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/*** File saoimage/wcslib/dsspos.c
*** October 21, 1999
*** By Jessica Mink, jmink@cfa.harvard.edu
*** Harvard-Smithsonian Center for Astrophysics
*** Copyright (C) 1995-2002
*** Smithsonian Astrophysical Observatory, Cambridge, MA, USA
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 WCSTools should be addressed as follows:
Internet email: jmink@cfa.harvard.edu
Postal address: Jessica Mink
Smithsonian Astrophysical Observatory
60 Garden St.
Cambridge, MA 02138 USA
* Module: dsspos.c (Plate solution WCS conversion)
* Purpose: Compute WCS from Digital Sky Survey plate fit
* Subroutine: dsspos() converts from pixel location to RA,Dec
* Subroutine: dsspix() converts from RA,Dec to pixel location
These functions are based on the astrmcal.c portion of GETIMAGE by
J. Doggett and the documentation distributed with the Digital Sky Survey.
*/
#include <math.h>
#include <string.h>
#include <stdio.h>
#include "wcs.h"
int
dsspos (xpix, ypix, wcs, xpos, ypos)
/* Routine to determine accurate position for pixel coordinates */
/* returns 0 if successful otherwise 1 = angle too large for projection; */
/* based on amdpos() from getimage */
/* Input: */
double xpix; /* x pixel number (RA or long without rotation) */
double ypix; /* y pixel number (dec or lat without rotation) */
struct WorldCoor *wcs; /* WCS parameter structure */
/* Output: */
double *xpos; /* Right ascension or longitude in degrees */
double *ypos; /* Declination or latitude in degrees */
{
double x, y, xmm, ymm, xmm2, ymm2, xmm3, ymm3, x2y2;
double xi, xir, eta, etar, raoff, ra, dec;
double cond2r = 1.745329252e-2;
double cons2r = 206264.8062470964;
double twopi = 6.28318530717959;
double ctan, ccos;
/* Ignore magnitude and color terms
double mag = 0.0;
double color = 0.0; */
/* Convert from image pixels to plate pixels */
x = xpix + wcs->x_pixel_offset - 1.0 + 0.5;
y = ypix + wcs->y_pixel_offset - 1.0 + 0.5;
/* Convert from pixels to millimeters */
xmm = (wcs->ppo_coeff[2] - x * wcs->x_pixel_size) / 1000.0;
ymm = (y * wcs->y_pixel_size - wcs->ppo_coeff[5]) / 1000.0;
xmm2 = xmm * xmm;
ymm2 = ymm * ymm;
xmm3 = xmm * xmm2;
ymm3 = ymm * ymm2;
x2y2 = xmm2 + ymm2;
/* Compute coordinates from x,y and plate model */
xi = wcs->x_coeff[ 0]*xmm + wcs->x_coeff[ 1]*ymm +
wcs->x_coeff[ 2] + wcs->x_coeff[ 3]*xmm2 +
wcs->x_coeff[ 4]*xmm*ymm + wcs->x_coeff[ 5]*ymm2 +
wcs->x_coeff[ 6]*(x2y2) + wcs->x_coeff[ 7]*xmm3 +
wcs->x_coeff[ 8]*xmm2*ymm + wcs->x_coeff[ 9]*xmm*ymm2 +
wcs->x_coeff[10]*ymm3 + wcs->x_coeff[11]*xmm*(x2y2) +
wcs->x_coeff[12]*xmm*x2y2*x2y2;
/* Ignore magnitude and color terms
+ wcs->x_coeff[13]*mag + wcs->x_coeff[14]*mag*mag +
wcs->x_coeff[15]*mag*mag*mag + wcs->x_coeff[16]*mag*xmm +
wcs->x_coeff[17]*mag*x2y2 + wcs->x_coeff[18]*mag*xmm*x2y2 +
wcs->x_coeff[19]*color; */
eta = wcs->y_coeff[ 0]*ymm + wcs->y_coeff[ 1]*xmm +
wcs->y_coeff[ 2] + wcs->y_coeff[ 3]*ymm2 +
wcs->y_coeff[ 4]*xmm*ymm + wcs->y_coeff[ 5]*xmm2 +
wcs->y_coeff[ 6]*(x2y2) + wcs->y_coeff[ 7]*ymm3 +
wcs->y_coeff[ 8]*ymm2*xmm + wcs->y_coeff[ 9]*ymm*xmm2 +
wcs->y_coeff[10]*xmm3 + wcs->y_coeff[11]*ymm*(x2y2) +
wcs->y_coeff[12]*ymm*x2y2*x2y2;
/* Ignore magnitude and color terms
+ wcs->y_coeff[13]*mag + wcs->y_coeff[14]*mag*mag +
wcs->y_coeff[15]*mag*mag*mag + wcs->y_coeff[16]*mag*ymm +
wcs->y_coeff[17]*mag*x2y2) + wcs->y_coeff[18]*mag*ymm*x2y2 +
wcs->y_coeff[19]*color; */
/* Convert to radians */
xir = xi / cons2r;
etar = eta / cons2r;
/* Convert to RA and Dec */
ctan = tan (wcs->plate_dec);
ccos = cos (wcs->plate_dec);
raoff = atan2 (xir / ccos, 1.0 - etar * ctan);
ra = raoff + wcs->plate_ra;
if (ra < 0.0) ra = ra + twopi;
*xpos = ra / cond2r;
dec = atan (cos (raoff) * ((etar + ctan) / (1.0 - (etar * ctan))));
*ypos = dec / cond2r;
return 0;
}
int
dsspix (xpos, ypos, wcs, xpix, ypix)
/* Routine to determine pixel coordinates for sky position */
/* returns 0 if successful otherwise 1 = angle too large for projection; */
/* based on amdinv() from getimage */
/* Input: */
double xpos; /* Right ascension or longitude in degrees */
double ypos; /* Declination or latitude in degrees */
struct WorldCoor *wcs; /* WCS parameter structure */
/* Output: */
double *xpix; /* x pixel number (RA or long without rotation) */
double *ypix; /* y pixel number (dec or lat without rotation) */
{
double div,xi,eta,x,y,xy,x2,y2,x2y,y2x,x3,y3,x4,y4,x2y2,cjunk,dx,dy;
double sypos,cypos,syplate,cyplate,sxdiff,cxdiff;
double f,fx,fy,g,gx,gy, xmm, ymm;
double conr2s = 206264.8062470964;
double tolerance = 0.0000005;
int max_iterations = 50;
int i;
double xr, yr; /* position in radians */
*xpix = 0.0;
*ypix = 0.0;
/* Convert RA and Dec in radians to standard coordinates on a plate */
xr = degrad (xpos);
yr = degrad (ypos);
sypos = sin (yr);
cypos = cos (yr);
if (wcs->plate_dec == 0.0)
wcs->plate_dec = degrad (wcs->yref);
syplate = sin (wcs->plate_dec);
cyplate = cos (wcs->plate_dec);
if (wcs->plate_ra == 0.0)
wcs->plate_ra = degrad (wcs->yref);
sxdiff = sin (xr - wcs->plate_ra);
cxdiff = cos (xr - wcs->plate_ra);
div = (sypos * syplate) + (cypos * cyplate * cxdiff);
if (div == 0.0)
return (1);
xi = cypos * sxdiff * conr2s / div;
eta = ((sypos * cyplate) - (cypos * syplate * cxdiff)) * conr2s / div;
/* Set initial value for x,y */
if (wcs->plate_scale == 0.0)
return (1);
xmm = xi / wcs->plate_scale;
ymm = eta / wcs->plate_scale;
/* Iterate by Newton's method */
for (i = 0; i < max_iterations; i++) {
/* X plate model */
xy = xmm * ymm;
x2 = xmm * xmm;
y2 = ymm * ymm;
x2y = x2 * ymm;
y2x = y2 * xmm;
x2y2 = x2 + y2;
cjunk = x2y2 * x2y2;
x3 = x2 * xmm;
y3 = y2 * ymm;
x4 = x2 * x2;
y4 = y2 * y2;
f = wcs->x_coeff[0]*xmm + wcs->x_coeff[1]*ymm +
wcs->x_coeff[2] + wcs->x_coeff[3]*x2 +
wcs->x_coeff[4]*xy + wcs->x_coeff[5]*y2 +
wcs->x_coeff[6]*x2y2 + wcs->x_coeff[7]*x3 +
wcs->x_coeff[8]*x2y + wcs->x_coeff[9]*y2x +
wcs->x_coeff[10]*y3 + wcs->x_coeff[11]*xmm*x2y2 +
wcs->x_coeff[12]*xmm*cjunk;
/* magnitude and color terms ignored
+ wcs->x_coeff[13]*mag +
wcs->x_coeff[14]*mag*mag + wcs->x_coeff[15]*mag*mag*mag +
wcs->x_coeff[16]*mag*xmm + wcs->x_coeff[17]*mag*(x2+y2) +
wcs->x_coeff[18]*mag*xmm*(x2+y2) + wcs->x_coeff[19]*color;
*/
/* Derivative of X model wrt x */
fx = wcs->x_coeff[0] + wcs->x_coeff[3]*2.0*xmm +
wcs->x_coeff[4]*ymm + wcs->x_coeff[6]*2.0*xmm +
wcs->x_coeff[7]*3.0*x2 + wcs->x_coeff[8]*2.0*xy +
wcs->x_coeff[9]*y2 + wcs->x_coeff[11]*(3.0*x2+y2) +
wcs->x_coeff[12]*(5.0*x4 +6.0*x2*y2+y4);
/* magnitude and color terms ignored
wcs->x_coeff[16]*mag + wcs->x_coeff[17]*mag*2.0*xmm +
wcs->x_coeff[18]*mag*(3.0*x2+y2);
*/
/* Derivative of X model wrt y */
fy = wcs->x_coeff[1] + wcs->x_coeff[4]*xmm +
wcs->x_coeff[5]*2.0*ymm + wcs->x_coeff[6]*2.0*ymm +
wcs->x_coeff[8]*x2 + wcs->x_coeff[9]*2.0*xy +
wcs->x_coeff[10]*3.0*y2 + wcs->x_coeff[11]*2.0*xy +
wcs->x_coeff[12]*4.0*xy*x2y2;
/* magnitude and color terms ignored
wcs->x_coeff[17]*mag*2.0*ymm +
wcs->x_coeff[18]*mag*2.0*xy;
*/
/* Y plate model */
g = wcs->y_coeff[0]*ymm + wcs->y_coeff[1]*xmm +
wcs->y_coeff[2] + wcs->y_coeff[3]*y2 +
wcs->y_coeff[4]*xy + wcs->y_coeff[5]*x2 +
wcs->y_coeff[6]*x2y2 + wcs->y_coeff[7]*y3 +
wcs->y_coeff[8]*y2x + wcs->y_coeff[9]*x2y +
wcs->y_coeff[10]*x3 + wcs->y_coeff[11]*ymm*x2y2 +
wcs->y_coeff[12]*ymm*cjunk;
/* magnitude and color terms ignored
wcs->y_coeff[13]*mag + wcs->y_coeff[14]*mag*mag +
wcs->y_coeff[15]*mag*mag*mag + wcs->y_coeff[16]*mag*ymm +
wcs->y_coeff[17]*mag*x2y2 +
wcs->y_coeff[18]*mag*ymm*x2y2 + wcs->y_coeff[19]*color;
*/
/* Derivative of Y model wrt x */
gx = wcs->y_coeff[1] + wcs->y_coeff[4]*ymm +
wcs->y_coeff[5]*2.0*xmm + wcs->y_coeff[6]*2.0*xmm +
wcs->y_coeff[8]*y2 + wcs->y_coeff[9]*2.0*xy +
wcs->y_coeff[10]*3.0*x2 + wcs->y_coeff[11]*2.0*xy +
wcs->y_coeff[12]*4.0*xy*x2y2;
/* magnitude and color terms ignored
wcs->y_coeff[17]*mag*2.0*xmm +
wcs->y_coeff[18]*mag*ymm*2.0*xmm;
*/
/* Derivative of Y model wrt y */
gy = wcs->y_coeff[0] + wcs->y_coeff[3]*2.0*ymm +
wcs->y_coeff[4]*xmm + wcs->y_coeff[6]*2.0*ymm +
wcs->y_coeff[7]*3.0*y2 + wcs->y_coeff[8]*2.0*xy +
wcs->y_coeff[9]*x2 + wcs->y_coeff[11]*(x2+3.0*y2) +
wcs->y_coeff[12]*(5.0*y4 + 6.0*x2*y2 + x4);
/* magnitude and color terms ignored
wcs->y_coeff[16]*mag + wcs->y_coeff[17]*mag*2.0*ymm +
wcs->y_coeff[18]*mag*(x2+3.0*y2);
*/
f = f - xi;
g = g - eta;
dx = ((-f * gy) + (g * fy)) / ((fx * gy) - (fy * gx));
dy = ((-g * fx) + (f * gx)) / ((fx * gy) - (fy * gx));
xmm = xmm + dx;
ymm = ymm + dy;
if ((fabs(dx) < tolerance) && (fabs(dy) < tolerance)) break;
}
/* Convert mm from plate center to plate pixels */
if (wcs->x_pixel_size == 0.0 || wcs->y_pixel_size == 0.0)
return (1);
x = (wcs->ppo_coeff[2] - xmm*1000.0) / wcs->x_pixel_size;
y = (wcs->ppo_coeff[5] + ymm*1000.0) / wcs->y_pixel_size;
/* Convert from plate pixels to image pixels */
*xpix = x - wcs->x_pixel_offset + 1.0 - 0.5;
*ypix = y - wcs->y_pixel_offset + 1.0 - 0.5;
/* If position is off of the image, return offscale code */
if (*xpix < 0.5 || *xpix > wcs->nxpix+0.5)
return -1;
if (*ypix < 0.5 || *ypix > wcs->nypix+0.5)
return -1;
return 0;
}
/* Mar 6 1995 Original version of this code
* May 4 1995 Fix eta cross terms which were all in y
* Jun 21 1995 Add inverse routine
* Oct 17 1995 Fix inverse routine (degrees -> radians)
* Nov 7 1995 Add half pixel to image coordinates to get astrometric
* plate coordinates
* Feb 26 1996 Fix plate to image pixel conversion error
*
* Mar 23 1998 Change names from plate*() to dss*()
* Apr 7 1998 Change amd_i_coeff to i_coeff
* Sep 4 1998 Fix possible divide by zero in dsspos() from Allen Harris, SAO
* Sep 10 1998 Fix possible divide by zero in dsspix() from Allen Harris, SAO
*
* Oct 21 1999 Drop declaration of cond2r in dsspix()
*/
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