[fitsbits] polar coordinates

[David Berry]

Walter wanted polar coordinates, by which I presume he wants zero radial
distance at the centre. Something perhaps like the linked screen shots show
below - basic polar coords on the left and a (slightly) logarithmic radial
coord on the right. These were produced using AST, which can do this sort
of thing.

David
 logpolar.png<https://docs.google.com/file/d/0B4jEb03bhCeOZi15d1JHQmxhemc/edit?usp=drive_web>



On 12 December 2013 15:26, Tom McGlynn <Thomas.A.McGlynn at nasa.gov> wrote:

> 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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