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
|
/*************************************************************************
* *
* Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith. *
* All rights reserved. Email: russ@q12.org Web: www.q12.org *
* *
* This library is free software; you can redistribute it and/or *
* modify it under the terms of EITHER: *
* (1) The GNU Lesser General Public License as published by the Free *
* Software Foundation; either version 2.1 of the License, or (at *
* your option) any later version. The text of the GNU Lesser *
* General Public License is included with this library in the *
* file LICENSE.TXT. *
* (2) The BSD-style license that is included with this library in *
* the file LICENSE-BSD.TXT. *
* *
* This library is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files *
* LICENSE.TXT and LICENSE-BSD.TXT for more details. *
* *
*************************************************************************/
#include <ode/common.h>
#include <ode/odemath.h>
// get some math functions under windows
#ifdef WIN32
#include <float.h>
#ifndef CYGWIN // added by andy for cygwin
#undef copysign
#define copysign(a,b) ((dReal)_copysign(a,b))
#endif // added by andy for cygwin
#endif
#undef dNormalize3
#undef dNormalize4
// this may be called for vectors `a' with extremely small magnitude, for
// example the result of a cross product on two nearly perpendicular vectors.
// we must be robust to these small vectors. to prevent numerical error,
// first find the component a[i] with the largest magnitude and then scale
// all the components by 1/a[i]. then we can compute the length of `a' and
// scale the components by 1/l. this has been verified to work with vectors
// containing the smallest representable numbers.
int dSafeNormalize3 (dVector3 a)
{
dReal a0,a1,a2,aa0,aa1,aa2,l;
dAASSERT (a);
a0 = a[0];
a1 = a[1];
a2 = a[2];
aa0 = dFabs(a0);
aa1 = dFabs(a1);
aa2 = dFabs(a2);
if (aa1 > aa0) {
if (aa2 > aa1) {
goto aa2_largest;
}
else { // aa1 is largest
a0 /= aa1;
a2 /= aa1;
l = dRecipSqrt (a0*a0 + a2*a2 + 1);
a[0] = a0*l;
a[1] = dCopySign(l,a1);
a[2] = a2*l;
}
}
else {
if (aa2 > aa0) {
aa2_largest: // aa2 is largest
a0 /= aa2;
a1 /= aa2;
l = dRecipSqrt (a0*a0 + a1*a1 + 1);
a[0] = a0*l;
a[1] = a1*l;
a[2] = dCopySign(l,a2);
}
else { // aa0 is largest
if (aa0 <= 0) {
a[0] = 1; // if all a's are zero, this is where we'll end up.
a[1] = 0; // return a default unit length vector.
a[2] = 0;
return 0;
}
a1 /= aa0;
a2 /= aa0;
l = dRecipSqrt (a1*a1 + a2*a2 + 1);
a[0] = dCopySign(l,a0);
a[1] = a1*l;
a[2] = a2*l;
}
}
return 1;
}
/* OLD VERSION */
/*
void dNormalize3 (dVector3 a)
{
dIASSERT (a);
dReal l = dDOT(a,a);
if (l > 0) {
l = dRecipSqrt(l);
a[0] *= l;
a[1] *= l;
a[2] *= l;
}
else {
a[0] = 1;
a[1] = 0;
a[2] = 0;
}
}
*/
void dNormalize3(dVector3 a)
{
_dNormalize3(a);
}
int dSafeNormalize4 (dVector4 a)
{
dAASSERT (a);
dReal l = dDOT(a,a)+a[3]*a[3];
if (l > 0) {
l = dRecipSqrt(l);
a[0] *= l;
a[1] *= l;
a[2] *= l;
a[3] *= l;
return 1;
}
else {
a[0] = 1;
a[1] = 0;
a[2] = 0;
a[3] = 0;
return 0;
}
}
void dNormalize4(dVector4 a)
{
_dNormalize4(a);
}
void dPlaneSpace (const dVector3 n, dVector3 p, dVector3 q)
{
dAASSERT (n && p && q);
if (dFabs(n[2]) > M_SQRT1_2) {
// choose p in y-z plane
dReal a = n[1]*n[1] + n[2]*n[2];
dReal k = dRecipSqrt (a);
p[0] = 0;
p[1] = -n[2]*k;
p[2] = n[1]*k;
// set q = n x p
q[0] = a*k;
q[1] = -n[0]*p[2];
q[2] = n[0]*p[1];
}
else {
// choose p in x-y plane
dReal a = n[0]*n[0] + n[1]*n[1];
dReal k = dRecipSqrt (a);
p[0] = -n[1]*k;
p[1] = n[0]*k;
p[2] = 0;
// set q = n x p
q[0] = -n[2]*p[1];
q[1] = n[2]*p[0];
q[2] = a*k;
}
}
|
