[fitsbits] CDELTn

[Francois Ochsenbein]

Sorry Mark, but my question was NOT related to WCS... 

It's just a matrix, cube, hypercube or whatever n-dimensional hyper-rectangle.
And on my side I'm perfectly happy with whatever convention for denegerate
axes -- I was just troubled by the fact that fv refuses a FITS file
having a CDELTi = 0 for these degenerate axes, and was wondering why.

--Francois

>
>
>On Wed 2007/09/19 10:30:04 +0200, Francois Ochsenbein wrote
>in a message to: fitsbits at nrao.edu
>
>>... I always understood that the coordinate value is
>>    CRVALn + (i-CRPIXn)*CDELTn
>>
>>which simply means that the value of the coordinate along this axis
>>is constant and equal to CRVALn, which seems to me perfectly correct
>>(a 1-point dimension is by definition a constant).
>
>Francois,
>
>It's perfectly illegal, Sect. 2.1.2 of WCS Paper I leaves no room for
>doubt:
>
>  "The PCi_j matrix must not be singular; it must have an inverse.
>   Furthermore, all CDELTi must be non-zero.  In other words,
>   invertibility means that transformations which project from an
>   initial coordinate system of dimensionality WCSAXES to a world
>   coordinate syetem of dimensionality less than WCSAXES are
>   forbidden."
>
>Why bother spending 10 years agreeing on a standard if people feel they
>can flout it in such a trivial and pointless way?  To reiterate:
>
>1) The coordinate transformation must be invertible.  In particular,
>   CRVALia must be non-zero and the PCi_ja (or CDi_ja) matrix must not
>   be singular.
>
>2) There is no connection between the image WCS and NAXISn - the WCS
>   doesn't know and doesn't care whether the image has degenerate axes.
>   NAXISn does not figure in the coordinate transformation equations,
>   not even for conventional types (COMPLEX, STOKES, CUBEFACE), and is
>   rarely even mentioned in any of the WCS papers.
>
>3) If CDELTia isn't meaningful, as for a degenerate axis, then simply
>   omit it.  It defaults to 1.0.
>
>Mark Calabretta
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