[fitsbits] polar coordinates

[Tom McGlynn]

I guess I'm a little unclear on the actual requirement here.  Are we 
trying to represent the plane of some theoretical disk, or are we 
viewing a disk from some other location and looking at its emission? 
Walter's original message suggested the second since the radius had 
units of degrees from the center of the disk.  If we wanted the first 
presumably the units of radius should be some physical dimension.

The former requires some tweaks to represent in standard WCS 
projections since they implicitly assume that we are projecting from 
the sphere to a plane, whereas this would be a plane->plane 
projection.  However we can just say that we are far away from the 
disk such that it subtends a small angle in the sky and is 
perpendicular to our line of sight.  Since the maximum angular radius 
is small (as small as we like) we can use any of the azimuthal 
projections using the center of the disk as our reference pixel. 
There will be a linear transformation of the angular radius to the 
physical radius.

If we are modelling the emission of the disk as seen from some finite 
radius, then again we can set the CRVALn to the center of the disk and 
everything falls out pretty straightfowardly.  Now the ARC projection 
is the one that linearly renders the angular radius (by definition) 
but other projections could be used as appropriate.  [If we are not on 
the axis perpendicular to the center of the disk, then it may be more 
convenient to choose the closest point of the disk as the coordinate 
origin rather than the center of the disk.]

In the first case we'd have NAXISn x | CDELTn | << 1 whereas in the 
second case we'd have NAXISn x | CDELT n | ~ 1 since we presume the 
disk is subtending a significant fraction of the sky.  The CRPIX's 
would be NAXISn/2 (assuming we are trying to cover the disk) and 
CRVALn=(0,90).  I don't know if LON/LAT--ARC is legal and if not I 
guess one has to use RA/DEC[-]--ARC.

	Regards,
	Tom

David Berry wrote:
> On 12 December 2013 13:48, Phil Hodge <hodge at stsci.edu> wrote:
>> Walter,
>>
>> Aside from the log, isn't this the ARC projection with CRVAL1 and CRVAL2
>> set to the right ascension and declination at the center of the
>> (theoretical) disk?
>
> I'm not sure how that would work. Can you give an example? Typing the following:
>
> NAXIS1  = 1000
> NAXIS2  = 1000
> CTYPE1  = 'RA---ARC'
> CTYPE2  = 'DEC--ARC'
> CRPIX1  = 500
> CRPIX2  = 500
> CDELT1  = -0.001
> CDELT2  = 0.001
> CRVAL1  = 45.0
> CRVAL2  = 45.0
>
> into the "Headers" box at
> http://starlink.jach.hawaii.edu/cgi-bin/ast/fits-plotter, putting
> "grid=1" into the "Plot settings" box, and pressing the "Submit"
> button just produces a roughly recti-linear grid as you might expect.
>
> I'm not sure how using an ARC projection gets round the issue that
> FITS-WCS can only describe latitude, not co-latitude.
>
> David
>
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