#include #include #include #include "fitsio2.h" /*--------------------------------------------------------------------------*/ int ffgics(fitsfile *fptr, /* I - FITS file pointer */ double *xrval, /* O - X reference value */ double *yrval, /* O - Y reference value */ double *xrpix, /* O - X reference pixel */ double *yrpix, /* O - Y reference pixel */ double *xinc, /* O - X increment per pixel */ double *yinc, /* O - Y increment per pixel */ double *rot, /* O - rotation angle (degrees) */ char *type, /* O - type of projection ('-tan') */ int *status) /* IO - error status */ /* read the values of the celestial coordinate system keywords. These values may be used as input to the subroutines that calculate celestial coordinates. (ffxypx, ffwldp) Modified in Nov 1999 to convert the CD matrix keywords back to the old CDELTn form, and to swap the axes if the dec-like axis is given first, and to assume default values if any of the keywords are not present. */ { int tstat; char ctype[FLEN_VALUE]; double cd11, cd21, cd22, cd12; double pi = 3.1415926535897932; double phia, phib, temp; double toler = .0002; /* tolerance for angles to agree (radians) */ if (*status > 0) return(*status); tstat = 0; if (ffgkyd(fptr, "CRVAL1", xrval, NULL, &tstat)) *xrval = 0.; tstat = 0; if (ffgkyd(fptr, "CRVAL2", yrval, NULL, &tstat)) *yrval = 0.; tstat = 0; if (ffgkyd(fptr, "CRPIX1", xrpix, NULL, &tstat)) *xrpix = 0.; tstat = 0; if (ffgkyd(fptr, "CRPIX2", yrpix, NULL, &tstat)) *yrpix = 0.; /* look for CDELTn first, then CDi_j keywords */ tstat = 0; if (ffgkyd(fptr, "CDELT1", xinc, NULL, &tstat)) { /* no CDELTn keyword, so look for the CD matrix */ tstat = 0; ffgkyd(fptr, "CD1_1", &cd11, NULL, &tstat); ffgkyd(fptr, "CD2_1", &cd21, NULL, &tstat); ffgkyd(fptr, "CD1_2", &cd12, NULL, &tstat); ffgkyd(fptr, "CD2_2", &cd22, NULL, &tstat); if (!tstat) /* convert CDi_j back to CDELTn */ { /* there are 2 ways to compute the angle: */ phia = atan2( cd21, cd11); phib = atan2(-cd12, cd22); /* ensure that phia <= phib */ temp = minvalue(phia, phib); phib = maxvalue(phia, phib); phia = temp; /* there is a possible 180 degree ambiguity in the angles */ /* so add 180 degress to the smaller value if the values */ /* differ by more than 90 degrees = pi/2 radians. */ /* (Later, we may decide to take the other solution by */ /* subtracting 180 degrees from the larger value). */ if ((phib - phia) > (pi / 2.)) phia += pi; if (fabs(phia - phib) > toler) { /* angles don't agree, so looks like there is some skewness */ /* between the axes. Return with an error to be safe. */ *status = APPROX_WCS_KEY; } phia = (phia + phib) /2.; /* use the average of the 2 values */ *xinc = cd11 / cos(phia); *yinc = cd22 / cos(phia); *rot = phia * 180. / pi; /* common usage is to have a positive yinc value. If it is */ /* negative, then subtract 180 degrees from rot and negate */ /* both xinc and yinc. */ if (*yinc < 0) { *xinc = -(*xinc); *yinc = -(*yinc); *rot = *rot - 180.; } } else /* no CD matrix keywords either */ { *xinc = 1.; tstat = 0; if (ffgkyd(fptr, "CDELT2", yinc, NULL, &tstat)) *yinc = 1.; tstat = 0; if (ffgkyd(fptr, "CROTA2", rot, NULL, &tstat)) *rot=0.; } } else { if (ffgkyd(fptr, "CDELT2", yinc, NULL, &tstat)) *yinc = 1.; tstat = 0; if (ffgkyd(fptr, "CROTA2", rot, NULL, &tstat)) *rot=0.; } /* get the type of projection, if any */ tstat = 0; if (ffgkys(fptr, "CTYPE1", ctype, NULL, &tstat)) type[0] = '\0'; else { /* copy the projection type string */ strncpy(type, &ctype[4], 4); type[4] = '\0'; /* check if RA and DEC are inverted */ if (!strncmp(ctype, "DEC-", 4) || !strncmp(ctype+1, "LAT", 3)) { /* the latitudinal axis is given first, so swap them */ /* this case was removed on 12/9. Apparently not correct. if ((*xinc / *yinc) < 0. ) *rot = -90. - (*rot); else */ *rot = 90. - (*rot); /* Empirical tests with ds9 show the y-axis sign must be negated */ /* and the xinc and yinc values must NOT be swapped. */ *yinc = -(*yinc); temp = *xrval; *xrval = *yrval; *yrval = temp; } } return(*status); } /*--------------------------------------------------------------------------*/ int ffgtcs(fitsfile *fptr, /* I - FITS file pointer */ int xcol, /* I - column containing the RA coordinate */ int ycol, /* I - column containing the DEC coordinate */ double *xrval, /* O - X reference value */ double *yrval, /* O - Y reference value */ double *xrpix, /* O - X reference pixel */ double *yrpix, /* O - Y reference pixel */ double *xinc, /* O - X increment per pixel */ double *yinc, /* O - Y increment per pixel */ double *rot, /* O - rotation angle (degrees) */ char *type, /* O - type of projection ('-sin') */ int *status) /* IO - error status */ /* read the values of the celestial coordinate system keywords from a FITS table where the X and Y or RA and DEC coordinates are stored in separate column. These values may be used as input to the subroutines that calculate celestial coordinates. (ffxypx, ffwldp) */ { char comm[FLEN_COMMENT],ctype[FLEN_VALUE],keynam[FLEN_KEYWORD]; int tstatus = 0; if (*status > 0) return(*status); ffkeyn("TCRVL",xcol,keynam,status); ffgkyd(fptr,keynam,xrval,comm,status); ffkeyn("TCRVL",ycol,keynam,status); ffgkyd(fptr,keynam,yrval,comm,status); ffkeyn("TCRPX",xcol,keynam,status); ffgkyd(fptr,keynam,xrpix,comm,status); ffkeyn("TCRPX",ycol,keynam,status); ffgkyd(fptr,keynam,yrpix,comm,status); ffkeyn("TCDLT",xcol,keynam,status); ffgkyd(fptr,keynam,xinc,comm,status); ffkeyn("TCDLT",ycol,keynam,status); ffgkyd(fptr,keynam,yinc,comm,status); ffkeyn("TCTYP",xcol,keynam,status); ffgkys(fptr,keynam,ctype,comm,status); if (*status > 0) { ffpmsg ("ffgtcs could not find all the celestial coordinate keywords"); return(*status = NO_WCS_KEY); } /* copy the projection type string */ strncpy(type, &ctype[4], 4); type[4] = '\0'; *rot=0.; /* default rotation is 0 */ ffkeyn("TCROT",ycol,keynam,status); ffgkyd(fptr,keynam,rot,comm,&tstatus); /* keyword may not exist */ return(*status); } /*--------------------------------------------------------------------------*/ int ffwldp(double xpix, double ypix, double xref, double yref, double xrefpix, double yrefpix, double xinc, double yinc, double rot, char *type, double *xpos, double *ypos, int *status) /* WDP 1/97: change the name of the routine from 'worldpos' to 'ffwldp' */ /* worldpos.c -- WCS Algorithms from Classic AIPS. Copyright (C) 1994 Associated Universities, Inc. Washington DC, USA. 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 Massachusetts Ave, Cambridge, MA 02139, USA. Correspondence concerning AIPS should be addressed as follows: Internet email: aipsmail@nrao.edu Postal address: AIPS Group National Radio Astronomy Observatory 520 Edgemont Road Charlottesville, VA 22903-2475 USA -=-=-=-=-=-=- These two ANSI C functions, worldpos() and xypix(), perform forward and reverse WCS computations for 8 types of projective geometries ("-SIN", "-TAN", "-ARC", "-NCP", "-GLS", "-MER", "-AIT" and "-STG"): worldpos() converts from pixel location to RA,Dec xypix() converts from RA,Dec to pixel location where "(RA,Dec)" are more generically (long,lat). These functions are based on the WCS implementation of Classic AIPS, an implementation which has been in production use for more than ten years. See the two memos by Eric Greisen ftp://fits.cv.nrao.edu/fits/documents/wcs/aips27.ps.Z ftp://fits.cv.nrao.edu/fits/documents/wcs/aips46.ps.Z for descriptions of the 8 projective geometries and the algorithms. Footnotes in these two documents describe the differences between these algorithms and the 1993-94 WCS draft proposal (see URL below). In particular, these algorithms support ordinary field rotation, but not skew geometries (CD or PC matrix cases). Also, the MER and AIT algorithms work correctly only for CRVALi=(0,0). Users should note that GLS projections with yref!=0 will behave differently in this code than in the draft WCS proposal. The NCP projection is now obsolete (it is a special case of SIN). WCS syntax and semantics for various advanced features is discussed in the draft WCS proposal by Greisen and Calabretta at: ftp://fits.cv.nrao.edu/fits/documents/wcs/wcs.all.ps.Z -=-=-=- The original version of this code was Emailed to D.Wells on Friday, 23 September by Bill Cotton , who described it as a "..more or less.. exact translation from the AIPSish..". Changes were made by Don Wells during the period October 11-13, 1994: 1) added GNU license and header comments 2) added testpos.c program to perform extensive circularity tests 3) changed float-->double to get more than 7 significant figures 4) testpos.c circularity test failed on MER and AIT. B.Cotton found that "..there were a couple of lines of code [in] the wrong place as a result of merging several Fortran routines." 5) testpos.c found 0h wraparound in xypix() and worldpos(). 6) E.Greisen recommended removal of various redundant if-statements, and addition of a 360d difference test to MER case of worldpos(). */ /*-----------------------------------------------------------------------*/ /* routine to determine accurate position for pixel coordinates */ /* returns 0 if successful otherwise: */ /* 1 = angle too large for projection; */ /* (WDP 1/97: changed the return value to 501 instead of 1) */ /* does: -SIN, -TAN, -ARC, -NCP, -GLS, -MER, -AIT projections */ /* anything else is linear (== -CAR) */ /* Input: */ /* f xpix x pixel number (RA or long without rotation) */ /* f ypiy y pixel number (dec or lat without rotation) */ /* d xref x reference coordinate value (deg) */ /* d yref y reference coordinate value (deg) */ /* f xrefpix x reference pixel */ /* f yrefpix y reference pixel */ /* f xinc x coordinate increment (deg) */ /* f yinc y coordinate increment (deg) */ /* f rot rotation (deg) (from N through E) */ /* c *type projection type code e.g. "-SIN"; */ /* Output: */ /* d *xpos x (RA) coordinate (deg) */ /* d *ypos y (dec) coordinate (deg) */ /*-----------------------------------------------------------------------*/ {double cosr, sinr, dx, dy, dz, temp, x, y, z; double sins, coss, dect, rat, dt, l, m, mg, da, dd, cos0, sin0; double dec0, ra0, decout, raout; double geo1, geo2, geo3; double cond2r=1.745329252e-2; double twopi = 6.28318530717959, deps = 1.0e-5; int i, itype; char ctypes[9][5] ={"-CAR","-SIN","-TAN","-ARC","-NCP", "-GLS", "-MER", "-AIT", "-STG"}; if (*status > 0) return(*status); /* Offset from ref pixel */ dx = (xpix-xrefpix) * xinc; dy = (ypix-yrefpix) * yinc; /* Take out rotation */ cosr = cos(rot*cond2r); sinr = sin(rot*cond2r); if (rot!=0.0) {temp = dx * cosr - dy * sinr; dy = dy * cosr + dx * sinr; dx = temp;} /* find type */ /* WDP 1/97: removed support for default type for better error checking */ /* itype = 0; default type is linear */ itype = -1; /* no default type */ for (i=0;i<9;i++) if (!strncmp(type, ctypes[i], 4)) itype = i; /* default, linear result for error return */ *xpos = xref + dx; *ypos = yref + dy; /* convert to radians */ ra0 = xref * cond2r; dec0 = yref * cond2r; l = dx * cond2r; m = dy * cond2r; sins = l*l + m*m; cos0 = cos(dec0); sin0 = sin(dec0); /* process by case */ switch (itype) { case 0: /* linear -CAR */ rat = ra0 + l; dect = dec0 + m; break; case 1: /* -SIN sin*/ if (sins>1.0) return(*status = 501); coss = sqrt (1.0 - sins); dt = sin0 * coss + cos0 * m; if ((dt>1.0) || (dt<-1.0)) return(*status = 501); dect = asin (dt); rat = cos0 * coss - sin0 * m; if ((rat==0.0) && (l==0.0)) return(*status = 501); rat = atan2 (l, rat) + ra0; break; case 2: /* -TAN tan */ x = cos0*cos(ra0) - l*sin(ra0) - m*cos(ra0)*sin0; y = cos0*sin(ra0) + l*cos(ra0) - m*sin(ra0)*sin0; z = sin0 + m* cos0; rat = atan2( y, x ); dect = atan ( z / sqrt(x*x+y*y) ); break; case 3: /* -ARC Arc*/ if (sins>=twopi*twopi/4.0) return(*status = 501); sins = sqrt(sins); coss = cos (sins); if (sins!=0.0) sins = sin (sins) / sins; else sins = 1.0; dt = m * cos0 * sins + sin0 * coss; if ((dt>1.0) || (dt<-1.0)) return(*status = 501); dect = asin (dt); da = coss - dt * sin0; dt = l * sins * cos0; if ((da==0.0) && (dt==0.0)) return(*status = 501); rat = ra0 + atan2 (dt, da); break; case 4: /* -NCP North celestial pole*/ dect = cos0 - m * sin0; if (dect==0.0) return(*status = 501); rat = ra0 + atan2 (l, dect); dt = cos (rat-ra0); if (dt==0.0) return(*status = 501); dect = dect / dt; if ((dect>1.0) || (dect<-1.0)) return(*status = 501); dect = acos (dect); if (dec0<0.0) dect = -dect; break; case 5: /* -GLS global sinusoid */ dect = dec0 + m; if (fabs(dect)>twopi/4.0) return(*status = 501); coss = cos (dect); if (fabs(l)>twopi*coss/2.0) return(*status = 501); rat = ra0; if (coss>deps) rat = rat + l / coss; break; case 6: /* -MER mercator*/ dt = yinc * cosr + xinc * sinr; if (dt==0.0) dt = 1.0; dy = (yref/2.0 + 45.0) * cond2r; dx = dy + dt / 2.0 * cond2r; dy = log (tan (dy)); dx = log (tan (dx)); geo2 = dt * cond2r / (dx - dy); geo3 = geo2 * dy; geo1 = cos (yref*cond2r); if (geo1<=0.0) geo1 = 1.0; rat = l / geo1 + ra0; if (fabs(rat - ra0) > twopi) return(*status = 501); /* added 10/13/94 DCW/EWG */ dt = 0.0; if (geo2!=0.0) dt = (m + geo3) / geo2; dt = exp (dt); dect = 2.0 * atan (dt) - twopi / 4.0; break; case 7: /* -AIT Aitoff*/ dt = yinc*cosr + xinc*sinr; if (dt==0.0) dt = 1.0; dt = dt * cond2r; dy = yref * cond2r; dx = sin(dy+dt)/sqrt((1.0+cos(dy+dt))/2.0) - sin(dy)/sqrt((1.0+cos(dy))/2.0); if (dx==0.0) dx = 1.0; geo2 = dt / dx; dt = xinc*cosr - yinc* sinr; if (dt==0.0) dt = 1.0; dt = dt * cond2r; dx = 2.0 * cos(dy) * sin(dt/2.0); if (dx==0.0) dx = 1.0; geo1 = dt * sqrt((1.0+cos(dy)*cos(dt/2.0))/2.0) / dx; geo3 = geo2 * sin(dy) / sqrt((1.0+cos(dy))/2.0); rat = ra0; dect = dec0; if ((l==0.0) && (m==0.0)) break; dz = 4.0 - l*l/(4.0*geo1*geo1) - ((m+geo3)/geo2)*((m+geo3)/geo2) ; if ((dz>4.0) || (dz<2.0)) return(*status = 501);; dz = 0.5 * sqrt (dz); dd = (m+geo3) * dz / geo2; if (fabs(dd)>1.0) return(*status = 501);; dd = asin (dd); if (fabs(cos(dd))1.0) return(*status = 501);; da = asin (da); rat = ra0 + 2.0 * da; dect = dd; break; case 8: /* -STG Sterographic*/ dz = (4.0 - sins) / (4.0 + sins); if (fabs(dz)>1.0) return(*status = 501); dect = dz * sin0 + m * cos0 * (1.0+dz) / 2.0; if (fabs(dect)>1.0) return(*status = 501); dect = asin (dect); rat = cos(dect); if (fabs(rat)1.0) return(*status = 501); rat = asin (rat); mg = 1.0 + sin(dect) * sin0 + cos(dect) * cos0 * cos(rat); if (fabs(mg)deps) rat = twopi/2.0 - rat; rat = ra0 + rat; break; default: /* fall through to here on error */ return(*status = 504); } /* return ra in range */ raout = rat; decout = dect; if (raout-ra0>twopi/2.0) raout = raout - twopi; if (raout-ra0<-twopi/2.0) raout = raout + twopi; if (raout < 0.0) raout += twopi; /* added by DCW 10/12/94 */ /* correct units back to degrees */ *xpos = raout / cond2r; *ypos = decout / cond2r; return(*status); } /* End of worldpos */ /*--------------------------------------------------------------------------*/ int ffxypx(double xpos, double ypos, double xref, double yref, double xrefpix, double yrefpix, double xinc, double yinc, double rot, char *type, double *xpix, double *ypix, int *status) /* WDP 1/97: changed name of routine from xypix to ffxypx */ /*-----------------------------------------------------------------------*/ /* routine to determine accurate pixel coordinates for an RA and Dec */ /* returns 0 if successful otherwise: */ /* 1 = angle too large for projection; */ /* 2 = bad values */ /* WDP 1/97: changed the return values to 501 and 502 instead of 1 and 2 */ /* does: -SIN, -TAN, -ARC, -NCP, -GLS, -MER, -AIT projections */ /* anything else is linear */ /* Input: */ /* d xpos x (RA) coordinate (deg) */ /* d ypos y (dec) coordinate (deg) */ /* d xref x reference coordinate value (deg) */ /* d yref y reference coordinate value (deg) */ /* f xrefpix x reference pixel */ /* f yrefpix y reference pixel */ /* f xinc x coordinate increment (deg) */ /* f yinc y coordinate increment (deg) */ /* f rot rotation (deg) (from N through E) */ /* c *type projection type code e.g. "-SIN"; */ /* Output: */ /* f *xpix x pixel number (RA or long without rotation) */ /* f *ypiy y pixel number (dec or lat without rotation) */ /*-----------------------------------------------------------------------*/ {double dx, dy, dz, r, ra0, dec0, ra, dec, coss, sins, dt, da, dd, sint; double l, m, geo1, geo2, geo3, sinr, cosr, cos0, sin0; double cond2r=1.745329252e-2, deps=1.0e-5, twopi=6.28318530717959; int i, itype; char ctypes[9][5] ={"-CAR","-SIN","-TAN","-ARC","-NCP", "-GLS", "-MER", "-AIT", "-STG"}; /* 0h wrap-around tests added by D.Wells 10/12/94: */ dt = (xpos - xref); if (dt > 180) xpos -= 360; if (dt < -180) xpos += 360; /* NOTE: changing input argument xpos is OK (call-by-value in C!) */ /* default values - linear */ dx = xpos - xref; dy = ypos - yref; /* dz = 0.0; */ /* Correct for rotation */ r = rot * cond2r; cosr = cos (r); sinr = sin (r); dz = dx*cosr + dy*sinr; dy = dy*cosr - dx*sinr; dx = dz; /* check axis increments - bail out if either 0 */ if ((xinc==0.0) || (yinc==0.0)) {*xpix=0.0; *ypix=0.0; return(*status = 502);} /* convert to pixels */ *xpix = dx / xinc + xrefpix; *ypix = dy / yinc + yrefpix; /* find type */ /* WDP 1/97: removed support for default type for better error checking */ /* itype = 0; default type is linear */ itype = -1; /* no default type */ for (i=0;i<9;i++) if (!strncmp(type, ctypes[i], 4)) itype = i; if (itype==0) return(*status); /* done if linear */ /* Non linear position */ ra0 = xref * cond2r; dec0 = yref * cond2r; ra = xpos * cond2r; dec = ypos * cond2r; /* compute direction cosine */ coss = cos (dec); sins = sin (dec); cos0 = cos (dec0); sin0 = sin (dec0); l = sin(ra-ra0) * coss; sint = sins * sin0 + coss * cos0 * cos(ra-ra0); /* process by case */ switch (itype) { case 1: /* -SIN sin*/ if (sint<0.0) return(*status = 501); m = sins * cos(dec0) - coss * sin(dec0) * cos(ra-ra0); break; case 2: /* -TAN tan */ if (sint<=0.0) return(*status = 501); if( cos0<0.001 ) { /* Do a first order expansion around pole */ m = (coss * cos(ra-ra0)) / (sins * sin0); m = (-m + cos0 * (1.0 + m*m)) / sin0; } else { m = ( sins/sint - sin0 ) / cos0; } if( fabs(sin(ra0)) < 0.3 ) { l = coss*sin(ra)/sint - cos0*sin(ra0) + m*sin(ra0)*sin0; l /= cos(ra0); } else { l = coss*cos(ra)/sint - cos0*cos(ra0) + m*cos(ra0)*sin0; l /= -sin(ra0); } break; case 3: /* -ARC Arc*/ m = sins * sin(dec0) + coss * cos(dec0) * cos(ra-ra0); if (m<-1.0) m = -1.0; if (m>1.0) m = 1.0; m = acos (m); if (m!=0) m = m / sin(m); else m = 1.0; l = l * m; m = (sins * cos(dec0) - coss * sin(dec0) * cos(ra-ra0)) * m; break; case 4: /* -NCP North celestial pole*/ if (dec0==0.0) return(*status = 501); /* can't stand the equator */ else m = (cos(dec0) - coss * cos(ra-ra0)) / sin(dec0); break; case 5: /* -GLS global sinusoid */ dt = ra - ra0; if (fabs(dec)>twopi/4.0) return(*status = 501); if (fabs(dec0)>twopi/4.0) return(*status = 501); m = dec - dec0; l = dt * coss; break; case 6: /* -MER mercator*/ dt = yinc * cosr + xinc * sinr; if (dt==0.0) dt = 1.0; dy = (yref/2.0 + 45.0) * cond2r; dx = dy + dt / 2.0 * cond2r; dy = log (tan (dy)); dx = log (tan (dx)); geo2 = dt * cond2r / (dx - dy); geo3 = geo2 * dy; geo1 = cos (yref*cond2r); if (geo1<=0.0) geo1 = 1.0; dt = ra - ra0; l = geo1 * dt; dt = dec / 2.0 + twopi / 8.0; dt = tan (dt); if (dttwopi/4.0) return(*status = 501); dt = yinc*cosr + xinc*sinr; if (dt==0.0) dt = 1.0; dt = dt * cond2r; dy = yref * cond2r; dx = sin(dy+dt)/sqrt((1.0+cos(dy+dt))/2.0) - sin(dy)/sqrt((1.0+cos(dy))/2.0); if (dx==0.0) dx = 1.0; geo2 = dt / dx; dt = xinc*cosr - yinc* sinr; if (dt==0.0) dt = 1.0; dt = dt * cond2r; dx = 2.0 * cos(dy) * sin(dt/2.0); if (dx==0.0) dx = 1.0; geo1 = dt * sqrt((1.0+cos(dy)*cos(dt/2.0))/2.0) / dx; geo3 = geo2 * sin(dy) / sqrt((1.0+cos(dy))/2.0); dt = sqrt ((1.0 + cos(dec) * cos(da))/2.0); if (fabs(dt)twopi/4.0) return(*status = 501); dd = 1.0 + sins * sin(dec0) + coss * cos(dec0) * cos(da); if (fabs(dd)