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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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