[fitsbits] WCS coordinates for North/South Pole composite image?

[Mark Calabretta]

On Thu 2003/03/13 14:28:20 CDT, Wayne Landsman wrote
in a message to: fitsbits at donar.cv.nrao.edu

>I have an image displaying the entire sky in a Zenithal Equal Area (ZEA) 
>projection, with the left side of the image centered on the North pole, 
>and the right side centered on the South pole.     The situation is very 
>similar to that described in Section 7.4.2 of Calabretta & Greisen 
>(2002, A&A, 395, 1077) who derive the WCS info for the North pole image 
>and the (different) WCS info for the South pole image.     However, I 
>want to view the two poles side by side -- is there any way to write WCS 
>coordinates that would work for the composite image?

Dear Wayne,

If I understand your situation correctly, you have a circle on the left
that covers the northern hemisphere, and a separate one adjacent to it on
the right that covers the southern hemisphere.

Essentially you have two separate projections.  However, you could define
a single image composed of your separate hemispheres and create a dual
coordinate description for it.  The first WCS would be centred on the
pixel which corresponds to the north pole, and the second on the south
pole.

Coordinates returned from the first WCS would only apply to the northern
hemisphere, and vice versa.  There will be points in the image which are
"outside the universe" for the first WCS, and vice versa.  Probably more
problematic, though, is that there will be points on the image that the
first WCS will return apparently legitimate, but spurious coordinates
for, and vice versa.  These would be readily distinguishable to you, as
a human, but general WCS interpreting software could not be expected
do the right thing without special training.  For example, a viewer which
displays coordinates at the cursor position would not know when to cut
over from the first WCS to the second.  However, it should be relatively
easy to adapt such a viewer to your dual WCS; in this case it would
probably be easiest for the viewer to display both coordinates and let
you decide.  Solutions for other applications may not be so simple.

Mark Calabretta
ATNF