[fitsbits] polar coordinates

[David Berry]

On 12 December 2013 14:32, Tom McGlynn <Thomas.A.McGlynn at nasa.gov> wrote:
> 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


True - the log axis would need to be fudged in some way to avoid the
singularity. Maybe use log(r+1) instead of log(r).

But I still can't see how you avoid the problem that FITS-WCS always
represents latitude rather than co-latitude. How does an application
know that it must add an extra (90-latitude) transformation at the
end?

David