source: trunk/FACT++/erfa/src/gc2gde.c@ 18403

Last change on this file since 18403 was 18348, checked in by tbretz, 9 years ago
File size: 6.7 KB
Line 
1#include "erfa.h"
2
3int eraGc2gde ( double a, double f, double xyz[3],
4 double *elong, double *phi, double *height )
5/*
6** - - - - - - - - - -
7** e r a G c 2 g d e
8** - - - - - - - - - -
9**
10** Transform geocentric coordinates to geodetic for a reference
11** ellipsoid of specified form.
12**
13** Given:
14** a double equatorial radius (Notes 2,4)
15** f double flattening (Note 3)
16** xyz double[3] geocentric vector (Note 4)
17**
18** Returned:
19** elong double longitude (radians, east +ve)
20** phi double latitude (geodetic, radians)
21** height double height above ellipsoid (geodetic, Note 4)
22**
23** Returned (function value):
24** int status: 0 = OK
25** -1 = illegal f
26** -2 = illegal a
27**
28** Notes:
29**
30** 1) This function is based on the GCONV2H Fortran subroutine by
31** Toshio Fukushima (see reference).
32**
33** 2) The equatorial radius, a, can be in any units, but meters is
34** the conventional choice.
35**
36** 3) The flattening, f, is (for the Earth) a value around 0.00335,
37** i.e. around 1/298.
38**
39** 4) The equatorial radius, a, and the geocentric vector, xyz,
40** must be given in the same units, and determine the units of
41** the returned height, height.
42**
43** 5) If an error occurs (status < 0), elong, phi and height are
44** unchanged.
45**
46** 6) The inverse transformation is performed in the function
47** eraGd2gce.
48**
49** 7) The transformation for a standard ellipsoid (such as ERFA_WGS84) can
50** more conveniently be performed by calling eraGc2gd, which uses a
51** numerical code to identify the required A and F values.
52**
53** Reference:
54**
55** Fukushima, T., "Transformation from Cartesian to geodetic
56** coordinates accelerated by Halley's method", J.Geodesy (2006)
57** 79: 689-693
58**
59** Copyright (C) 2013-2015, NumFOCUS Foundation.
60** Derived, with permission, from the SOFA library. See notes at end of file.
61*/
62{
63 double aeps2, e2, e4t, ec2, ec, b, x, y, z, p2, absz, p, s0, pn, zc,
64 c0, c02, c03, s02, s03, a02, a0, a03, d0, f0, b0, s1,
65 cc, s12, cc2;
66
67
68/* ------------- */
69/* Preliminaries */
70/* ------------- */
71
72/* Validate ellipsoid parameters. */
73 if ( f < 0.0 || f >= 1.0 ) return -1;
74 if ( a <= 0.0 ) return -2;
75
76/* Functions of ellipsoid parameters (with further validation of f). */
77 aeps2 = a*a * 1e-32;
78 e2 = (2.0 - f) * f;
79 e4t = e2*e2 * 1.5;
80 ec2 = 1.0 - e2;
81 if ( ec2 <= 0.0 ) return -1;
82 ec = sqrt(ec2);
83 b = a * ec;
84
85/* Cartesian components. */
86 x = xyz[0];
87 y = xyz[1];
88 z = xyz[2];
89
90/* Distance from polar axis squared. */
91 p2 = x*x + y*y;
92
93/* Longitude. */
94 *elong = p2 > 0.0 ? atan2(y, x) : 0.0;
95
96/* Unsigned z-coordinate. */
97 absz = fabs(z);
98
99/* Proceed unless polar case. */
100 if ( p2 > aeps2 ) {
101
102 /* Distance from polar axis. */
103 p = sqrt(p2);
104
105 /* Normalization. */
106 s0 = absz / a;
107 pn = p / a;
108 zc = ec * s0;
109
110 /* Prepare Newton correction factors. */
111 c0 = ec * pn;
112 c02 = c0 * c0;
113 c03 = c02 * c0;
114 s02 = s0 * s0;
115 s03 = s02 * s0;
116 a02 = c02 + s02;
117 a0 = sqrt(a02);
118 a03 = a02 * a0;
119 d0 = zc*a03 + e2*s03;
120 f0 = pn*a03 - e2*c03;
121
122 /* Prepare Halley correction factor. */
123 b0 = e4t * s02 * c02 * pn * (a0 - ec);
124 s1 = d0*f0 - b0*s0;
125 cc = ec * (f0*f0 - b0*c0);
126
127 /* Evaluate latitude and height. */
128 *phi = atan(s1/cc);
129 s12 = s1 * s1;
130 cc2 = cc * cc;
131 *height = (p*cc + absz*s1 - a * sqrt(ec2*s12 + cc2)) /
132 sqrt(s12 + cc2);
133 } else {
134
135 /* Exception: pole. */
136 *phi = ERFA_DPI / 2.0;
137 *height = absz - b;
138 }
139
140/* Restore sign of latitude. */
141 if ( z < 0 ) *phi = -*phi;
142
143/* OK status. */
144 return 0;
145
146}
147/*----------------------------------------------------------------------
148**
149**
150** Copyright (C) 2013-2015, NumFOCUS Foundation.
151** All rights reserved.
152**
153** This library is derived, with permission, from the International
154** Astronomical Union's "Standards of Fundamental Astronomy" library,
155** available from http://www.iausofa.org.
156**
157** The ERFA version is intended to retain identical functionality to
158** the SOFA library, but made distinct through different function and
159** file names, as set out in the SOFA license conditions. The SOFA
160** original has a role as a reference standard for the IAU and IERS,
161** and consequently redistribution is permitted only in its unaltered
162** state. The ERFA version is not subject to this restriction and
163** therefore can be included in distributions which do not support the
164** concept of "read only" software.
165**
166** Although the intent is to replicate the SOFA API (other than
167** replacement of prefix names) and results (with the exception of
168** bugs; any that are discovered will be fixed), SOFA is not
169** responsible for any errors found in this version of the library.
170**
171** If you wish to acknowledge the SOFA heritage, please acknowledge
172** that you are using a library derived from SOFA, rather than SOFA
173** itself.
174**
175**
176** TERMS AND CONDITIONS
177**
178** Redistribution and use in source and binary forms, with or without
179** modification, are permitted provided that the following conditions
180** are met:
181**
182** 1 Redistributions of source code must retain the above copyright
183** notice, this list of conditions and the following disclaimer.
184**
185** 2 Redistributions in binary form must reproduce the above copyright
186** notice, this list of conditions and the following disclaimer in
187** the documentation and/or other materials provided with the
188** distribution.
189**
190** 3 Neither the name of the Standards Of Fundamental Astronomy Board,
191** the International Astronomical Union nor the names of its
192** contributors may be used to endorse or promote products derived
193** from this software without specific prior written permission.
194**
195** THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
196** "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
197** LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
198** FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
199** COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
200** INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
201** BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
202** LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
203** CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
204** LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
205** ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
206** POSSIBILITY OF SUCH DAMAGE.
207**
208*/
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