[fitsbits] polar coordinates

[William Thompson]

We have a similar situation in solar astronomy.  One commonly used 
coordinate system expresses coordinates in elongation angle from Sun 
center, and the position angle counter-clockwise from the solar north 
pole.  To work this into the WCS, I had to map the elongation angle E 
into a latitude defined as E-90, i.e. make Sun-center the south pole of 
the system.  I chose the south pole instead of the north pole, so that 
the angle still increased in the usual fashion.  It's not an optimal 
solution, but it does make it WCS-compatible.

The part about taking the log of the polar angle should be fairly easy 
to incorporate into WCS.  This is just a new spherical projection, which 
would have to be properly defined and signaled with a unique projection 
code.  There is a precedent to adding new projections which are 
otherwise compatible with the WCS formalism.

Bill Thompson

On 12/11/2013 9:01 AM, David Berry wrote:
> On 11 December 2013 13:19, Walter Jaffe <jaffe at strw.leidenuniv.nl> wrote:
>> I find nothing in the FITS standard document about representing the sky
>> in polar coordinates.  One of my clients wishes to represent a
>> theoretical model of disk emission in polar logarithmic coordinates.
>> In other words CTYPE1 is LOG(RADIUS) (common log of
>> radius in degrees on the sky) and
>> CTYPE2 is PA (or POSITION ANGLE), (degrees E from North).
>>
>> Has this been discussed before?  Is there a straightforward
>> convention?
> I don't think you can do this in FITS-WCS. Firstly, I'm not aware of
> any way of specifying an axis as co-latitude rather than latitude, and
> secondly I'm not aware of any way of specifying an axis as log of a
> projected sky axis (maybe paper IV may have covered this but we do not
> yet have a published paper IV).
>
> Maybe this is a good example of why we need a more flexible WCS system...
>
> For what it's worth, you could do what you want using the AST library.
> But obviously, when exporting the data you would need to use
> AST-native encoding of the WCS rather than standard FITS-WCS encoding,
> so this would restrict the applications that could use the WCS.
>
> David
>
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