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/* fitswcs.c *%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% * * Part of: LDACTools+ * * Author: E.BERTIN (IAP) * * Contents: Read and write WCS header info. * * Last modify: 04/01/2008 * *%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% */ #ifdef HAVE_CONFIG_H #include "config.h" #endif #ifdef HAVE_MATHIMF_H #include <mathimf.h> #else #include <math.h> #endif #include <stdio.h> #include <stdlib.h> #include <string.h> #include "fits/fitscat_defs.h" #include "fits/fitscat.h" #include "fitswcs.h" #include "wcscelsys.h" #include "wcs/wcs.h" #include "wcs/lin.h" #include "wcs/tnx.h" #include "wcs/poly.h" /******* copy_wcs ************************************************************ PROTO wcsstruct *copy_wcs(wcsstruct *wcsin) PURPOSE Copy a WCS (World Coordinate System) structure. INPUT WCS structure to be copied. OUTPUT pointer to a copy of the input structure. NOTES Actually, only FITS parameters are copied. Lower-level structures such as those created by the WCS or TNX libraries are generated. AUTHOR E. Bertin (IAP) VERSION 31/08/2002 ***/ wcsstruct *copy_wcs(wcsstruct *wcsin) { wcsstruct *wcs; /* Copy the basic stuff */ QMEMCPY(wcsin, wcs, wcsstruct, 1); /* The PROJP WCS parameters */ QMEMCPY(wcsin->projp, wcs->projp, double, wcs->naxis*100); /* Set other structure pointers to NULL (they'll have to be reallocated) */ wcs->wcsprm = NULL; wcs->lin = NULL; wcs->cel = NULL; wcs->prj = NULL; wcs->tnx_lngcor = copy_tnxaxis(wcsin->tnx_lngcor); wcs->tnx_latcor = copy_tnxaxis(wcsin->tnx_latcor); wcs->inv_x = wcs->inv_y = NULL; QCALLOC(wcs->wcsprm, struct wcsprm, 1); /* Test if the WCS is recognized and a celestial pair is found */ wcsset(wcs->naxis,(const char(*)[9])wcs->ctype, wcs->wcsprm); /* Initialize other WCS structures */ init_wcs(wcs); /* Invert projection corrections */ invert_wcs(wcs); /* Find the range of coordinates */ range_wcs(wcs); return wcs; } /******* create_wcs *********************************************************** PROTO wcsstruct *create_wcs(char **ctype, double *crval, double *crpix, double *cdelt, int *naxisn, int naxis) PURPOSE Generate a simple WCS (World Coordinate System) structure. INPUT Pointer to an array of char strings with WCS projection on each axis, pointer to an array of center coordinates (double), pointer to an array of device coordinates (double), pointer to an array of pixel scales (double), pointer to an array of image dimensions (int), number of dimensions. OUTPUT pointer to a WCS structure. NOTES If a pointer is set to null, the corresponding variables are set to default values. AUTHOR E. Bertin (IAP) VERSION 09/08/2006 ***/ wcsstruct *create_wcs(char **ctype, double *crval, double *crpix, double *cdelt, int *naxisn, int naxis) { wcsstruct *wcs; int l; QCALLOC(wcs, wcsstruct, 1); wcs->naxis = naxis; QCALLOC(wcs->projp, double, naxis*100); wcs->nprojp = 0; wcs->longpole = wcs->latpole = 999.0; for (l=0; l<naxis; l++) { wcs->naxisn[l] = naxisn? naxisn[l] : 360.0; /*-- The default WCS projection system is an all-sky Aitoff projection */ if (ctype) strncpy(wcs->ctype[l], ctype[l], 8); else if (l==0) strncpy(wcs->ctype[l], "RA---AIT", 8); else if (l==1) strncpy(wcs->ctype[l], "DEC--AIT", 8); wcs->crval[l] = crval? crval[l]: 0.0; wcs->crpix[l] = crpix? crpix[l]: 0.0; wcs->cdelt[l] = 1.0; wcs->cd[l*(naxis+1)] = cdelt? cdelt[l] : 1.0; } wcs->epoch = wcs->equinox = 2000.0; QCALLOC(wcs->wcsprm, struct wcsprm, 1); /* Test if the WCS is recognized and a celestial pair is found */ wcsset(wcs->naxis,(const char(*)[9])wcs->ctype, wcs->wcsprm); /* Initialize other WCS structures */ init_wcs(wcs); /* Invert projection corrections */ invert_wcs(wcs); /* Find the range of coordinates */ range_wcs(wcs); return wcs; } /******* init_wcs ************************************************************ PROTO void init_wcs(wcsstruct *wcs) PURPOSE Initialize astrometry and WCS (World Coordinate System) structures. INPUT WCS structure. OUTPUT -. NOTES -. AUTHOR E. Bertin (IAP) VERSION 17/05/2007 ***/ void init_wcs(wcsstruct *wcs) { int l,n,lng,lat,naxis; naxis = wcs->naxis; if (wcs->lin) { free(wcs->lin->cdelt); free(wcs->lin->crpix); free(wcs->lin->pc); free(wcs->lin->piximg); free(wcs->lin->imgpix); free(wcs->lin); } QCALLOC(wcs->lin, struct linprm, 1); QCALLOC(wcs->lin->cdelt, double, naxis); QCALLOC(wcs->lin->crpix, double, naxis); QCALLOC(wcs->lin->pc, double, naxis*naxis); if (wcs->cel) free(wcs->cel); QCALLOC(wcs->cel, struct celprm, 1); if (wcs->prj) free(wcs->prj); QCALLOC(wcs->prj, struct prjprm, 1); if (wcs->inv_x) { poly_end(wcs->inv_x); wcs->inv_x = NULL; } if (wcs->inv_y) { poly_end(wcs->inv_y); wcs->inv_y = NULL; } /* Set WCS flags to 0: structures will be reinitialized by the WCS library */ wcs->lin->flag = wcs->cel->flag = wcs->prj->flag = 0; wcs->lin->naxis = naxis; /* wcsprm structure */ lng = wcs->lng = wcs->wcsprm->lng; lat = wcs->lat = wcs->wcsprm->lat; /* linprm structure */ for (l=0; l<naxis; l++) { wcs->lin->crpix[l] = wcs->crpix[l]; wcs->lin->cdelt[l] = 1.0; } for (l=0; l<naxis*naxis; l++) wcs->lin->pc[l] = wcs->cd[l]; /* celprm structure */ if (lng>=0) { wcs->cel->ref[0] = wcs->crval[lng]; wcs->cel->ref[1] = wcs->crval[lat]; } else { wcs->cel->ref[0] = wcs->crval[0]; wcs->cel->ref[1] = wcs->crval[1]; } wcs->cel->ref[2] = wcs->longpole; wcs->cel->ref[3] = wcs->latpole; /* prjprm structure */ wcs->prj->r0 = wcs->r0; wcs->prj->tnx_lngcor = wcs->tnx_lngcor; wcs->prj->tnx_latcor = wcs->tnx_latcor; if (lng>=0) { n = 0; for (l=100; l--;) { wcs->prj->p[l] = wcs->projp[l+lat*100]; /* lat comes first for ... */ wcs->prj->p[l+100] = wcs->projp[l+lng*100];/* ... compatibility reasons */ if (!n && (wcs->prj->p[l] || wcs->prj->p[l+100])) n = l+1; } wcs->nprojp = n; } /* Check-out chirality */ wcs->chirality = wcs_chirality(wcs); /* Initialize Equatorial <=> Celestial coordinate system transforms */ init_wcscelsys(wcs); return; } /******* init_wcscelsys ******************************************************* PROTO void init_wcscelsys(wcsstruct *wcs) PURPOSE Initialize Equatorial <=> Celestial coordinate system transforms. INPUT WCS structure. OUTPUT -. NOTES -. AUTHOR E. Bertin (IAP) VERSION 18/07/2006 ***/ void init_wcscelsys(wcsstruct *wcs) { double *mat, a0,d0,ap,dp,ap2,y; int s,lng,lat; lng = wcs->wcsprm->lng; lat = wcs->wcsprm->lat; /* Is it a celestial system? If not, exit! */ if (lng==lat) { wcs->celsysconvflag = 0; return; } /* Find the celestial system */ for (s=0; *celsysname[s][0] && strncmp(wcs->ctype[lng], celsysname[s][0], 4); s++); /* Is it a known, non-equatorial system? If not, exit! */ if (!s || !*celsysname[s][0]) { wcs->celsysconvflag = 0; return; } wcs->celsys = (celsysenum)s; /* Some shortcuts */ a0 = celsysorig[s][0]*DEG; d0 = celsysorig[s][1]*DEG; ap = celsyspole[s][0]*DEG; dp = celsyspole[s][1]*DEG; /* First compute in the output referential the longitude of the south pole */ y = sin(ap - a0); /* x = cos(d0)*(cos(d0)*sin(dp)*cos(ap-a0)-sin(d0)*cos(dp)); ap2 = atan2(y,x); */ ap2 = asin(cos(d0)*y) ; /* Equatorial <=> Celestial System transformation parameters */ mat = wcs->celsysmat; mat[0] = ap; mat[1] = ap2; mat[2] = cos(dp); mat[3] = sin(dp); wcs->celsysconvflag = 1; return; } /******* read_wcs ************************************************************* PROTO wcsstruct *read_wcs(tabstruct *tab) PURPOSE Read WCS (World Coordinate System) info in the FITS header. INPUT tab structure. OUTPUT -. NOTES -. AUTHOR E. Bertin (IAP) VERSION 02/01/2008 ***/ wcsstruct *read_wcs(tabstruct *tab) { #define FITSREADF(buf, k, val, def) \ {if (fitsread(buf,k, &val, H_FLOAT,T_DOUBLE) != RETURN_OK) \ val = def; \ } #define FITSREADI(buf, k, val, def) \ {if (fitsread(buf,k, &val, H_INT,T_LONG) != RETURN_OK) \ val = def; \ } #define FITSREADS(buf, k, str, def) \ {if (fitsread(buf,k,str, H_STRING,T_STRING) != RETURN_OK) \ strcpy(str, (def)); \ } char str[MAXCHARS]; char wstr1[TNX_MAXCHARS], wstr2[TNX_MAXCHARS]; wcsstruct *wcs; double drota; int j, l, naxis; char name[16], *buf, *filename, *ptr; buf = tab->headbuf; filename = (tab->cat? tab->cat->filename : strcpy(name, "internal header")); FITSREADS(buf, "OBJECT ", str, "Unnamed"); QCALLOC(wcs, wcsstruct, 1); if (tab->naxis > NAXIS) { warning("Maximum number of dimensions supported by this version of the ", "software exceeded\n"); tab->naxis = 2; } wcs->naxis = naxis = tab->naxis; QCALLOC(wcs->projp, double, naxis*100); for (l=0; l<naxis; l++) { wcs->naxisn[l] = tab->naxisn[l]; sprintf(str, "CTYPE%-3d", l+1); FITSREADS(buf, str, str, ""); strncpy(wcs->ctype[l], str, 8); sprintf(str, "CUNIT%-3d", l+1); FITSREADS(buf, str, str, "deg"); strncpy(wcs->cunit[l], str, 32); sprintf(str, "CRVAL%-3d", l+1); FITSREADF(buf, str, wcs->crval[l], 0.0); sprintf(str, "CRPIX%-3d", l+1); FITSREADF(buf, str, wcs->crpix[l], 1.0); sprintf(str, "CDELT%-3d", l+1); FITSREADF(buf, str, wcs->cdelt[l], 1.0); sprintf(str, "CRDER%-3d", l+1); FITSREADF(buf, str, wcs->crder[l], 0.0); sprintf(str, "CSYER%-3d", l+1); FITSREADF(buf, str, wcs->csyer[l], 0.0); if (fabs(wcs->cdelt[l]) < 1e-30) error(EXIT_FAILURE, "*Error*: CDELT parameters out of range in ", filename); } if (fitsfind(buf, "CD?_????")!=RETURN_ERROR) { /*-- If CD keywords exist, use them for the linear mapping terms... */ for (l=0; l<naxis; l++) for (j=0; j<naxis; j++) { sprintf(str, "CD%d_%d", l+1, j+1); FITSREADF(buf, str, wcs->cd[l*naxis+j], l==j?1.0:0.0) } } else if (fitsfind(buf, "PC00?00?")!=RETURN_ERROR) /*-- ...If PC keywords exist, use them for the linear mapping terms... */ for (l=0; l<naxis; l++) for (j=0; j<naxis; j++) { sprintf(str, "PC%03d%03d", l+1, j+1); FITSREADF(buf, str, wcs->cd[l*naxis+j], l==j?1.0:0.0) wcs->cd[l*naxis+j] *= wcs->cdelt[l]; } else { /*-- ...otherwise take the obsolete CROTA2 parameter */ FITSREADF(buf, "CROTA2 ", drota, 0.0) wcs->cd[3] = wcs->cd[0] = cos(drota*DEG); wcs->cd[1] = -(wcs->cd[2] = sin(drota*DEG)); wcs->cd[0] *= wcs->cdelt[0]; wcs->cd[2] *= wcs->cdelt[0]; wcs->cd[1] *= wcs->cdelt[1]; wcs->cd[3] *= wcs->cdelt[1]; } QCALLOC(wcs->wcsprm, struct wcsprm, 1); /* Test if the WCS is recognized and a celestial pair is found */ if (!wcsset(wcs->naxis,(const char(*)[9])wcs->ctype, wcs->wcsprm) && wcs->wcsprm->flag<999) { char *pstr; double date; int biss, dpar[3]; /*-- Coordinate reference frame */ /*-- Search for an observation date expressed in Julian days */ FITSREADF(buf, "MJD-OBS ", date, -1.0); /*-- Precession date (defined from Ephemerides du Bureau des Longitudes) */ /*-- in Julian years from 2000.0 */ if (date>0.0) wcs->obsdate = 2000.0 - (MJD2000 - date)/365.25; else { /*---- Search for an observation date expressed in "civilian" format */ FITSREADS(buf, "DATE-OBS ", str, ""); if (*str) { /*------ Decode DATE-OBS format: DD/MM/YY or YYYY-MM-DD */ for (l=0; l<3 && (pstr = strtok_r(l?NULL:str,"/- ", &ptr)); l++) dpar[l] = atoi(pstr); if (l<3 || !dpar[0] || !dpar[1] || !dpar[2]) { /*-------- If DATE-OBS value corrupted or incomplete, assume 2000-1-1 */ warning("Invalid DATE-OBS value in header: ", str); dpar[0] = 2000; dpar[1] = 1; dpar[2] = 1; } else if (strchr(str, '/') && dpar[0]<32 && dpar[2]<100) { j = dpar[0]; dpar[0] = dpar[2]+1900; dpar[2] = j; } biss = (dpar[0]%4)?0:1; /*------ Convert date to MJD */ date = -678956 + (365*dpar[0]+dpar[0]/4) - biss + ((dpar[1]>2?((int)((dpar[1]+1)*30.6)-63+biss) :((dpar[1]-1)*(63+biss))/2) + dpar[2]); wcs->obsdate = 2000.0 - (MJD2000 - date)/365.25; } else /*------ Well if really no date is found */ wcs->obsdate = 0.0; } FITSREADF(buf, "EPOCH", wcs->epoch, 2000.0); FITSREADF(buf, "EQUINOX", wcs->equinox, wcs->epoch); FITSREADS(buf, "RADECSYS", str, wcs->equinox >= 2000.0? "ICRS" : (wcs->equinox<1984.0? "FK4" : "FK5")); if (!strcmp(str, "ICRS")) wcs->radecsys = RDSYS_ICRS; else if (!strcmp(str, "FK5")) wcs->radecsys = RDSYS_FK5; else if (!strcmp(str, "FK4")) { if (wcs->equinox == 2000.0) { FITSREADF(buf, "EPOCH ", wcs->equinox, 1950.0); FITSREADF(buf, "EQUINOX", wcs->equinox, wcs->equinox); } wcs->radecsys = RDSYS_FK4; warning("FK4 precession formulae not yet implemented:\n", " Astrometry may be slightly inaccurate"); } else if (!strcmp(str, "FK4-NO-E")) { if (wcs->equinox == 2000.0) { FITSREADF(buf, "EPOCH", wcs->equinox, 1950.0); FITSREADF(buf, "EQUINOX", wcs->equinox, wcs->equinox); } wcs->radecsys = RDSYS_FK4_NO_E; warning("FK4 precession formulae not yet implemented:\n", " Astrometry may be slightly inaccurate"); } else if (!strcmp(str, "GAPPT")) { wcs->radecsys = RDSYS_GAPPT; warning("GAPPT reference frame not yet implemented:\n", " Astrometry may be slightly inaccurate"); } else { warning("Using ICRS instead of unknown astrometric reference frame: ", str); wcs->radecsys = RDSYS_ICRS; } /*-- Projection parameters */ if (!strcmp(wcs->wcsprm->pcode, "TNX")) { /*---- IRAF's TNX projection: decode these #$!?@#!! WAT parameters */ if (fitsfind(buf, "WAT?????") != RETURN_ERROR) { /*------ First we need to concatenate strings */ pstr = wstr1; sprintf(str, "WAT1_001"); for (j=2; fitsread(buf,str,pstr,H_STRINGS,T_STRING)==RETURN_OK; j++) { sprintf(str, "WAT1_%03d", j); pstr += strlen(pstr); } pstr = wstr2; sprintf(str, "WAT2_001"); for (j=2; fitsread(buf,str,pstr,H_STRINGS,T_STRING)==RETURN_OK; j++) { sprintf(str, "WAT2_%03d", j); pstr += strlen(pstr); } /*------ LONGPOLE defaulted to 180 deg if not found */ if ((pstr = strstr(wstr1, "longpole")) || (pstr = strstr(wstr2, "longpole"))) pstr = strpbrk(pstr, "1234567890-+."); wcs->longpole = pstr? atof(pstr) : 999.0; wcs->latpole = 999.0; /*------ RO defaulted to 180/PI if not found */ if ((pstr = strstr(wstr1, "ro")) || (pstr = strstr(wstr2, "ro"))) pstr = strpbrk(pstr, "1234567890-+."); wcs->r0 = pstr? atof(pstr) : 0.0; /*------ Read the remaining TNX parameters */ if ((pstr = strstr(wstr1, "lngcor")) || (pstr = strstr(wstr2, "lngcor"))) wcs->tnx_lngcor = read_tnxaxis(pstr); if (!wcs->tnx_lngcor) error(EXIT_FAILURE, "*Error*: incorrect TNX parameters in ", filename); if ((pstr = strstr(wstr1, "latcor")) || (pstr = strstr(wstr2, "latcor"))) wcs->tnx_latcor = read_tnxaxis(pstr); if (!wcs->tnx_latcor) error(EXIT_FAILURE, "*Error*: incorrect TNX parameters in ", filename); } } else { FITSREADF(buf, "LONGPOLE", wcs->longpole, 999.0); FITSREADF(buf, "LATPOLE ", wcs->latpole, 999.0); /*---- Old convention */ if (fitsfind(buf, "PROJP???") != RETURN_ERROR) for (j=0; j<10; j++) { sprintf(str, "PROJP%-3d", j); FITSREADF(buf, str, wcs->projp[j], 0.0); } /*---- New convention */ if (fitsfind(buf, "PV?_????") != RETURN_ERROR) for (l=0; l<naxis; l++) for (j=0; j<100; j++) { sprintf(str, "PV%d_%d", l+1, j); FITSREADF(buf, str, wcs->projp[j+l*100], 0.0); } } } /* Initialize other WCS structures */ init_wcs(wcs); /* Find the range of coordinates */ range_wcs(wcs); /* Invert projection corrections */ invert_wcs(wcs); #undef FITSREADF #undef FITSREADI #undef FITSREADS return wcs; } /******* write_wcs *********************************************************** PROTO void write_wcs(tabstruct *tab, wcsstruct *wcs) PURPOSE Write WCS (World Coordinate System) info in the FITS header. INPUT tab structure, WCS structure. OUTPUT -. NOTES -. AUTHOR E. Bertin (IAP) VERSION 17/07/2006 ***/ void write_wcs(tabstruct *tab, wcsstruct *wcs) { char str[MAXCHARS]; int j, l, naxis; naxis = wcs->naxis; addkeywordto_head(tab, "BITPIX ", "Bits per pixel"); fitswrite(tab->headbuf, "BITPIX ", &tab->bitpix, H_INT, T_LONG); addkeywordto_head(tab, "NAXIS ", "Number of axes"); fitswrite(tab->headbuf, "NAXIS ", &wcs->naxis, H_INT, T_LONG); for (l=0; l<naxis; l++) { sprintf(str, "NAXIS%-3d", l+1); addkeywordto_head(tab, str, "Number of pixels along this axis"); fitswrite(tab->headbuf, str, &wcs->naxisn[l], H_INT, T_LONG); } addkeywordto_head(tab, "EQUINOX ", "Mean equinox"); fitswrite(tab->headbuf, "EQUINOX ", &wcs->equinox, H_FLOAT, T_DOUBLE); addkeywordto_head(tab, "RADECSYS", "Astrometric system"); switch(wcs->radecsys) { case RDSYS_ICRS: fitswrite(tab->headbuf, "RADECSYS", "ICRS", H_STRING, T_STRING); break; case RDSYS_FK5: fitswrite(tab->headbuf, "RADECSYS", "FK5", H_STRING, T_STRING); break; case RDSYS_FK4: fitswrite(tab->headbuf, "RADECSYS", "FK4", H_STRING, T_STRING); break; case RDSYS_FK4_NO_E: fitswrite(tab->headbuf, "RADECSYS", "FK4-NO-E", H_STRING, T_STRING); break; case RDSYS_GAPPT: fitswrite(tab->headbuf, "RADECSYS", "GAPPT", H_STRING, T_STRING); break; default: error(EXIT_FAILURE, "*Error*: unknown RADECSYS type in write_wcs()", ""); } for (l=0; l<naxis; l++) { sprintf(str, "CTYPE%-3d", l+1); addkeywordto_head(tab, str, "WCS projection type for this axis"); fitswrite(tab->headbuf, str, wcs->ctype[l], H_STRING, T_STRING); sprintf(str, "CUNIT%-3d", l+1); addkeywordto_head(tab, str, "Axis unit"); fitswrite(tab->headbuf, str, wcs->cunit[l], H_STRING, T_STRING); sprintf(str, "CRVAL%-3d", l+1); addkeywordto_head(tab, str, "World coordinate on this axis"); fitswrite(tab->headbuf, str, &wcs->crval[l], H_EXPO, T_DOUBLE); sprintf(str, "CRPIX%-3d", l+1); addkeywordto_head(tab, str, "Reference pixel on this axis"); fitswrite(tab->headbuf, str, &wcs->crpix[l], H_EXPO, T_DOUBLE); for (j=0; j<naxis; j++) { sprintf(str, "CD%d_%d", l+1, j+1); addkeywordto_head(tab, str, "Linear projection matrix"); fitswrite(tab->headbuf, str, &wcs->cd[l*naxis+j], H_EXPO, T_DOUBLE); } for (j=0; j<100; j++) if (wcs->projp[j+100*l] != 0.0) { sprintf(str, "PV%d_%d", l+1, j); addkeywordto_head(tab, str, "Projection distortion parameter"); fitswrite(tab->headbuf, str, &wcs->projp[j+100*l], H_EXPO, T_DOUBLE); } } /* Update the tab data */ readbasic_head(tab); return; } /******* end_wcs ************************************************************** PROTO void end_wcs(wcsstruct *wcs) PURPOSE Free WCS (World Coordinate System) infos. INPUT WCS structure. OUTPUT -. NOTES . AUTHOR E. Bertin (IAP) VERSION 24/05/2000 ***/ void end_wcs(wcsstruct *wcs) { if (wcs) { if (wcs->lin) { free(wcs->lin->cdelt); free(wcs->lin->crpix); free(wcs->lin->pc); free(wcs->lin->piximg); free(wcs->lin->imgpix); free(wcs->lin); } free(wcs->cel); free(wcs->prj); free(wcs->wcsprm); free_tnxaxis(wcs->tnx_lngcor); free_tnxaxis(wcs->tnx_latcor); poly_end(wcs->inv_x); poly_end(wcs->inv_y); free(wcs->projp); free(wcs); } return; } /******* wcs_supproj ********************************************************* PROTO int wcs_supproj(char *name) PURPOSE Tell if a projection system is supported or not. INPUT Proposed projection code name. OUTPUT RETURN_OK if projection is supported, RETURN_ERROR otherwise. NOTES -. AUTHOR E. Bertin (IAP) VERSION 24/05/2000 ***/ int wcs_supproj(char *name) { char projcode[26][5] = {"AZP", "TAN", "SIN", "STG", "ARC", "ZPN", "ZEA", "AIR", "CYP", "CAR", "MER", "CEA", "COP", "COD", "COE", "COO", "BON", "PCO", "GLS", "PAR", "AIT", "MOL", "CSC", "QSC", "TSC", "NONE"}; int i; for (i=0; i<26; i++) if (!strcmp(name, projcode[i])) return RETURN_OK; return RETURN_ERROR; } /******* invert_wcs *********************************************************** PROTO void invert_wcs(wcsstruct *wcs) PURPOSE Invert WCS projection mapping (using a polynomial). INPUT WCS structure. OUTPUT -. NOTES . AUTHOR E. Bertin (IAP) VERSION 06/11/2003 ***/ void invert_wcs(wcsstruct *wcs) { polystruct *poly; double pixin[NAXIS],raw[NAXIS],rawmin[NAXIS]; double *outpos,*outpost, *lngpos,*lngpost, *latpos,*latpost, lngstep,latstep, rawsize, epsilon; int group[] = {1,1}; /* Don't ask, this is needed by poly_init()! */ int i,j,lng,lat,deg, tnxflag, maxflag; /* Check first that inversion is not straightforward */ lng = wcs->wcsprm->lng; lat = wcs->wcsprm->lat; if (!strcmp(wcs->wcsprm->pcode, "TNX")) tnxflag = 1; else if (!strcmp(wcs->wcsprm->pcode, "TAN") && (wcs->projp[1+lng*100] || wcs->projp[1+lat*100])) tnxflag = 0; else return; /* We define x as "longitude" and y as "latitude" projections */ /* We assume that PCxx cross-terms with additional dimensions are small */ /* Sample the whole image with a regular grid */ lngstep = wcs->naxisn[lng]/(WCS_NGRIDPOINTS-1.0); latstep = wcs->naxisn[lat]/(WCS_NGRIDPOINTS-1.0); QMALLOC(outpos, double, 2*WCS_NGRIDPOINTS2); QMALLOC(lngpos, double, WCS_NGRIDPOINTS2); QMALLOC(latpos, double, WCS_NGRIDPOINTS2); for (i=0; i<wcs->naxis; i++) raw[i] = rawmin[i] = 0.5; outpost = outpos; lngpost = lngpos; latpost = latpos; for (j=WCS_NGRIDPOINTS; j--; raw[lat]+=latstep) { raw[lng] = rawmin[lng]; for (i=WCS_NGRIDPOINTS; i--; raw[lng]+=lngstep) { if (linrev(raw, wcs->lin, pixin)) error(EXIT_FAILURE, "*Error*: incorrect linear conversion in ", wcs->wcsprm->pcode); *(lngpost++) = pixin[lng]; *(latpost++) = pixin[lat]; if (tnxflag) { *(outpost++) = pixin[lng] +raw_to_tnxaxis(wcs->tnx_lngcor,pixin[lng],pixin[lat]); *(outpost++) = pixin[lat] +raw_to_tnxaxis(wcs->tnx_latcor,pixin[lng],pixin[lat]); } else { raw_to_pv(wcs->prj,pixin[lng],pixin[lat], outpost, outpost+1); outpost += 2; } } } /* Invert "longitude" */ /* Compute the extent of the pixel in reduced projected coordinates */ linrev(rawmin, wcs->lin, pixin); pixin[lng] += ARCSEC/DEG; linfwd(pixin, wcs->lin, raw); rawsize = sqrt((raw[lng]-rawmin[lng])*(raw[lng]-rawmin[lng]) +(raw[lat]-rawmin[lat])*(raw[lat]-rawmin[lat]))*DEG/ARCSEC; if (!rawsize) error(EXIT_FAILURE, "*Error*: incorrect linear conversion in ", wcs->wcsprm->pcode); epsilon = WCS_INVACCURACY/rawsize; /* Find the lowest degree polynom */ poly = NULL; /* to avoid gcc -Wall warnings */ maxflag = 1; for (deg=1; deg<=WCS_INVMAXDEG && maxflag; deg++) { if (deg>1) poly_end(poly); poly = poly_init(group, 2, °, 1); poly_fit(poly, outpos, lngpos, NULL, WCS_NGRIDPOINTS2, NULL); maxflag = 0; outpost = outpos; lngpost = lngpos; for (i=WCS_NGRIDPOINTS2; i--; outpost+=2) if (fabs(poly_func(poly, outpost)-*(lngpost++))>epsilon) { maxflag = 1; break; } } if (maxflag) warning("Significant inaccuracy likely to occur in projection",""); /* Now link the created structure */ wcs->prj->inv_x = wcs->inv_x = poly; /* Invert "latitude" */ /* Compute the extent of the pixel in reduced projected coordinates */ linrev(rawmin, wcs->lin, pixin); pixin[lat] += ARCSEC/DEG; linfwd(pixin, wcs->lin, raw); rawsize = sqrt((raw[lng]-rawmin[lng])*(raw[lng]-rawmin[lng]) +(raw[lat]-rawmin[lat])*(raw[lat]-rawmin[lat]))*DEG/ARCSEC; if (!rawsize) error(EXIT_FAILURE, "*Error*: incorrect linear conversion in ", wcs->wcsprm->pcode); epsilon = WCS_INVACCURACY/rawsize; /* Find the lowest degree polynom */ maxflag = 1; for (deg=1; deg<=WCS_INVMAXDEG && maxflag; deg++) { if (deg>1) poly_end(poly); poly = poly_init(group, 2, °, 1); poly_fit(poly, outpos, latpos, NULL, WCS_NGRIDPOINTS2, NULL); maxflag = 0; outpost = outpos; latpost = latpos; for (i=WCS_NGRIDPOINTS2; i--; outpost+=2) if (fabs(poly_func(poly, outpost)-*(latpost++))>epsilon) { maxflag = 1; break; } } if (maxflag) warning("Significant inaccuracy likely to occur in projection",""); /* Now link the created structure */ wcs->prj->inv_y = wcs->inv_y = poly; /* Free memory */ free(outpos); free(lngpos); free(latpos); return; } /******* range_wcs *********************************************************** PROTO void range_wcs(wcsstruct *wcs) PURPOSE Find roughly the range of WCS coordinates on all axes, and typical pixel scales. INPUT WCS structure. OUTPUT -. NOTES . AUTHOR E. Bertin (IAP) VERSION 09/08/2006 ***/ void range_wcs(wcsstruct *wcs) { double step[NAXIS], raw[NAXIS], rawmin[NAXIS], world[NAXIS], world2[NAXIS]; double *worldmin, *worldmax, *scale, *worldc, rad, radmax, lc; int linecount[NAXIS]; int i,j, naxis, npoints, lng,lat; naxis = wcs->naxis; /* World range */ npoints = 1; worldmin = wcs->wcsmin; worldmax = wcs->wcsmax; /* First, find the center and use it as a reference point for lng */ lng = wcs->lng; lat = wcs->lat; for (i=0; i<naxis; i++) raw[i] = (wcs->naxisn[i]+1.0)/2.0; if (raw_to_wcs(wcs, raw, world)) { /*-- Oops no mapping there! So explore the image in an increasingly large */ /*-- domain to find a better "center" (now we know there must be angular */ /*-- coordinates) */ for (j=0; j<100; j++) { for (i=0; i<naxis; i++) raw[i] += wcs->naxisn[i]/100.0*(0.5-(double)rand()/RAND_MAX); if (!raw_to_wcs(wcs, raw, world)) break; } } if (lng!=lat) lc = fmod(world[lng]+180.0, 360.0); else { lc = 0.0; /* to avoid gcc -Wall warnings */ lng = -1; } /* Pixel scales at image center */ scale = wcs->wcsscale; for (i=0; i<naxis; i++) { if ((i==lng || i==lat) && lng!=lat) wcs->pixscale = scale[i] = sqrt(wcs_scale(wcs, raw)); else { raw[i] += 1.0; raw_to_wcs(wcs, raw, world2); scale[i] = fabs(world2[i] - world[i]); raw[i] -= 1.0; if (lng==lat) wcs->pixscale = scale[i]; } wcs->wcsscalepos[i] = world[i]; } /* Find "World limits" */ for (i=0; i<naxis; i++) { raw[i] = rawmin[i] = 0.5; step[i] = wcs->naxisn[i]/(WCS_NRANGEPOINTS-1.0); npoints *= WCS_NRANGEPOINTS; worldmax[i] = -(worldmin[i] = 1e31); linecount[i] = 0; } radmax = 0.0; worldc = wcs->wcsscalepos; for (j=npoints; j--;) { raw_to_wcs(wcs, raw, world); for (i=0; i<naxis; i++) { /*---- Handle longitudes around 0 */ if (i==lng && world[i]>lc) world[i] -= 359.9999; if (world[i]<worldmin[i]) worldmin[i] = world[i]; if (world[i]>worldmax[i]) worldmax[i] = world[i]; } /*-- Compute maximum distance to center */ if ((rad=wcs_dist(wcs, world, worldc)) > radmax) radmax = rad; for (i=0; i<naxis; i++) { raw[i] += step[i]; if (++linecount[i]<WCS_NRANGEPOINTS) break; else { linecount[i] = 0; /* No need to initialize it to 0! */ raw[i] = rawmin[i]; } } } wcs->wcsmaxradius = radmax; if (lng!=lat) { if (worldmax[lat]<-90.0) worldmax[lat] = -90.0; if (worldmax[lat]>90.0) worldmax[lat] = 90.0; } return; } /******* frame_wcs *********************************************************** PROTO void frame_wcs(wcsstruct *wcsin, wcsstruct *wcsout) PURPOSE Find the x and y limits of an input frame in an output image. INPUT WCS structure of the input frame, WCS structure of the output frame. OUTPUT -. NOTES . AUTHOR E. Bertin (IAP) VERSION 29/12/2004 ***/ void frame_wcs(wcsstruct *wcsin, wcsstruct *wcsout) { double rawin[NAXIS], rawout[NAXIS], world[NAXIS]; int linecount[NAXIS]; double worldc; int *min, *max, i,j, naxis, npoints, out, swapflag; naxis = wcsin->naxis; /* World range */ npoints = 1; min = wcsin->outmin; max = wcsin->outmax; for (i=0; i<naxis; i++) { rawin[i] = 0.5; /* Lower pixel limits */ npoints *= WCS_NRANGEPOINTS; max[i] = -(min[i] = 1<<30); linecount[i] = 0; } /* Check if lng and lat are swapped between in and out wcs (vicious idea!) */ swapflag = (((wcsin->lng != wcsout->lng) || (wcsin->lat != wcsout->lat)) && (wcsin->lng != wcsin->lat) && (wcsout->lng != wcsout->lat)); for (j=npoints; j--;) { if (!raw_to_wcs(wcsin, rawin, world)) { if (swapflag) { worldc = world[wcsout->lat]; world[wcsout->lat] = world[wcsin->lat]; world[wcsin->lat] = worldc; } if (!wcs_to_raw(wcsout, world, rawout)) for (i=0; i<naxis; i++) { if ((out=(int)(rawout[i]+0.499))<min[i]) min[i] = out; if (out>max[i]) max[i] = out; } } for (i=0; i<naxis; i++) { rawin[i] = 0.5 + 0.5*wcsin->naxisn[i] *(1-cos(PI*(linecount[i]+1.0)/(WCS_NRANGEPOINTS-1))); if (++linecount[i]<WCS_NRANGEPOINTS) break; else { linecount[i] = 0; /* No need to initialize it to 0! */ rawin[i] = 0.5; } } } /* Just add a little margin, in case of... */ for (i=0; i<naxis; i++) { if (min[i]>-2147483647) min[i] -= 2; if (max[i]>2147483647) max[i] += 2; } return; } /******* reaxe_wcs *********************************************************** PROTO int reaxe_wcs(wcsstruct *wcs, int lng, int lat) PURPOSE Reformulate a wcs structure to match lng and lat axis indices INPUT WCS structure, longitude index, latitude index. OUTPUT RETURN_OK if successful, RETURN_ERROR otherwise. NOTES . AUTHOR E. Bertin (IAP) VERSION 20/11/2003 ***/ int reaxe_wcs(wcsstruct *wcs, int lng, int lat) { char strlng[80], strlat[80]; double dlng,dlat,dlng2,dlat2; int l, ilng,ilat,olng,olat, naxis; olng = wcs->lng; olat = wcs->lat; if (lng<0 || lat<0 || olng<0 || olat<0) return RETURN_ERROR; ilng = wcs->naxisn[olng]; ilat = wcs->naxisn[olat]; wcs->naxisn[lng] = ilng; wcs->naxisn[lat] = ilat; strcpy(strlng, wcs->ctype[olng]); strcpy(strlat, wcs->ctype[olat]); strcpy(wcs->ctype[lng], strlng); strcpy(wcs->ctype[lat], strlat); dlng = wcs->crval[olng]; dlat = wcs->crval[olat]; wcs->crval[lng] = dlng; wcs->crval[lat] = dlat; naxis = wcs->naxis; dlng = wcs->cd[olng+olng*naxis]; dlng2 = wcs->cd[olng+olat*naxis]; dlat = wcs->cd[olat+olat*naxis]; dlat2 = wcs->cd[olat+olng*naxis]; wcs->cd[lng+lng*naxis] = dlng2; wcs->cd[lng+lat*naxis] = dlng; wcs->cd[lat+lat*naxis] = dlat2; wcs->cd[lat+lng*naxis] = dlat; for (l=0; l<100; l++) { dlng = wcs->projp[l+olng*100]; dlat = wcs->projp[l+olat*100]; wcs->projp[l+lng*100] = dlng; wcs->projp[l+lat*100] = dlat; } /*-- Reinitialize wcs */ wcsset(wcs->naxis,(const char(*)[9])wcs->ctype, wcs->wcsprm); /*-- Initialize other WCS structures */ init_wcs(wcs); /*-- Find the range of coordinates */ range_wcs(wcs); return RETURN_OK; } /******* celsys_to_eq ********************************************************* PROTO int celsys_to_eq(wcsstruct *wcs, double *wcspos) PURPOSE Convert arbitrary celestial coordinates to equatorial. INPUT WCS structure, Coordinate vector. OUTPUT RETURN_OK if mapping successful, RETURN_ERROR otherwise. NOTES -. AUTHOR E. Bertin (IAP) VERSION 08/02/2007 ***/ int celsys_to_eq(wcsstruct *wcs, double *wcspos) { double *mat, a2,d2,sd2,cd2cp,sd,x,y; int lng, lat; mat = wcs->celsysmat; a2 = wcspos[lng = wcs->wcsprm->lng]*DEG - mat[1]; d2 = wcspos[lat = wcs->wcsprm->lat]*DEG; /* A bit of spherical trigonometry... */ /* Compute the latitude... */ sd2 = sin(d2); cd2cp = cos(d2)*mat[2]; sd = sd2*mat[3]-cd2cp*cos(a2); /* ...and the longitude */ y = cd2cp*sin(a2); x = sd2 - sd*mat[3]; wcspos[lng] = fmod((atan2(y,x) + mat[0])/DEG+360.0, 360.0); wcspos[lat] = asin(sd)/DEG; return RETURN_OK; } /******* eq_to_celsys ********************************************************* PROTO int eq_to_celsys(wcsstruct *wcs, double *wcspos) PURPOSE Convert equatorial to arbitrary celestial coordinates. INPUT WCS structure, Coordinate vector. OUTPUT RETURN_OK if mapping successful, RETURN_ERROR otherwise. NOTES -. AUTHOR E. Bertin (IAP) VERSION 08/02/2007 ***/ int eq_to_celsys(wcsstruct *wcs, double *wcspos) { double *mat, a,d,sd2,cdcp,sd,x,y; int lng, lat; mat = wcs->celsysmat; a = wcspos[lng = wcs->wcsprm->lng]*DEG - mat[0]; d = wcspos[lat = wcs->wcsprm->lat]*DEG; /* A bit of spherical trigonometry... */ /* Compute the latitude... */ sd = sin(d); cdcp = cos(d)*mat[2]; sd2 = sd*mat[3]+cdcp*cos(a); /* ...and the longitude */ y = cdcp*sin(a); x = sd2*mat[3]-sd; wcspos[lng] = fmod((atan2(y,x) + mat[1])/DEG+360.0, 360.0); wcspos[lat] = asin(sd2)/DEG; return RETURN_OK; } /******* raw_to_wcs *********************************************************** PROTO int raw_to_wcs(wcsstruct *, double *, double *) PURPOSE Convert raw (pixel) coordinates to WCS (World Coordinate System). INPUT WCS structure, Pointer to the array of input coordinates, Pointer to the array of output coordinates. OUTPUT RETURN_OK if mapping successful, RETURN_ERROR otherwise. NOTES -. AUTHOR E. Bertin (IAP) VERSION 08/02/2007 ***/ int raw_to_wcs(wcsstruct *wcs, double *pixpos, double *wcspos) { double imgcrd[NAXIS], phi,theta; int i; if (wcsrev((const char(*)[9])wcs->ctype, wcs->wcsprm, pixpos, wcs->lin,imgcrd, wcs->prj, &phi, &theta, wcs->crval, wcs->cel, wcspos)) { for (i=0; i<wcs->naxis; i++) wcspos[i] = WCS_NOCOORD; return RETURN_ERROR; } /* If needed, convert from a different coordinate system to equatorial */ if (wcs->celsysconvflag) celsys_to_eq(wcs, wcspos); return RETURN_OK; } /******* wcs_to_raw *********************************************************** PROTO int wcs_to_raw(wcsstruct *, double *, double *) PURPOSE Convert WCS (World Coordinate System) coords to raw (pixel) coords. INPUT WCS structure, Pointer to the array of input coordinates, Pointer to the array of output coordinates. OUTPUT RETURN_OK if mapping successful, RETURN_ERROR otherwise. NOTES -. AUTHOR E. Bertin (IAP) VERSION 08/02/2007 ***/ int wcs_to_raw(wcsstruct *wcs, double *wcspos, double *pixpos) { double imgcrd[NAXIS], phi,theta; int i; /* If needed, convert to a coordinate system different from equatorial */ if (wcs->celsysconvflag) eq_to_celsys(wcs, wcspos); if (wcsfwd((const char(*)[9])wcs->ctype,wcs->wcsprm,wcspos, wcs->crval, wcs->cel,&phi,&theta,wcs->prj, imgcrd,wcs->lin,pixpos)) { for (i=0; i<wcs->naxis; i++) pixpos[i] = WCS_NOCOORD; return RETURN_ERROR; } return RETURN_OK; } /******* red_to_raw ********************************************************** PROTO int red_to_raw(wcsstruct *, double *, double *) PURPOSE Convert reduced (World Coordinate System) coords to raw (pixel) coords. INPUT WCS structure, Pointer to the array of input (reduced) coordinates, Pointer to the array of output (pixel) coordinates. OUTPUT RETURN_OK if mapping successful, RETURN_ERROR otherwise. NOTES -. AUTHOR E. Bertin (IAP) VERSION 23/10/2003 ***/ int red_to_raw(wcsstruct *wcs, double *redpos, double *pixpos) { struct wcsprm *wcsprm; double offset; wcsprm = wcs->wcsprm; /* Initialize if required */ if (wcsprm && wcsprm->flag != WCSSET) { if (wcsset(wcs->naxis, (const char(*)[9])wcs->ctype, wcsprm)) return RETURN_ERROR; } if (wcsprm && wcsprm->flag != 999 && wcsprm->cubeface != -1) { /*-- Separation between faces */ offset = (wcs->prj->r0 == 0.0 ? 90.0 : wcs->prj->r0*PI/2.0); /*-- Stack faces in a cube */ if (redpos[wcs->lat] < -0.5*offset) { redpos[wcs->lat] += offset; redpos[wcsprm->cubeface] = 5.0; } else if (redpos[wcs->lat] > 0.5*offset) { redpos[wcs->lat] -= offset; redpos[wcsprm->cubeface] = 0.0; } else if (redpos[wcs->lng] > 2.5*offset) { redpos[wcs->lng] -= 3.0*offset; redpos[wcsprm->cubeface] = 4.0; } else if (redpos[wcs->lng] > 1.5*offset) { redpos[wcs->lng] -= 2.0*offset; redpos[wcsprm->cubeface] = 3.0; } else if (redpos[wcs->lng] > 0.5*offset) { redpos[wcs->lng] -= offset; redpos[wcsprm->cubeface] = 2.0; } else redpos[wcsprm->cubeface] = 1.0; } /* Apply forward linear transformation */ if (linfwd(redpos, wcs->lin, pixpos)) return RETURN_ERROR; return RETURN_OK; } /******* raw_to_red ********************************************************** PROTO int raw_to_red(wcsstruct *, double *, double *) PURPOSE Convert raw (pixel) coordinates to reduced WCS coordinates. INPUT WCS structure, Pointer to the array of input (pixel) coordinates, Pointer to the array of output (reduced) coordinates. OUTPUT RETURN_OK if mapping successful, RETURN_ERROR otherwise. NOTES -. AUTHOR E. Bertin (IAP) VERSION 23/10/2003 ***/ int raw_to_red(wcsstruct *wcs, double *pixpos, double *redpos) { struct wcsprm *wcsprm; double offset; int face; wcsprm = wcs->wcsprm; /* Initialize if required */ if (wcsprm && wcsprm->flag != WCSSET) { if (wcsset(wcs->naxis, (const char(*)[9])wcs->ctype, wcsprm)) return RETURN_ERROR; } /* Apply reverse linear transformation */ if (linrev(pixpos, wcs->lin, redpos)) return RETURN_ERROR; if (wcsprm && wcsprm->flag != 999 && wcsprm->cubeface != -1) { /*-- Do we have a CUBEFACE axis? */ face = (int)(redpos[wcsprm->cubeface] + 0.5); if (fabs(redpos[wcsprm->cubeface]-face) > 1e-10) return RETURN_ERROR; /*-- Separation between faces. */ offset = (wcs->prj->r0 == 0.0 ? 90.0 : wcs->prj->r0*PI/2.0); /*-- Lay out faces in a plane. */ switch (face) { case 0: redpos[wcs->lat] += offset; break; case 1: break; case 2: redpos[wcs->lng] += offset; break; case 3: redpos[wcs->lng] += offset*2; break; case 4: redpos[wcs->lng] += offset*3; break; case 5: redpos[wcs->lat] -= offset; break; default: return RETURN_ERROR; } } return RETURN_OK; } /******* wcs_dist *********************************************************** PROTO double wcs_dist(wcsstruct *wcs, double *wcspos1, double *wcspos2) PURPOSE Compute the angular distance between 2 points on the sky. INPUT WCS structure, Pointer to the first array of world coordinates, Pointer to the second array of world coordinates. OUTPUT Angular distance (in degrees) between points. NOTES -. AUTHOR E. Bertin (IAP) VERSION 24/07/2002 ***/ double wcs_dist(wcsstruct *wcs, double *wcspos1, double *wcspos2) { double d, dp; int i, lng, lat; lng = wcs->lng; lat = wcs->lat; if (lat!=lng) { /*-- We are operating in angular coordinates */ d = sin(wcspos1[lat]*DEG)*sin(wcspos2[lat]*DEG) + cos(wcspos1[lat]*DEG)*cos(wcspos2[lat]*DEG) *cos((wcspos1[lng]-wcspos2[lng])*DEG); return d>-1.0? (d<1.0 ? acos(d)/DEG : 0.0) : 180.0; } else { d = 0.0; for (i=0; i<wcs->naxis; i++) { dp = wcspos1[i] - wcspos2[i]; d += dp*dp; } return sqrt(d); } } /******* wcs_scale *********************************************************** PROTO double wcs_scale(wcsstruct *wcs, double *pixpos) PURPOSE Compute the sky area equivalent to a local pixel. INPUT WCS structure, Pointer to the array of local raw coordinates, OUTPUT -. NOTES -. AUTHOR E. Bertin (IAP) VERSION 03/01/2008 ***/ double wcs_scale(wcsstruct *wcs, double *pixpos) { double wcspos[NAXIS], wcspos1[NAXIS], wcspos2[NAXIS], pixpos2[NAXIS]; double dpos1,dpos2; int lng, lat; if (raw_to_wcs(wcs, pixpos, wcspos)) return 0.0; lng = wcs->lng; lat = wcs->lat; if (lng == lat) { lng = 0; lat = 1; } /* Compute pixel scale */ pixpos2[lng] = pixpos[lng] + 1.0; pixpos2[lat] = pixpos[lat]; if (raw_to_wcs(wcs, pixpos2, wcspos1)) return 0.0; pixpos2[lng] -= 1.0; pixpos2[lat] += 1.0; if (raw_to_wcs(wcs, pixpos2, wcspos2)) return 0.0; dpos1 = wcspos1[lng]-wcspos[lng]; dpos2 = wcspos2[lng]-wcspos[lng]; if (wcs->lng!=wcs->lat) { if (dpos1>180.0) dpos1 -= 360.0; else if (dpos1<-180.0) dpos1 += 360.0; if (dpos2>180.0) dpos2 -= 360.0; else if (dpos2<-180.0) dpos2 += 360.0; return fabs((dpos1*(wcspos2[lat]-wcspos[lat]) -(wcspos1[lat]-wcspos[lat])*dpos2)*cos(wcspos[lat]*DEG)); } else return fabs((dpos1*(wcspos2[lat]-wcspos[lat]) -(wcspos1[lat]-wcspos[lat])*dpos2)); } /****** wcs jacobian ********************************************************* PROTO double wcs_jacobian(wcsstruct *wcs, double *pixpos, double *jacob) PURPOSE Compute the local Jacobian matrice of the astrometric deprojection. INPUT WCS structure, Pointer to the array of local raw coordinates, Pointer to the jacobian array (output). OUTPUT Determinant over spatial coordinates (=pixel area), or -1.0 if mapping was unsuccesful. NOTES Memory must have been allocated (naxis*naxis*sizeof(double)) for the Jacobian array. AUTHOR E. Bertin (IAP) VERSION 11/10/2007 ***/ double wcs_jacobian(wcsstruct *wcs, double *pixpos, double *jacob) { double pixpos0[NAXIS], wcspos0[NAXIS], wcspos[NAXIS], dpos; int i,j, lng,lat,naxis; lng = wcs->lng; lat = wcs->lat; naxis = wcs->naxis; for (i=0; i<naxis; i++) pixpos0[i] = pixpos[i]; if (raw_to_wcs(wcs, pixpos0, wcspos0) == RETURN_ERROR) return -1.0; for (i=0; i<naxis; i++) { pixpos0[i] += 1.0; if (raw_to_wcs(wcs, pixpos0, wcspos) == RETURN_ERROR) return -1.0; pixpos0[i] -= 1.0; for (j=0; j<naxis; j++) { dpos = wcspos[j]-wcspos0[j]; if (lng!=lat && j==lng) { if (dpos>180.0) dpos -= 360.0; else if (dpos<-180.0) dpos += 360.0; dpos *= cos(wcspos0[lat]*DEG); } jacob[j*naxis+i] = dpos; } } if (lng==lat) { lng = 0; lat = 1; } return fabs(jacob[lng+naxis*lng]*jacob[lat+naxis*lat] - jacob[lat+naxis*lng]*jacob[lng+naxis*lat]); } /******* wcs_chirality ******************************************************* PROTO int wcs_chirality(wcsstruct *wcs) PURPOSE Compute the chirality of a WCS projection. INPUT WCS structure. OUTPUT +1 if determinant of matrix is positive, -1 if negative, 0 if null. NOTES -. AUTHOR E. Bertin (IAP) VERSION 26/09/2006 ***/ int wcs_chirality(wcsstruct *wcs) { double a; int lng,lat, naxis; lng = wcs->lng; lat = wcs->lat; naxis = wcs->naxis; if (lng==lat && naxis>=2) { lng = 0; lat = 1; } a = wcs->cd[lng*naxis+lng]*wcs->cd[lat*naxis+lat] - wcs->cd[lng*naxis+lat]*wcs->cd[lat*naxis+lng]; return a>TINY? 1 : (a<-TINY? -1 : 0); } /****** precess_wcs ********************************************************** PROTO void precess_wcs(wcsstruct *wcs, double yearin, double yearout) PURPOSE Precess the content of a WCS structure according to the equinox. INPUT WCS structure, Input year, Output year. OUTPUT -. NOTES Epoch for coordinates should be J2000 (FK5 system). AUTHOR E. Bertin (IAP) VERSION 04/01/2008 ***/ void precess_wcs(wcsstruct *wcs, double yearin, double yearout) { double crval[NAXIS],a[NAXIS*NAXIS],b[NAXIS*NAXIS], *c,*at, val, cas, sas, angle, dalpha; int i,j,k, lng,lat, naxis; lng = wcs->lng; lat = wcs->lat; if (lat==lng || yearin==yearout) return; naxis = wcs->naxis; /* Precess to year out */ precess(yearin, wcs->crval[lng], wcs->crval[lat], yearout, &crval[lng], &crval[lat]); dalpha = (crval[lng] - wcs->crval[lng])*DEG; /* Compute difference angle with the north axis between start and end */ angle = (dalpha!=0.0 && (crval[lat] - wcs->crval[lat])*DEG != 0.0) ? 180.0 - (atan2(sin(dalpha), cos(crval[lat]*DEG)*tan(wcs->crval[lat]*DEG) - sin(crval[lat]*DEG)*cos(dalpha)) + atan2(sin(dalpha), cos(wcs->crval[lat]*DEG)*tan(crval[lat]*DEG) - sin(wcs->crval[lat]*DEG)*cos(dalpha)))/DEG : 0.0; /* A = C*B */ c = wcs->cd; /* The B matrix is made of 2 numbers */ cas = cos(angle*DEG); sas = sin(-angle*DEG); for (i=0; i<naxis; i++) b[i+i*naxis] = 1.0; b[lng+lng*naxis] = cas; b[lat+lng*naxis] = -sas; b[lng+lat*naxis] = sas; b[lat+lat*naxis] = cas; at = a; for (j=0; j<naxis; j++) for (i=0; i<naxis; i++) { val = 0.0; for (k=0; k<naxis; k++) val += c[k+j*naxis]*b[i+k*naxis]; *(at++) = val; } at = a; for (i=0; i<naxis*naxis; i++) *(c++) = *(at++); wcs->crval[lng] = crval[lng]; wcs->crval[lat] = crval[lat]; wcs->equinox = yearout; /* Initialize other WCS structures */ init_wcs(wcs); /* Find the range of coordinates */ range_wcs(wcs); /* Invert projection corrections */ invert_wcs(wcs); return; } /********************************* precess ***********************************/ /* precess equatorial coordinates according to the equinox (from Ephemerides du Bureau des Longitudes 1992). Epoch for coordinates should be J2000 (FK5 system). */ void precess(double yearin, double alphain, double deltain, double yearout, double *alphaout, double *deltaout) { double dzeta,theta,z, t1,t1t1, t2,t2t2,t2t2t2, cddsadz, cddcadz, cdd, sdd, adz, cdin,sdin,ct,st,caindz; alphain *= DEG; deltain *= DEG; t1 = (yearin - 2000.0)/1000.0; t2 = (yearout - yearin)/1000.0; t1t1 = t1*t1; t2t2t2 = (t2t2 = t2*t2)*t2; theta = (97171.735e-06 - 413.691e-06*t1 - 1.052e-06 * t1t1) * t2 + (-206.846e-06 - 1.052e-06*t1) * t2t2 - 202.812e-06 * t2t2t2; dzeta = (111808.609e-06 + 677.071e-06*t1 - 0.674e-06 * t1t1) * t2 + (146.356e-06 - 1.673e-06*t1) * t2t2 + 87.257e-06 * t2t2t2; z = (111808.609e-06 +677.071e-06*t1 - 0.674e-06 * t1t1) * t2 + (530.716e-06 + 0.320e-06*t1) * t2t2 + 88.251e-06 * t2t2t2; cddsadz = (cdin=cos(deltain)) * sin(alphain+dzeta); cddcadz = -(sdin=sin(deltain))*(st=sin(theta)) +cdin*(ct=cos(theta))*(caindz=cos(alphain+dzeta)); sdd = sdin*ct + cdin*st*caindz; cdd = cos(*deltaout = asin(sdd)); adz = asin(cddsadz/cdd); if (cddcadz<0.0) adz = PI - adz; if (adz<0.0) adz += 2.0*PI; adz += z; *alphaout = adz/DEG; *deltaout /= DEG; return; } /********************************* b2j ***********************************/ /* conver equatorial coordinates from equinox and epoch B1950 to equinox and epoch J2000 for extragalactic sources (from Aoki et al. 1983). */ void b2j(double yearobs, double alphain, double deltain, double *alphaout, double *deltaout) { int i,j; double a[3] = {-1.62557e-6, -0.31919e-6, -0.13843e-6}, ap[3] = {1.245e-3, -1.580e-3, -0.659e-3}, m[6][6] = { { 0.9999256782, -0.0111820611, -0.0048579477, 0.00000242395018, -0.00000002710663, -0.00000001177656}, { 0.0111820610, 0.9999374784, -0.0000271765, 0.00000002710663, 0.00000242397878, -0.00000000006587}, { 0.0048579479, -0.0000271474, 0.9999881997, 0.00000001177656, -0.00000000006582, 0.00000242410173}, {-0.000551, -0.238565, 0.435739, 0.99994704, -0.01118251, -0.00485767}, { 0.238514, -0.002662, -0.008541, 0.01118251, 0.99995883, -0.00002718}, {-0.435623, 0.012254, 0.002117, 0.00485767, -0.00002714, 1.00000956}}, a1[3], r[3], ro[3], r1[3], r2[3], v1[3], v[3]; double cai, sai, cdi, sdi, dotp, rmod, alpha, delta, t1 = (yearobs - 1950.0)/100.0; alphain *= PI/180.0; deltain *= PI/180.0; cai = cos(alphain); sai = sin(alphain); cdi = cos(deltain); sdi = sin(deltain); ro[0] = cdi*cai; ro[1] = cdi*sai; ro[2] = sdi; dotp = 0.0; for (i=0; i<3; i++) { a1[i] = a[i]+ap[i]*ARCSEC*t1; dotp += a1[i]*ro[i]; } for (i=0; i<3; i++) { r1[i] = ro[i] - a1[i] + dotp*ro[i]; r[i] = v[i] = v1[i] = 0.0; } for (j=0; j<6; j++) for (i=0; i<6; i++) { if (j<3) r[j] += m[j][i]*(i<3?r1[i]:v1[i-3]); else v[j-3] += m[j][i]*(i<3?r1[i]:v1[i-3]); } rmod = 0.0; for (i=0; i<3; i++) { r2[i] = r[i]+v[i]*ARCSEC*(t1-0.5); rmod += r2[i]*r2[i]; } rmod = sqrt(rmod); delta = asin(r2[2]/rmod); alpha = acos(r2[0]/cos(delta)/rmod); if (r2[1]<0) alpha = 2*PI - alpha; *alphaout = alpha*180.0/PI; *deltaout = delta*180.0/PI; return; } /*********************************** j2b *************************************/ /* conver equatorial coordinates from equinox and epoch J2000 to equinox and epoch B1950 for extragalactic sources (from Aoki et al. 1983, after inversion of their matrix and some custom arrangements). */ void j2b(double yearobs, double alphain, double deltain, double *alphaout, double *deltaout) { int i,j; double a[3] = {-1.62557e-6, -0.31919e-6, -0.13843e-6}, ap[3] = {1.245e-3, -1.580e-3, -0.659e-3}, m[6][6] = { { 0.9999256794678425, 0.01118148281196562, 0.004859003848996022, -2.423898417033081e-06,-2.710547600126671e-08,-1.177738063266745e-08}, {-0.01118148272969232, 0.9999374849247641, -2.717708936468247e-05, 2.710547578707874e-08,-2.423927042585208e-06, 6.588254898401055e-11}, {-0.00485900399622881, -2.715579322970546e-05, 0.999988194643078, 1.177738102358923e-08, 6.582788892816657e-11,-2.424049920613325e-06}, {-0.0005508458576414713, 0.2384844384742432, -0.4356144527773499, 0.9999043171308133, 0.01118145410120206, 0.004858518651645554}, {-0.2385354433560954, -0.002664266996872802, 0.01225282765749546, -0.01118145417187502, 0.9999161290795875, -2.717034576263522e-05}, { 0.4357269351676567, -0.008536768476441086, 0.002113420799663768, -0.004858518477064975, -2.715994547222661e-05, 0.9999668385070383}}, a1[3], r[3], ro[3], r1[3], r2[3], v1[3], v[3]; double cai, sai, cdi, sdi, dotp, rmod, alpha, delta, t1; /* Convert Julian years from J2000.0 to tropic centuries from B1950.0 */ t1 = ((yearobs - 2000.0) + (MJD2000 - MJD1950)/365.25)*JU2TROP/100.0; alphain *= DEG; deltain *= DEG; cai = cos(alphain); sai = sin(alphain); cdi = cos(deltain); sdi = sin(deltain); r[0] = cdi*cai; r[1] = cdi*sai; r[2] = sdi; for (i=0; i<3; i++) v[i] = r2[i] = v1[i] = 0.0; for (j=0; j<6; j++) for (i=0; i<6; i++) if (j<3) r2[j] += m[j][i]*(i<3?r[i]:v[i-3]); else v1[j-3] += m[j][i]*(i<3?r[i]:v[i-3]); for (i=0; i<3; i++) r1[i] = r2[i]+v1[i]*ARCSEC*t1; dotp = 0.0; for (i=0; i<3; i++) { a1[i] = a[i]+ap[i]*ARCSEC*t1; dotp += a1[i]*(r1[i]+a1[i]); } dotp = 2.0/(sqrt(1+4.0*dotp)+1.0); rmod = 0.0; for (i=0; i<3; i++) { ro[i] = dotp*(r1[i]+a1[i]); rmod += ro[i]*ro[i]; } rmod = sqrt(rmod); delta = asin(ro[2]/rmod); alpha = acos(ro[0]/cos(delta)/rmod); if (ro[1]<0) alpha = 2.0*PI - alpha; *alphaout = alpha/DEG; *deltaout = delta/DEG; return; } /******************************** degtosexal *********************************/ /* Convert degrees to hh mm ss.xx alpha coordinates. */ char *degtosexal(double alpha, char *str) { int hh, mm; double ss; if (alpha>=0.0 && alpha <360.0) { hh = (int)(alpha/15.0); mm = (int)(60.0*(alpha/15.0 - hh)); ss = 60.0*(60.0*(alpha/15.0 - hh) - mm); } else hh = mm = ss = 0.0; sprintf(str,"%02d:%02d:%05.2f", hh, mm, ss); return str; } /******************************** degtosexde *********************************/ /* Convert degrees to dd dm ds.x delta coordinates. */ char *degtosexde(double delta, char *str) { char sign; double ds; int dd, dm; sign = delta<0.0?'-':'+'; delta = fabs(delta); if (delta>=-90.0 && delta <=90.0) { dd = (int)delta; dm = (int)(60.0*(delta - dd)); ds = 60.0*fabs(60.0*(delta - dd) - dm); } else dd = dm = ds = 0.0; sprintf(str,"%c%02d:%02d:%04.1f", sign, dd, dm, ds); return str; } /******************************** sextodegal *********************************/ /* Convert hh mm ss.xxx alpha coordinates to degrees. */ double sextodegal(char *hms) { double val; char *ptr; val = atof(strtok_r(hms, ": \t", &ptr))*15.0; /* Hours */ val += atof(strtok_r(NULL, ": \t", &ptr))/4.0; /* Minutes */ val += atof(strtok_r(NULL, ": \t", &ptr))/240.0; /* Seconds */ return val; } /******************************** sextodegde *********************************/ /* Convert dd dm ds.xxx delta coordinates to degrees. */ double sextodegde(char *dms) { double val, sgn; char *str, *ptr; str = strtok_r(dms, ": \t", &ptr); sgn = (strchr(str, '-') ? -1.0:1.0); val = atof(dms); /* Degrees */ val += atof(strtok_r(NULL, ": \t", &ptr))*sgn/60.0; /* Minutes */ val += atof(strtok_r(NULL, ": \t", &ptr))*sgn/3600.0; /* Seconds */ return val; }
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