[fitsbits] polar coordinates

[Tom McGlynn]

Phil's take sounds right to me.... But use of the log is pretty weird. 
  The origin of the projection would represent the entire real circle 
at 1 degree radius.  It's unclear how one would represent data within 
the innermost 1 degree.  Including the real origin in the projection 
would be akin to including the poles in a Mercator projection: it 
would require an infinite map.

Seems like something like arcsinh(r) might lead to a better behaved 
projection.  That leaves the origin linear and has logarithmic 
behavior for large r.  You could probably do a pretty good 
approximation of that over a reasonable range using a standard ZPN 
projection with some universal set of coefficients.  I don't know if 
you can do that with log given its singularity at the origin.

    Regards,
    Tom McGlynn


Phil Hodge 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?
>
> Phil
>
> On 12/11/2013 08:19 AM, Walter Jaffe 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?
>>
>> Walter
>>
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