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) 2013-2014, 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) 2013-2014, 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