File Coverage

erfasrc/src/tpors.c

Criterion	Covered	Total	%
statement	0	21	0.0
branch	0	6	0.0
condition			n/a
subroutine			n/a
pod			n/a
total	0	27	0.0

line	stmt	bran	code
1			#include "erfa.h"
2
3	0		int eraTpors(double xi, double eta, double a, double b,
4			double a01, double b01, double a02, double b02)
5			/*
6			** - - - - - - - - -
7			** e r a T p o r s
8			** - - - - - - - - -
9			**
10			** In the tangent plane projection, given the rectangular coordinates
11			** of a star and its spherical coordinates, determine the spherical
12			** coordinates of the tangent point.
13			**
14			** Given:
15			** xi,eta double rectangular coordinates of star image (Note 2)
16			** a,b double star's spherical coordinates (Note 3)
17			**
18			** Returned:
19			** a01,b01 double tangent point's spherical coordinates, Soln. 1
20			** a02,b02 double tangent point's spherical coordinates, Soln. 2
21			**
22			** Returned (function value):
23			** int number of solutions:
24			** 0 = no solutions returned (Note 5)
25			** 1 = only the first solution is useful (Note 6)
26			** 2 = both solutions are useful (Note 6)
27			**
28			** Notes:
29			**
30			** 1) The tangent plane projection is also called the "gnomonic
31			** projection" and the "central projection".
32			**
33			** 2) The eta axis points due north in the adopted coordinate system.
34			** If the spherical coordinates are observed (RA,Dec), the tangent
35			** plane coordinates (xi,eta) are conventionally called the
36			** "standard coordinates". If the spherical coordinates are with
37			** respect to a right-handed triad, (xi,eta) are also right-handed.
38			** The units of (xi,eta) are, effectively, radians at the tangent
39			** point.
40			**
41			** 3) All angular arguments are in radians.
42			**
43			** 4) The angles a01 and a02 are returned in the range 0-2pi. The
44			** angles b01 and b02 are returned in the range +/-pi, but in the
45			** usual, non-pole-crossing, case, the range is +/-pi/2.
46			**
47			** 5) Cases where there is no solution can arise only near the poles.
48			** For example, it is clearly impossible for a star at the pole
49			** itself to have a non-zero xi value, and hence it is meaningless
50			** to ask where the tangent point would have to be to bring about
51			** this combination of xi and dec.
52			**
53			** 6) Also near the poles, cases can arise where there are two useful
54			** solutions. The return value indicates whether the second of the
55			** two solutions returned is useful; 1 indicates only one useful
56			** solution, the usual case.
57			**
58			** 7) The basis of the algorithm is to solve the spherical triangle PSC,
59			** where P is the north celestial pole, S is the star and C is the
60			** tangent point. The spherical coordinates of the tangent point are
61			** [a0,b0]; writing rho^2 = (xi^2+eta^2) and r^2 = (1+rho^2), side c
62			** is then (pi/2-b), side p is sqrt(xi^2+eta^2) and side s (to be
63			** found) is (pi/2-b0). Angle C is given by sin(C) = xi/rho and
64			** cos(C) = eta/rho. Angle P (to be found) is the longitude
65			** difference between star and tangent point (a-a0).
66			**
67			** 8) This function is a member of the following set:
68			**
69			** spherical vector solve for
70			**
71			** eraTpxes eraTpxev xi,eta
72			** eraTpsts eraTpstv star
73			** > eraTpors < eraTporv origin
74			**
75			** Called:
76			** eraAnp normalize angle into range 0 to 2pi
77			**
78			** References:
79			**
80			** Calabretta M.R. & Greisen, E.W., 2002, "Representations of
81			** celestial coordinates in FITS", Astron.Astrophys. 395, 1077
82			**
83			** Green, R.M., "Spherical Astronomy", Cambridge University Press,
84			** 1987, Chapter 13.
85			**
86			** Copyright (C) 2013-2020, NumFOCUS Foundation.
87			** Derived, with permission, from the SOFA library. See notes at end of file.
88			*/
89			{
90			double xi2, r, sb, cb, rsb, rcb, w2, w, s, c;
91
92
93	0		xi2 = xi*xi;
94	0		r = sqrt(1.0 + xi2 + eta*eta);
95	0		sb = sin(b);
96	0		cb = cos(b);
97	0		rsb = r*sb;
98	0		rcb = r*cb;
99	0		w2 = rcb*rcb - xi2;
100	0	0	if ( w2 >= 0.0 ) {
101	0		w = sqrt(w2);
102	0		s = rsb - eta*w;
103	0		c = rsb*eta + w;
104	0	0	if ( xi == 0.0 && w == 0.0 ) w = 1.0;
105	0		*a01 = eraAnp(a - atan2(xi,w));
106	0		*b01 = atan2(s,c);
107	0		w = -w;
108	0		s = rsb - eta*w;
109	0		c = rsb*eta + w;
110	0		*a02 = eraAnp(a - atan2(xi,w));
111	0		*b02 = atan2(s,c);
112	0	0	return (fabs(rsb) < 1.0) ? 1 : 2;
113			} else {
114			return 0;
115			}
116
117			/* Finished. */
118
119			}
120			/*----------------------------------------------------------------------
121			**
122			**
123			** Copyright (C) 2013-2020, NumFOCUS Foundation.
124			** All rights reserved.
125			**
126			** This library is derived, with permission, from the International
127			** Astronomical Union's "Standards of Fundamental Astronomy" library,
128			** available from http://www.iausofa.org.
129			**
130			** The ERFA version is intended to retain identical functionality to
131			** the SOFA library, but made distinct through different function and
132			** file names, as set out in the SOFA license conditions. The SOFA
133			** original has a role as a reference standard for the IAU and IERS,
134			** and consequently redistribution is permitted only in its unaltered
135			** state. The ERFA version is not subject to this restriction and
136			** therefore can be included in distributions which do not support the
137			** concept of "read only" software.
138			**
139			** Although the intent is to replicate the SOFA API (other than
140			** replacement of prefix names) and results (with the exception of
141			** bugs; any that are discovered will be fixed), SOFA is not
142			** responsible for any errors found in this version of the library.
143			**
144			** If you wish to acknowledge the SOFA heritage, please acknowledge
145			** that you are using a library derived from SOFA, rather than SOFA
146			** itself.
147			**
148			**
149			** TERMS AND CONDITIONS
150			**
151			** Redistribution and use in source and binary forms, with or without
152			** modification, are permitted provided that the following conditions
153			** are met:
154			**
155			** 1 Redistributions of source code must retain the above copyright
156			** notice, this list of conditions and the following disclaimer.
157			**
158			** 2 Redistributions in binary form must reproduce the above copyright
159			** notice, this list of conditions and the following disclaimer in
160			** the documentation and/or other materials provided with the
161			** distribution.
162			**
163			** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
164			** the International Astronomical Union nor the names of its
165			** contributors may be used to endorse or promote products derived
166			** from this software without specific prior written permission.
167			**
168			** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
169			** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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171			** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
172			** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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176			** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
177			** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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179			** POSSIBILITY OF SUCH DAMAGE.
180			**
181			*/