Subject: World Coordinates Proposal

From: egreisen at primate.CV.NRAO.EDU (Eric Greisen)
Date: Sat, 7 Nov 92 16:47:56 EST

The current tempest over this question illustrates why the initial design of
FITS deliberately remained silent on coordinates questions.  It is my hope
that I can codify and clarify the coordinates that have been in wide use in the
FITS community and produce a proposal.  In the mean time, I feel I am forced
to address this question:

Steve Allen writes

>>The question boils down to another question:  Are FITS images representing
>>binned data or sampled data?  How do you tell?

Robert Hanisch replies:

> This issue was discussed during the meeting in Boston, and it was agreed
> that the proposal has to be revised to indicate the conventions being
> used.  The consensus was that for FITS, pixel (1,1) is the pixel in the lower
> left-hand corner of an image and that for the purpose of the WCS, this
> pixel represents data from 0.5 to 1.5 in pixel coordinates.  This clarification
> will be added to the proposal.

Let me add my agreement.  There is only one unique location in an N-dimensional
voxel, its center in each of the N dimensions.  This has always been the intent
of CRPIXmmm in the FITS design.  I do not understand how that decides one way or
the other whether the data are sampled or binned - that is a separate question
with an instrument-dependent answer.

I disagree that FITS pixel (1,1) represents the "lower left-hand" of anything.
(1,1) is the first pixel value in a Fortran-array sense.  Where it is placed
in a display depends on many things such as the sign of the coordinate
increments and the like.  If you send AIPS an image with a negative increment
on the declination axis, it will display the image with (1,1) at the upper
left corner, for example.

Steve Allen writes

> This is significantly different from the common practice in computer graphics
> (CG) where the first pixel in an array is the pixel with
> the integer tag 0 which has floating point boundaries 0.0 and 1.0
> (edges of pixel are integral).

Mostly computer graphics ignores pixels and plots the whole universe - or its
current instanciation - from 0.0 to 1.0.  You are then defining coordinates
to be at the upper side of the pixel since FITS does define the first pixel
to be pixel number 1.  Is that any more unique than the lower side?  Only the
center is unique.  The coordinates given in CRVALnnn are at the center of pixel
CRPIXnnn.  Of course - things like this may explain some of the complaints
about VLA positions and discrepancies between positions from various
observatories.

Eric W. Greisen
egreisen at nrao.edu