1 #include "erfa.h"
2
eraPap(double a[3],double b[3])3 double eraPap(double a[3], double b[3])
4 /*
5 ** - - - - - - -
6 ** e r a P a p
7 ** - - - - - - -
8 **
9 ** Position-angle from two p-vectors.
10 **
11 ** Given:
12 ** a double[3] direction of reference point
13 ** b double[3] direction of point whose PA is required
14 **
15 ** Returned (function value):
16 ** double position angle of b with respect to a (radians)
17 **
18 ** Notes:
19 **
20 ** 1) The result is the position angle, in radians, of direction b with
21 ** respect to direction a. It is in the range -pi to +pi. The
22 ** sense is such that if b is a small distance "north" of a the
23 ** position angle is approximately zero, and if b is a small
24 ** distance "east" of a the position angle is approximately +pi/2.
25 **
26 ** 2) The vectors a and b need not be of unit length.
27 **
28 ** 3) Zero is returned if the two directions are the same or if either
29 ** vector is null.
30 **
31 ** 4) If vector a is at a pole, the result is ill-defined.
32 **
33 ** Called:
34 ** eraPn decompose p-vector into modulus and direction
35 ** eraPm modulus of p-vector
36 ** eraPxp vector product of two p-vectors
37 ** eraPmp p-vector minus p-vector
38 ** eraPdp scalar product of two p-vectors
39 **
40 ** Copyright (C) 2013-2020, NumFOCUS Foundation.
41 ** Derived, with permission, from the SOFA library. See notes at end of file.
42 */
43 {
44 double am, au[3], bm, st, ct, xa, ya, za, eta[3], xi[3], a2b[3], pa;
45
46
47 /* Modulus and direction of the a vector. */
48 eraPn(a, &am, au);
49
50 /* Modulus of the b vector. */
51 bm = eraPm(b);
52
53 /* Deal with the case of a null vector. */
54 if ((am == 0.0) || (bm == 0.0)) {
55 st = 0.0;
56 ct = 1.0;
57 } else {
58
59 /* The "north" axis tangential from a (arbitrary length). */
60 xa = a[0];
61 ya = a[1];
62 za = a[2];
63 eta[0] = -xa * za;
64 eta[1] = -ya * za;
65 eta[2] = xa*xa + ya*ya;
66
67 /* The "east" axis tangential from a (same length). */
68 eraPxp(eta, au, xi);
69
70 /* The vector from a to b. */
71 eraPmp(b, a, a2b);
72
73 /* Resolve into components along the north and east axes. */
74 st = eraPdp(a2b, xi);
75 ct = eraPdp(a2b, eta);
76
77 /* Deal with degenerate cases. */
78 if ((st == 0.0) && (ct == 0.0)) ct = 1.0;
79 }
80
81 /* Position angle. */
82 pa = atan2(st, ct);
83
84 return pa;
85
86 }
87 /*----------------------------------------------------------------------
88 **
89 **
90 ** Copyright (C) 2013-2020, NumFOCUS Foundation.
91 ** All rights reserved.
92 **
93 ** This library is derived, with permission, from the International
94 ** Astronomical Union's "Standards of Fundamental Astronomy" library,
95 ** available from http://www.iausofa.org.
96 **
97 ** The ERFA version is intended to retain identical functionality to
98 ** the SOFA library, but made distinct through different function and
99 ** file names, as set out in the SOFA license conditions. The SOFA
100 ** original has a role as a reference standard for the IAU and IERS,
101 ** and consequently redistribution is permitted only in its unaltered
102 ** state. The ERFA version is not subject to this restriction and
103 ** therefore can be included in distributions which do not support the
104 ** concept of "read only" software.
105 **
106 ** Although the intent is to replicate the SOFA API (other than
107 ** replacement of prefix names) and results (with the exception of
108 ** bugs; any that are discovered will be fixed), SOFA is not
109 ** responsible for any errors found in this version of the library.
110 **
111 ** If you wish to acknowledge the SOFA heritage, please acknowledge
112 ** that you are using a library derived from SOFA, rather than SOFA
113 ** itself.
114 **
115 **
116 ** TERMS AND CONDITIONS
117 **
118 ** Redistribution and use in source and binary forms, with or without
119 ** modification, are permitted provided that the following conditions
120 ** are met:
121 **
122 ** 1 Redistributions of source code must retain the above copyright
123 ** notice, this list of conditions and the following disclaimer.
124 **
125 ** 2 Redistributions in binary form must reproduce the above copyright
126 ** notice, this list of conditions and the following disclaimer in
127 ** the documentation and/or other materials provided with the
128 ** distribution.
129 **
130 ** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
131 ** the International Astronomical Union nor the names of its
132 ** contributors may be used to endorse or promote products derived
133 ** from this software without specific prior written permission.
134 **
135 ** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
136 ** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
137 ** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
138 ** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
139 ** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
140 ** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
141 ** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
142 ** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
143 ** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
144 ** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
145 ** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
146 ** POSSIBILITY OF SUCH DAMAGE.
147 **
148 */
149