Subject: Thoughts regarding CSC, QSC, and TSC Projections in WCS Document

From: Jeff Bloch <jbloch at alexis>
Date: Sat, 11 Nov 1995 22:20:03 -0700

From the comments I heard at the recent ADASS meeting, it seems that the 
WCS document may soon be ratified as a standard for representing most 
types of coordinate projections for FITS data.

I have a question about the software philosophical approach (I know that
FITS is NOT defined by software) in thinking about how the CSC, QSC, and
TSC projections fit into the overall scheme. For all of the other all-sky
systems in which the whole sky can be represented on a single flat plane,
the pixel coordinate in the single flat plane will yield the unique sky
coordinate (singularities and boundaries aside). CSC, QSC, and TSC
projections display the whole sky on six square "panes" arranged in a
sideways "T" for display purposes.  But they are stored in the FITS file
as a cube of NxNx6 pixel array elements, according to the description, and
requires an extra "CUBEFACE" axis description keyword.  For all other all
sky projections, a single image plane can be extracted from the FITS file,
and then the header keywords are used as per the WCS definitions to
convert pixel locations to coordinates and vice versa. For these CSC, QSC,
and TSC projections, the display software has to do something very
different: first pull out the six panes, display them as a sideways "T",
and then keep track of a new image coordinate system in this image in
which the display software has to determine which "pane" is being
considered before the WCS FITS header info can be used to do conversions. 

I think the issue that I am trying to get clarification on is that the
document describes how the QSC, CSC, and TSC all sky image projections
should be arranged on the page, but this arrangement does not correspond
to the storage convention of a stack of faces or an image cube, unlike 
all the other projections.

A situation which illustrates the need for clarification is if an all sky
map in these systems were stored in a FITS file on one flat plane like
they are displayed in the document. Does the current WCS definition allow
this alternative? I agree that four panes would be wasted but that is how
the image would be displayed on a flat screen or page, and in some
circumstances may make map manipulation and display more manageable. 

Any generic software that can deal with FITS file maps in any WCS 
standard coordinate system will have to face this issue.

I think that these projections are valuable for medium resolution sky 
surveys and allow for simple operations on square arrays for things like 
point source searches, which for projections like Hammer-Aitoff, are 
problematic near the map edges due to distortions.

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Jeffrey Bloch					Office:    (505) 665-2568
Astrophysics and Radiation Measurements Group	ALEXIS SOC:(505) 665-5975
Los Alamos National Laboratory			FAX:	   (505) 665-4414
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From: "Dr. Immanuel Freedman" <immanuel at mother.com>
Date: 13 Nov 1995 17:14:31 GMT

Jeffrey

Historically, COBE used the stack of 6 N*N cubefaces throughout the processing, but
a single FITS pane was often constructed for display or preliminary analysis.  The
only data now extant in this format - to the best of my knowledge - are COBE & EUVE.

I would be happy if the data could be stored as a COMPRESSED single pane, so that
the ease of point-based processing is maintained and their is no storage penalty.

The beauty of the QSC, CSC & TSC systems is that the Jacobian is constant almost
everywhere.  

Dr. Immanuel Freedmn
(916) 759 8673

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From: Jeff Bloch <jbloch at alexis>
Date: Mon, 13 Nov 1995 17:09:55 -0700

Per Dr. Freedman's comments and some more thinking on the subject, I 
wonder if a seventh "CUBEFACE" number can be defined in the WCS document 
which indicates that the FITS image contains the  QSC, CSC & TSC 
projections on a single flat plane in the sideways "T" configuration? I 
think that there is enough info in the rest of the header to still 
uniquely transform pixel locations to positions in that case. The 
interpreting software will have to be a little more clever in determining 
which face a particular pixel resides on before applying the WCS 
algorithms, but I think this is very managable.