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/*============================================================================
*
* WCSLIB - an implementation of the FITS WCS proposal.
* Copyright (C) 1995-2002, Mark Calabretta
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser 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
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 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 2.7 2002/04/03 01:25:29 mcalabre Exp $
*===========================================================================*/
#include <math.h>
#include "wcslib.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 wcslib.h, which includes wcstrig.h, sph.h
* Dec 20 1999 Doug Mink - Define copysign only if it is not already defined
*
* Jan 5 2000 Doug Mink - Drop copysign
*
* Sep 19 2001 Doug Mink - No change for WCSLIB 2.7
*/
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