FACT++  1.0
rm2v.c
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1 #include "erfa.h"
2 
3 void eraRm2v(double r[3][3], double w[3])
4 /*
5 ** - - - - - - - -
6 ** e r a R m 2 v
7 ** - - - - - - - -
8 **
9 ** Express an r-matrix as an r-vector.
10 **
11 ** Given:
12 ** r double[3][3] rotation matrix
13 **
14 ** Returned:
15 ** w double[3] rotation vector (Note 1)
16 **
17 ** Notes:
18 **
19 ** 1) A rotation matrix describes a rotation through some angle about
20 ** some arbitrary axis called the Euler axis. The "rotation vector"
21 ** returned by this function has the same direction as the Euler axis,
22 ** and its magnitude is the angle in radians. (The magnitude and
23 ** direction can be separated by means of the function eraPn.)
24 **
25 ** 2) If r is null, so is the result. If r is not a rotation matrix
26 ** the result is undefined; r must be proper (i.e. have a positive
27 ** determinant) and real orthogonal (inverse = transpose).
28 **
29 ** 3) The reference frame rotates clockwise as seen looking along
30 ** the rotation vector from the origin.
31 **
32 ** Copyright (C) 2013-2015, NumFOCUS Foundation.
33 ** Derived, with permission, from the SOFA library. See notes at end of file.
34 */
35 {
36  double x, y, z, s2, c2, phi, f;
37 
38 
39  x = r[1][2] - r[2][1];
40  y = r[2][0] - r[0][2];
41  z = r[0][1] - r[1][0];
42  s2 = sqrt(x*x + y*y + z*z);
43  if (s2 > 0) {
44  c2 = r[0][0] + r[1][1] + r[2][2] - 1.0;
45  phi = atan2(s2, c2);
46  f = phi / s2;
47  w[0] = x * f;
48  w[1] = y * f;
49  w[2] = z * f;
50  } else {
51  w[0] = 0.0;
52  w[1] = 0.0;
53  w[2] = 0.0;
54  }
55 
56  return;
57 
58 }
59 /*----------------------------------------------------------------------
60 **
61 **
62 ** Copyright (C) 2013-2015, NumFOCUS Foundation.
63 ** All rights reserved.
64 **
65 ** This library is derived, with permission, from the International
66 ** Astronomical Union's "Standards of Fundamental Astronomy" library,
67 ** available from http://www.iausofa.org.
68 **
69 ** The ERFA version is intended to retain identical functionality to
70 ** the SOFA library, but made distinct through different function and
71 ** file names, as set out in the SOFA license conditions. The SOFA
72 ** original has a role as a reference standard for the IAU and IERS,
73 ** and consequently redistribution is permitted only in its unaltered
74 ** state. The ERFA version is not subject to this restriction and
75 ** therefore can be included in distributions which do not support the
76 ** concept of "read only" software.
77 **
78 ** Although the intent is to replicate the SOFA API (other than
79 ** replacement of prefix names) and results (with the exception of
80 ** bugs; any that are discovered will be fixed), SOFA is not
81 ** responsible for any errors found in this version of the library.
82 **
83 ** If you wish to acknowledge the SOFA heritage, please acknowledge
84 ** that you are using a library derived from SOFA, rather than SOFA
85 ** itself.
86 **
87 **
88 ** TERMS AND CONDITIONS
89 **
90 ** Redistribution and use in source and binary forms, with or without
91 ** modification, are permitted provided that the following conditions
92 ** are met:
93 **
94 ** 1 Redistributions of source code must retain the above copyright
95 ** notice, this list of conditions and the following disclaimer.
96 **
97 ** 2 Redistributions in binary form must reproduce the above copyright
98 ** notice, this list of conditions and the following disclaimer in
99 ** the documentation and/or other materials provided with the
100 ** distribution.
101 **
102 ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
103 ** the International Astronomical Union nor the names of its
104 ** contributors may be used to endorse or promote products derived
105 ** from this software without specific prior written permission.
106 **
107 ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
108 ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
109 ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
110 ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
111 ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
112 ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
113 ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
114 ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
115 ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
116 ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
117 ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
118 ** POSSIBILITY OF SUCH DAMAGE.
119 **
120 */
eraRm2v
void eraRm2v(double r[3][3], double w[3])
Definition: rm2v.c:3