[fitsbits] CDELTn

[Mark Calabretta]

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