FT drx = rx - tx;
FT dry = ry - ty;
FT drz = rz - tz;
FT drt = CGAL_NTS square(drx) + CGAL_NTS square(dry) +
CGAL_NTS square(drz) + (twt - rwt);
Sign cmp;
// Projection on the (xy) plane.
cmp = sign_of_determinant(dpx, dpy, dpt,
dqx, dqy, dqt,
drx, dry, drt);
if (cmp != ZERO)
return cmp * sign_of_determinant(px-rx, py-ry,
qx-rx, qy-ry);
// Projection on the (xz) plane.
cmp = sign_of_determinant(dpx, dpz, dpt,
dqx, dqz, dqt,
drx, drz, drt);
if (cmp != ZERO)
return cmp * sign_of_determinant(px-rx, pz-rz,
qx-rx, qz-rz);
// Projection on the (yz) plane.
cmp = sign_of_determinant(dpy, dpz, dpt,
dqy, dqz, dqt,
dry, drz, drt);
return cmp * sign_of_determinant(py-ry, pz-rz,
qy-ry, qz-rz);
}
template <class FT>
Oriented_side
power_testC3( const FT &px, const FT &py, const FT &pz, const FT &pwt,
const FT &qx, const FT &qy, const FT &qz, const FT &qwt,
const FT &tx, const FT &ty, const FT &tz, const FT &twt)
{
// Same translation as above.
FT dpx = px - tx;
FT dpy = py - ty;
FT dpz = pz - tz;
FT dpt = CGAL_NTS square(dpx) + CGAL_NTS square(dpy) +
CGAL_NTS square(dpz) + (twt - pwt);
FT dqx = qx - tx;
FT dqy = qy - ty;
FT dqz = qz - tz;
FT dqt = CGAL_NTS square(dqx) + CGAL_NTS square(dqy) +
CGAL_NTS square (dqz) + (twt - qwt);
Comparison_result cmp;
// We do an orthogonal projection on the (x) axis, if possible.
cmp = CGAL_NTS compare(px, qx);
if (cmp != EQUAL)
return cmp * sign_of_determinant(dpx, dpt, dqx, dqt);
// We do an orthogonal projection on the (y) axis, if possible.
cmp = CGAL_NTS compare(py, qy);
if (cmp != EQUAL)
return cmp * sign_of_determinant(dpy, dpt, dqy, dqt);
// We do an orthogonal projection on the (z) axis.
cmp = CGAL_NTS compare(pz, qz);
return cmp * sign_of_determinant(dpz, dpt, dqz, dqt);
}
template <class FT>
Oriented_side
power_testC3(const FT &pwt, const FT &qwt)
{
return CGAL_NTS compare(qwt, pwt);
}
CGAL_END_NAMESPACE
#endif // CGAL_REGULAR_TRIANGULATION_FTC3_H
|
