STC position angles

[Steve Allen]

Section 4.5.2.5 introduces the notion of Position Angle.
This sets off alarm bells from my exposure to differential geometry.

Position angle needs a metric, and to be meaningful for angles that
metric probably has to be a Euclidean metric which is part of a
well-defined reference frame.

I think that there is no way to stress the following too strongly:
Pixel coordinates in a FITS array or table do not have a metric.
When creating a FITS array there may be effects such as binning,
non-adjacency, lack of orthogonality and other issues.

If FITS data have merely a "linear" WCS (and the default pixel
coordinates are the principal example of such) then there is no
metric.  In the absence of a well-defined reference frame there is no
a priori justification to presume that the axes are orthonormal, or
that the metric signature is Riemannian.

World Coordinates associated with FITS data may have a metric,
but that depends on whether or not those World Coordinates
are associated with a well-defined reference frame.

With the CCD mosaic on the HIRES instrument at Keck Observatory it is
routine to read out the detectors binned 3 x 1.  (Even if we were
reading out 1 x 1, it would be incorrect to presume that the pixels
were square.)  We have already faced issues of this sort regarding the
meaning of world coordinates and angles in the ds9 image viewer.
As a result we have found that the meaning of a position angle of an
ellipse in ds9 is not clearly defined.

For that reason I wonder whether, for the purposes of interpretation
by machines, it might be better to encode the PositionAngle
information as a coordinate pair along the two axes which are relevant
to the coordinate system in question.

In any case I think the notion of position angle measured from
"X" toward "Y" should not be permitted unless it can be
made absolutely clear that it is only permissible in cases where
X and Y have a clearly-defined Euclidean metric.

--
Steve Allen                 <sla at ucolick.org>                   WGS-84 (GPS)
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