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/* manage WCS headers both classic and PLAT scale variety.
*
* N.B. the FITS standard says the center of the first pixel in the file is
* at pixel coordinates [1,1]. The functions here-in expect the caller to
* refer to this pixel as [0,0].
*/
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <string.h>
#include "astro.h"
#include "ip.h"
static int dsswcs (FImage *fip);
static int dssxy2RADec (FImage *fip, double X, double Y, double *rap,
double *decp);
static int worldpos (double xpix, double ypix, double xref, double yref,
double xrefpix, double yrefpix, double xinc, double yinc, double rot,
char *type, double *xpos, double *ypos);
static int xypix (double xpos, double ypos, double xref, double yref,
double xrefpix, double yrefpix, double xinc, double yinc, double rot,
char *type, double *xpix, double *ypix);
static int setWCScache (FImage *fip);
/* given a 0-based x/y location over the given image, return ra and dec, rads.
* we require the C* fields in the header.
* return 0 if all ok, else -1.
*/
int
xy2RADec (fip, x, y, rap, decp)
FImage *fip;
double x, y;
double *rap, *decp;
{
double xpos; /* x (RA) coordinate (deg) */
double ypos; /* y (dec) coordinate (deg) */
if (setWCScache (fip) < 0)
return (-1);
/* CRPIXn assume pixels are 1-based */
if (worldpos(x+1, y+1, fip->xref, fip->yref, fip->xrefpix, fip->yrefpix,
fip->xinc, fip->yinc, fip->rot, fip->type, &xpos, &ypos) < 0)
return (-1);
*rap = degrad (xpos);
range (rap, 2*PI);
*decp = degrad (ypos);
return (0);
}
/* given an ra and dec, rads, return 0-based x/y location over the given image.
* we require the C* fields in the header.
* return 0 if all ok, else -1.
*/
int
RADec2xy (fip, ra, dec, xp, yp)
FImage *fip;
double ra, dec;
double *xp, *yp;
{
double xpos; /* x (RA) coordinate (deg) */
double ypos; /* y (dec) coordinate (deg) */
if (setWCScache (fip) < 0)
return (-1);
xpos = raddeg(ra);
ypos = raddeg(dec);
if (xypix(xpos, ypos, fip->xref, fip->yref, fip->xrefpix, fip->yrefpix,
fip->xinc, fip->yinc, fip->rot, fip->type, xp, yp) < 0)
return (-1);
/* CRPIXn assume pixels are 1-based */
*xp -= 1;
*yp -= 1;
return (0);
}
/* given a DSS image, build the WCS headers.
* return 0 if ok, else return -1.
*/
static int
dsswcs (fip)
FImage *fip;
{
double a0, d0, a1, d1;
double px, py;
double pltscale;
double rot;
/* find RA and Dec at the center of our image */
if (dssxy2RADec (fip, fip->sw/2.0, fip->sh/2.0, &a0, &d0) < 0)
return (-1);
/* use center as reference */
setRealFITS (fip, "CRPIX1", fip->sw/2.0, 10, NULL);
setRealFITS (fip, "CRPIX2", fip->sh/2.0, 10, NULL);
setRealFITS (fip, "CRVAL1", raddeg(a0), 10, NULL);
setRealFITS (fip, "CRVAL2", raddeg(d0), 10, NULL);
/* set scale */
if (getRealFITS (fip, "PLTSCALE", &pltscale) < 0
|| getRealFITS (fip, "XPIXELSZ", &px) < 0
|| getRealFITS (fip, "YPIXELSZ", &py) < 0) {
return(-1);
}
setRealFITS (fip, "CDELT1", -pltscale*px/3600000.0, 10, NULL);
setRealFITS (fip, "CDELT2", pltscale*py/3600000.0, 10, NULL);
/* coord sys */
setStringFITS (fip, "CTYPE1", "RA---TAN", NULL);
setStringFITS (fip, "CTYPE2", "DEC--TAN", NULL);
/* find rotation CW to make N up.
* TODO: ugly! gotta better way??
*/
if (dssxy2RADec (fip, fip->sw/2.0, 0.0, &a1, &d1) < 0)
return (-1);
if (d0 < 0) {
double A = a0-a1;
double b = PI/2+d0;
double c = PI/2+d1;
rot = raddeg(atan2(c*sin(A), c*cos(A)-b)) - 180;
} else {
double A = a1-a0;
double b = PI/2-d0;
double c = PI/2-d1;
rot = raddeg(atan2(c*sin(A), c*cos(A)-b));
}
setRealFITS (fip, "CROTA2", rot, 10, "Derived from DSS");
return (0);
}
/* convert pixel coords to ra/dec, using DSS header fields.
* this is all based on the equations on pages 14-16 of The Digitized Sky
* Survey release notes.
* return 0 if ok, else -1.
*/
static int
dssxy2RADec (fip, X, Y, rap, decp)
FImage *fip;
double X, Y;
double *rap, *decp;
{
char buf[128];
double cnpix1, cnpix2;
double a[14], b[14];
double rh, rm, rs;
double dd, dm, ds;
double xc, px, yc, py;
double x, y, x2y2;
double pltscale;
double rac, decc, ra;
double xi, nu;
double tandecc;
int i;
if (getRealFITS (fip, "CNPIX1", &cnpix1) < 0
|| getRealFITS (fip, "CNPIX2", &cnpix2) < 0) {
return(-1);
}
if (getRealFITS (fip, "PLTSCALE", &pltscale) < 0
|| getRealFITS (fip, "PPO3", &xc) < 0
|| getRealFITS (fip, "PPO6", &yc) < 0
|| getRealFITS (fip, "XPIXELSZ", &px) < 0
|| getRealFITS (fip, "YPIXELSZ", &py) < 0) {
return(-1);
}
X += cnpix1 - 0.5;
Y += cnpix2 - 0.5;
x = (xc - px*X)/1000.0;
y = (py*Y - yc)/1000.0;
for (i = 1; i <= 13; i++) {
char ax[32], ay[32];
(void) sprintf (ax, "AMDX%d", i);
(void) sprintf (ay, "AMDY%d", i);
if (getRealFITS (fip, ax, &a[i]) < 0 ||
getRealFITS (fip, ay, &b[i]) < 0) {
return (-1);
}
}
x2y2 = x*x + y*y;
xi = a[1]*x + a[2]*y + a[3] + a[4]*x*x + a[5]*x*y + a[6]*y*y
+ a[7]*x2y2 + a[8]*x*x*x + a[9]*x*x*y + a[10]*x*y*y
+ a[11]*y*y*y + a[12]*x*x2y2 + a[13]*x*x2y2*x2y2;
xi = degrad(xi/3600.0);
nu = b[1]*y + b[2]*x + b[3] + b[4]*y*y + b[5]*x*y + b[6]*x*x
+ b[7]*x2y2 + b[8]*y*y*y + b[9]*x*y*y + b[10]*x*x*y
+ b[11]*x*x*x + b[12]*y*x2y2 + b[13]*y*x2y2*x2y2;
nu = degrad(nu/3600.0);
if (getRealFITS (fip, "PLTRAH", &rh) < 0
|| getRealFITS (fip, "PLTRAM", &rm) < 0
|| getRealFITS (fip, "PLTRAS", &rs) < 0
|| getRealFITS (fip, "PLTDECD", &dd) < 0
|| getRealFITS (fip, "PLTDECM", &dm) < 0
|| getRealFITS (fip, "PLTDECS", &ds) < 0
|| getStringFITS (fip, "PLTDECSN", buf) < 0) {
return(-1);
}
rac = rs/3600.0 + rm/60.0 + rh;
rac = hrrad(rac);
decc = ds/3600.0 + dm/60.0 + dd;
if (buf[0] == '-')
decc = -decc;
decc = degrad(decc);
tandecc = tan(decc);
ra = atan2 (xi/cos(decc), 1.0-nu*tandecc) + rac;
if (ra < 0)
ra += 2*PI;
*rap = ra;
*decp = atan (((nu + tandecc)*cos(ra-rac))/(1.0 - nu*tandecc));
return (0);
}
/* load the WCS cache if not already set up.
* return 0 if ok, else -1
*/
static int
setWCScache (fip)
FImage *fip;
{
FITSRow typestr;
double tmp;
if (fip->wcsset)
return (0);
/* if have DSS convert to WCS so we know we can go both ways.
* only dss RD->xy I can find solves from xy->RD YUK!
*/
if (getRealFITS (fip, "PLTRAH", &tmp) == 0) {
if (dsswcs (fip) < 0)
return (-1);
}
if (getRealFITS (fip, "CRVAL1", &fip->xref) < 0) return (-1);
if (getRealFITS (fip, "CRVAL2", &fip->yref) < 0) return (-1);
if (getRealFITS (fip, "CRPIX1", &fip->xrefpix) < 0) return (-1);
if (getRealFITS (fip, "CRPIX2", &fip->yrefpix) < 0) return (-1);
if (getRealFITS (fip, "CDELT1", &fip->xinc) < 0) return (-1);
if (getRealFITS (fip, "CDELT2", &fip->yinc) < 0) return (-1);
if (getRealFITS (fip, "CROTA2", &fip->rot) < 0) return (-1);
if (getStringFITS (fip, "CTYPE1", typestr) < 0) return (-1);
if (strncmp (typestr, "RA--", 4)) return (-1);
strncpy (fip->type, typestr+4, sizeof(fip->type)-1);
fip->wcsset = 1;
return (0);
}
/* 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 <bcotton@gorilla.cv.nrao.edu>,
who described it as a "..more or less.. exact translation from the
AIPSish..". Changes were made by Don Wells <dwells@nrao.edu>
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().
*/
static int worldpos(xpix, ypix, xref, yref, xrefpix, yrefpix, xinc, yinc, rot,
type, xpos, ypos)
double xpix;
double ypix;
double xref;
double yref;
double xrefpix;
double yrefpix;
double xinc;
double yinc;
double rot;
char *type;
double *xpos;
double *ypos;
/*-----------------------------------------------------------------------*/
/* routine to determine accurate position for pixel coordinates */
/* returns 0 if successful otherwise: */
/* 1 = angle too large for projection; */
/* does: -SIN, -TAN, -ARC, -NCP, -GLS, -MER, -AIT projections */
/* anything else is linear */
/* 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, tmp;
double sins, coss, dect=0, rat=0, 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;
static char ctypes[8][5] ={"-SIN","-TAN","-ARC","-NCP", "-GLS", "-MER",
"-AIT", "-STG"};
/* 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)
{tmp = dx * cosr - dy * sinr;
dy = dy * cosr + dx * sinr;
dx = tmp;}
/* find type */
itype = 0; /* default type is linear */
for (i=0;i<8;i++) if (!strncmp(type, ctypes[i], 4)) itype = i+1;
/* 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;
decout = 0.0;
raout = 0.0;
cos0 = cos(dec0);
sin0 = sin(dec0);
/* process by case */
switch (itype) {
case 0: /* linear */
rat = ra0 + l;
dect = dec0 + m;
break;
case 1: /* -SIN sin*/
if (sins>1.0) return 1;
coss = sqrt (1.0 - sins);
dt = sin0 * coss + cos0 * m;
if ((dt>1.0) || (dt<-1.0)) return 1;
dect = asin (dt);
rat = cos0 * coss - sin0 * m;
if ((rat==0.0) && (l==0.0)) return 1;
rat = atan2 (l, rat) + ra0;
break;
case 2: /* -TAN tan */
if (sins>1.0) return 1;
dect = cos0 - m * sin0;
if (dect==0.0) return 1;
rat = ra0 + atan2 (l, dect);
dect = atan (cos(rat-ra0) * (m * cos0 + sin0) / dect);
break;
case 3: /* -ARC Arc*/
if (sins>=twopi*twopi/4.0) return 1;
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 1;
dect = asin (dt);
da = coss - dt * sin0;
dt = l * sins * cos0;
if ((da==0.0) && (dt==0.0)) return 1;
rat = ra0 + atan2 (dt, da);
break;
case 4: /* -NCP North celestial pole*/
dect = cos0 - m * sin0;
if (dect==0.0) return 1;
rat = ra0 + atan2 (l, dect);
dt = cos (rat-ra0);
if (dt==0.0) return 1;
dect = dect / dt;
if ((dect>1.0) || (dect<-1.0)) return 1;
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 1;
coss = cos (dect);
if (fabs(l)>twopi*coss/2.0) return 1;
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 1; /* 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 1;
dz = 0.5 * sqrt (dz);
dd = (m+geo3) * dz / geo2;
if (fabs(dd)>1.0) return 1;
dd = asin (dd);
if (fabs(cos(dd))<deps) return 1;
da = l * dz / (2.0 * geo1 * cos(dd));
if (fabs(da)>1.0) return 1;
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 1;
dect = dz * sin0 + m * cos0 * (1.0+dz) / 2.0;
if (fabs(dect)>1.0) return 1;
dect = asin (dect);
rat = cos(dect);
if (fabs(rat)<deps) return 1;
rat = l * (1.0+dz) / (2.0 * rat);
if (fabs(rat)>1.0) return 1;
rat = asin (rat);
mg = 1.0 + sin(dect) * sin0 + cos(dect) * cos0 * cos(rat);
if (fabs(mg)<deps) return 1;
mg = 2.0 * (sin(dect) * cos0 - cos(dect) * sin0 * cos(rat)) / mg;
if (fabs(mg-m)>deps) rat = twopi/2.0 - rat;
rat = ra0 + rat;
break;
}
/* 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 0;
} /* End of worldpos */
static int xypix(xpos, ypos, xref, yref, xrefpix, yrefpix, xinc, yinc, rot,
type, xpix, ypix)
double xpos;
double ypos;
double xref;
double yref;
double xrefpix;
double yrefpix;
double xinc;
double yinc;
double rot;
char *type;
double *xpix;
double *ypix;
/*-----------------------------------------------------------------------*/
/* 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 */
/* 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=0, geo1, geo2, geo3, sinr, cosr;
double cond2r=1.745329252e-2, deps=1.0e-5, twopi=6.28318530717959;
int i, itype;
static char ctypes[8][5] ={"-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 2;}
/* convert to pixels */
*xpix = dx / xinc + xrefpix;
*ypix = dy / yinc + yrefpix;
/* find type */
itype = 0; /* default type is linear */
for (i=0;i<8;i++) if (!strncmp(type, ctypes[i], 4)) itype = i+1;
if (itype==0) return 0; /* 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);
l = sin(ra-ra0) * coss;
sint = sins * sin(dec0) + coss * cos(dec0) * cos(ra-ra0);
/* process by case */
switch (itype) {
case 1: /* -SIN sin*/
if (sint<0.0) return 1;
m = sins * cos(dec0) - coss * sin(dec0) * cos(ra-ra0);
break;
case 2: /* -TAN tan */
if (sint<=0.0) return 1;
m = sins * sin(dec0) + coss * cos(dec0) * cos(ra-ra0);
l = l / m;
m = (sins * cos(dec0) - coss * sin(dec0) * cos(ra-ra0)) / m;
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 1; /* 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 1;
if (fabs(dec0)>twopi/4.0) return 1;
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 (dt<deps) return 2;
m = geo2 * log (dt) - geo3;
break;
case 7: /* -AIT Aitoff*/
l = 0.0;
m = 0.0;
da = (ra - ra0) / 2.0;
if (fabs(da)>twopi/4.0) return 1;
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)<deps) return 3;
l = 2.0 * geo1 * cos(dec) * sin(da) / dt;
m = geo2 * sin(dec) / dt - geo3;
break;
case 8: /* -STG Sterographic*/
da = ra - ra0;
if (fabs(dec)>twopi/4.0) return 1;
dd = 1.0 + sins * sin(dec0) + coss * cos(dec0) * cos(da);
if (fabs(dd)<deps) return 1;
dd = 2.0 / dd;
l = l * dd;
m = dd * (sins * cos(dec0) - coss * sin(dec0) * cos(da));
break;
} /* end of itype switch */
/* back to degrees */
dx = l / cond2r;
dy = m / cond2r;
/* Correct for rotation */
dz = dx*cosr + dy*sinr;
dy = dy*cosr - dx*sinr;
dx = dz;
/* convert to pixels */
*xpix = dx / xinc + xrefpix;
*ypix = dy / yinc + yrefpix;
return 0;
} /* end xypix */
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