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);
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
worldpos determines accurate position for pixel coordinates. It returns
0 if successful, 1 if the angle too large for projection.
Input: xpix x pixel number (RA or long without rotation) ypiy y pixel number (dec or lat without rotation) xref x reference coordinate value (deg) yref y reference coordinate value (deg) xrefpix x reference pixel yrefpix y reference pixel xinc x coordinate increment (deg) yinc y coordinate increment (deg) rot rotation (deg) (from N through E) *type projection type code e.g. "-SIN" Valid are: -SIN, -TAN, -ARC, -NCP, -GLS, -MER, -AIT projections, anything else is linear. Output: *xpos x (RA) coordinate (deg) *ypos y (dec) coordinate (deg)
xypix determines accurate pixel coordinates for an RA and Dec. It returns 0 if successful otherwise: 1 if the angle too large for projection; 2 if bad values Input: xpos x (RA) coordinate (deg) ypos y (dec) coordinate (deg) xref x reference coordinate value (deg) yref y reference coordinate value (deg) xrefpix x reference pixel yrefpix y reference pixel xinc x coordinate increment (deg) yinc y coordinate increment (deg) rot rotation (deg) (from N through E) *type projection type code e.g. "-SIN"; Valid are: -SIN, -TAN, -ARC, -NCP, -GLS, -MER, -AIT projections, anything else is linear. Output: *xpix x pixel number (RA or long without rotation) *ypiy y pixel number (dec or lat without rotation)
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
0 no error
-1
-2
Coordinate SystemsThe following table is a list of the currently described
coordinate systems. The ones implements in these routines are marked with
a *.
FITS Number Name Comments
code code
---- ------ ----------------------- -----------------------------------
DEF 0 Default = Cartesian
AZP 1 Zenithal perspective projp1 required
TAN* 2 Gnomic AZP w/ projp1 = 0
SIN* 3 Orthographic AZP w/ projp1 = Infinity (>10^14)
STG* 4 Stereographic AZP w/ projp1 = 1
ARC* 5 Zenithal Equidistant
ZPN 6 Zenithal polynomial prop1-projp9 required, useless
ZEA 7 Zenithal equal area
AIR 8 Airy projp1 required
CYP 9 Cylindrical perspective projp1 and projp2 required
CAR 10 Cartesian
MER* 11 Mercator
CEA 12 Cylindrical equal area projp1 required
COP 13 Conical perspective projp1 and projp2 required
COD 14 Conical equidistant projp1 and projp2 required
COE 15 Conical equal area projp1 and projp2 required
COO 16 Conical orthomorphic projp1 and projp2 required
BON 17 Bonne’s equal area projp1 required
PCO 18 Polyconic
GLS* 19 Sinusoidal
PAR 20 Parabolic
AIT* 21 Hammer-Aitoff
MOL 22 Mollweide
CSC 23 Cobe Quadrilateralized convergence of inverse is poor
Spherical Cube
QSC 24 Quadrilateralized
Spherical Cube
TSC 25 Tangential Spherical Cube
Copyright
Copyright (C) 1994
Associated Universities, Inc. Washington DC, 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
Mark Calabretta’s WCSLIB: http://www.atnf.csiro.au/people/mcalabre/WCS/index.html
Jessica Mink’s WCSTOOLS: http://tdc-www.harvard.edu/wcstools/
13-oct-94 doc written PJT 2-sep-2021 note that wcstools also keeps a copy PJT