WCS questions

[Mark Calabretta]

On Mon 1996/12/09 21:25:56 GMT, William Thompson wrote
in a message to: fitsbits at fits.cv.nrao.edu

>Good luck.  I'm personally not convinced that the WCS will ever be compatible
>with datasets that are not in some way related to the celestial sphere.  It's
>just a completely different mindset.  For example, the response from Mark
>Calabretta

If you're saying that WCS doesn't account for spherical deformations such as
oblateness then I agree, it wasn't designed for that purpose (although you
could apply a first-order approximation for oblateness through the PC matrix).

Otherwise, the difference between mapping a sphere from the inside (i.e. the
celestial sphere) and mapping it from the outside (e.g. planetary cartography)
is essentially just that of changing the sign of the native longitude.

The following should work for a near-sided azimuthal perspective projection:

   1) Choose the PC matrix to give (x',y') however you want it, with
      correction for rotation, skewness and unequal scaling.
   2) Set the sign of CDELT1 to flip the coordinate system (seen from outside
      rather than inside) and also scale (x',y') to (x,y) in "degrees".
   3) Use AZP with mu < -1 for a near-sided projection.

If you want to transform pixel coordinates to (x',y') then just apply the PC
matrix to (i,j).  If you want (PLON,PLAT) then apply the whole WCS algorithm.

>still seems to me to be saying that the WCS folks expect to be able to project
>the data onto the sky.  Otherwise, what is meant here by degrees?

The scaling of (x,y) to "degrees" means that (PLON-PLON0, PLAT-PLAT0) is
approximately equal to (x-x0, y-y0) for small deviations from the field centre
(for default LONGPOLE).  This AIPS WCS convention is retained for backwards
compatibility.

>The idea of defining the coordinates to be in units of the solar radius seems
>like a good one, at least at first blush.  There are some questions that do
>come to mind:

The main problem I see is that the limb in a near-sided perspective projection
may fall short of a hemisphere.  You might get into trouble comparing (x',y')
coordinates of two AZP projections with differing mu if mu is not large enough
(e.g. spacecraft-generated images).  In this case you really would have to
compare planetary lng/lat.

Mark Calabretta
ATNF