[fitswcs] unambiguous rotation angle

[Steve Allen]

On Wed 2002-01-16T18:16:37 -0500, Doug Mink hath writ:
> I spent the good part of a summer several years ago trying to get
> an unambiguous rotation angle out of a CD matrix and found that it
> is impossible analytically.  Separating the signed CDELTs out from
> the rotation makes some processing easier.

Please don't let this start a flamewar that gets into the way of
constructive WCS communications.

I suppose this is applies to a case where there is a 2-d image of the
sky that wants to be "unrotated".  We live in a 4-d universe, and one
person's space is another's time.

Such a 2-d image is really just a projection of that 4-d universe, and
its 2-d PC matrix is a projection from a 4-d PC matrix.  The metric
for the 4-d space is not Euclidean but Lorentz.  The process of
extracting a Euclidean angle from the Minkowski space will differ
between observers with different boosts, hence the differential
aberration of the field which we simplistically describe as a shear.

(This ignores the much larger terrestrial effect of differential
refraction.  All of this, by the way, might be significantly
clarified if concatenation of WCSs were allowed so that each step
implemented a particular bit of physics or optics.)

What definition of "unambiguous rotation angle" was intended?

--
Steve Allen          UCO/Lick Observatory       Santa Cruz, CA 95064
sla at ucolick.org      Voice: +1 831 459 3046     http://www.ucolick.org/~sla
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