[fitsbits] CDELTn

[Doug Tody]

Hi Mark -

I agree that this can be a useful approach when one wants to implement
a higher dimensional model which can handle lower dimensional cases as a
limiting case.  The problem comes when naive 2D programs encounter higher
dimensional "image" with degenerate axes.  The solution (which I think we
actually adopted) was to separate the image NDIM and WCSDIM, so that the
WCS dimensionality could exceed the actual sampled image dimensionality.

Getting back to CDELT, I agree it should be an error if it is zero
(default should be 1.0), however this is tied to the sampled image matrix
(NDIM) so it is at least partially decoupled from the WCS.

In general, numeric FITS keywords should probably default to zero, but
specific data models such as CD and CDELT can override this, and specify
that the default is something else, such as the unitary matrix or CDELT=1.

(Not sure what the point is in discussing this now since it is in the
standards, but this is some of the thinking way back when).

	- Doug



On Fri, 21 Sep 2007, Mark Calabretta wrote:

>
> On Thu 2007/09/20 20:42:46 CST, Doug Tody wrote
> in a message to: Thierry Forveille <Thierry.Forveille at ujf-grenoble.fr>
> and copied to: fitsbits at donar.cv.nrao.edu,
>       "LC's NoSpam Newsreading account" <nospam at mi.iasf.cnr.it>
>
> >The degenerate axis view might make sense for a very few things which
> >are often sampled (polarization, frequency/velocity, possibly time),
> >where a common model can be used whether or not a given physical
> >"axis" is sampled (Characterization in VO is similar).  But in the
> >general case, applied to any "image" attribute, this is a poor model.
>
> I agree that it's overkill to use a degenerate axis when a header
> keyword could do the job (except that no keywords are currently
> defined for that job).
>
> However, the real power and importance of degenerate axes is as
> illustrated in the header construction example given in Sect. 7.4.3 of
> WCS Paper II.  This shows how a degenerate axis may be used to define
> varying (ra,dec) along the length of a long-slit spectrograph.
>
> This clever idiom predates the WCS papers by a long way - originally it
> was based on CROTAn.  However, it was never formally documented and so
> apparently never caught on outside the radio community.  Paper II now
> firmly establishes it as the way that such coordinate problems are
> handled.
>
> Cheers, Mark
>
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