1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
|
/*============================================================================
*
* WCSLIB - an implementation of the FITS WCS proposal.
* Copyright (C) 1995-1999, Mark Calabretta
*
* This library is free software; you can redistribute it and/or modify it
* under the terms of the GNU Library General Public License as published
* by the Free Software Foundation; either version 2 of the License, or (at
* your option) any later version.
*
* This library is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Library
* General Public License for more details.
*
* You should have received a copy of the GNU Library General Public License
* along with this library; if not, write to the Free Software Foundation,
* Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
*
* Correspondence concerning WCSLIB may be directed to:
* Internet email: mcalabre@atnf.csiro.au
* Postal address: Dr. Mark Calabretta,
* Australia Telescope National Facility,
* P.O. Box 76,
* Epping, NSW, 2121,
* AUSTRALIA
*
*=============================================================================
*
* C routines for the spherical coordinate transformations used by the FITS
* "World Coordinate System" (WCS) convention.
*
* Summary of routines
* -------------------
* The spherical coordinate transformations are implemented via separate
* functions for the transformation in each direction.
*
* Forward transformation; sphfwd()
* --------------------------------
* Transform celestial coordinates to the native coordinates of a projection.
*
* Given:
* lng,lat double Celestial longitude and latitude, in degrees.
* eul[5] double Euler angles for the transformation:
* 0: Celestial longitude of the native pole, in
* degrees.
* 1: Celestial colatitude of the native pole, or
* native colatitude of the celestial pole, in
* degrees.
* 2: Native longitude of the celestial pole, in
* degrees.
* 3: cos(eul[1])
* 4: sin(eul[1])
*
* Returned:
* phi, double Longitude and latitude in the native coordinate
* theta system of the projection, in degrees.
*
* Function return value:
* int Error status
* 0: Success.
*
* Reverse transformation; sphrev()
* --------------------------------
* Transform native coordinates of a projection to celestial coordinates.
*
* Given:
* phi, double Longitude and latitude in the native coordinate
* theta system of the projection, in degrees.
* eul[5] double Euler angles for the transformation:
* 0: Celestial longitude of the native pole, in
* degrees.
* 1: Celestial colatitude of the native pole, or
* native colatitude of the celestial pole, in
* degrees.
* 2: Native longitude of the celestial pole, in
* degrees.
* 3: cos(eul[1])
* 4: sin(eul[1])
*
* Returned:
* lng,lat double Celestial longitude and latitude, in degrees.
*
* Function return value:
* int Error status
* 0: Success.
*
* Author: Mark Calabretta, Australia Telescope National Facility
* $Id: sph.c,v 1.1.1.1 2008-10-21 09:10:12 cizzo Exp $
*===========================================================================*/
#include <math.h>
#include "vimoswcslib.h"
#ifndef __STDC__
#ifndef const
#define const
#endif
#endif
const double tol = 1.0e-5;
int sphfwd (lng, lat, eul, phi, theta)
const double lat, lng, eul[5];
double *phi, *theta;
{
double coslat, coslng, dlng, dphi, sinlat, sinlng, x, y, z;
coslat = cosdeg (lat);
sinlat = sindeg (lat);
dlng = lng - eul[0];
coslng = cosdeg (dlng);
sinlng = sindeg (dlng);
/* Compute the native longitude. */
x = sinlat*eul[4] - coslat*eul[3]*coslng;
if (fabs(x) < tol) {
/* Rearrange formula to reduce roundoff errors. */
x = -cosdeg (lat+eul[1]) + coslat*eul[3]*(1.0 - coslng);
}
y = -coslat*sinlng;
if (x != 0.0 || y != 0.0) {
dphi = atan2deg (y, x);
} else {
/* Change of origin of longitude. */
dphi = dlng - 180.0;
}
*phi = eul[2] + dphi;
/* Normalize the native longitude. */
if (*phi > 180.0) {
*phi -= 360.0;
} else if (*phi < -180.0) {
*phi += 360.0;
}
/* Compute the native latitude. */
if (fmod(dlng,180.0) == 0.0) {
*theta = lat + coslng*eul[1];
if (*theta > 90.0) *theta = 180.0 - *theta;
if (*theta < -90.0) *theta = -180.0 - *theta;
} else {
z = sinlat*eul[3] + coslat*eul[4]*coslng;
/* Use an alternative formula for greater numerical accuracy. */
if (fabs(z) > 0.99) {
if (z < 0)
*theta = -acosdeg (sqrt(x*x+y*y));
else
*theta = acosdeg (sqrt(x*x+y*y));
} else {
*theta = asindeg (z);
}
}
return 0;
}
/*-----------------------------------------------------------------------*/
int sphrev (phi, theta, eul, lng, lat)
const double phi, theta, eul[5];
double *lng, *lat;
{
double cosphi, costhe, dlng, dphi, sinphi, sinthe, x, y, z;
costhe = cosdeg (theta);
sinthe = sindeg (theta);
dphi = phi - eul[2];
cosphi = cosdeg (dphi);
sinphi = sindeg (dphi);
/* Compute the celestial longitude. */
x = sinthe*eul[4] - costhe*eul[3]*cosphi;
if (fabs(x) < tol) {
/* Rearrange formula to reduce roundoff errors. */
x = -cosdeg (theta+eul[1]) + costhe*eul[3]*(1.0 - cosphi);
}
y = -costhe*sinphi;
if (x != 0.0 || y != 0.0) {
dlng = atan2deg (y, x);
} else {
/* Change of origin of longitude. */
dlng = dphi + 180.0;
}
*lng = eul[0] + dlng;
/* Normalize the celestial longitude. */
if (eul[0] >= 0.0) {
if (*lng < 0.0) *lng += 360.0;
} else {
if (*lng > 0.0) *lng -= 360.0;
}
if (*lng > 360.0) {
*lng -= 360.0;
} else if (*lng < -360.0) {
*lng += 360.0;
}
/* Compute the celestial latitude. */
if (fmod(dphi,180.0) == 0.0) {
*lat = theta + cosphi*eul[1];
if (*lat > 90.0) *lat = 180.0 - *lat;
if (*lat < -90.0) *lat = -180.0 - *lat;
} else {
z = sinthe*eul[3] + costhe*eul[4]*cosphi;
/* Use an alternative formula for greater numerical accuracy. */
if (fabs(z) > 0.99) {
if (z < 0)
*lat = -acosdeg (sqrt(x*x+y*y));
else
*lat = acosdeg (sqrt(x*x+y*y));
} else {
*lat = asindeg (z);
}
}
return 0;
}
/* Dec 20 1999 Doug Mink - Change cosd() and sind() to cosdeg() and sindeg()
* Dec 20 1999 Doug Mink - Include vimoswcslib.h, which includes vimoswcstrig.h, sph.h
* Dec 20 1999 Doug Mink - Define copysign only if it is not already defined
* Jan 5 2000 Doug Mink - Drop copysign
*/
|
