[Plplot-devel] I have discovered an experimental solution of the long-standing parallelogram issue

[Alan W. I. <ir...@be...>]

For those unaware of what the parallelogram issue is, please have a look
at the first attachment which was generated by

examples/c/x01c -dev pngcairo -geometry 800x400 -ori 0.2 -o test.png

This 18 deg rotation has turned the rectangles of this example into
parallelograms, and the text rendered by the device driver is obviously
written at incorrect angles. If you try similar experiments with -dev xwin
or -dev qtwidget you also get identical incorrect parallelograms. The issue
disappears for unity aspect ratios, and for integral -ori values so we
haven't worried about it that much over the years, but nevertheless it has
always nagged me that nobody could figure this out.

The relevant affine transformations are implemented in calc_diori in
plcore.c via calls to various plP_affine* functions.  There is also
commented out code there that has the same effect, but I replaced that quite
a while ago with the series of plP_affine* calls because I thought that gave
a better feeling for all the fundamental affine transformations involved.

Today, I did an experiment with gdb that showed that internal coordinates
were used for the scaling part of the affine transformation rather than raw
device coordinates.  In retrospect this should make no difference since
device coordinates are simply scaled by the same factor in X and Y.  But at
the time, I thought I was on to something so I starting experimenting and
discovered that if lx (the X length) was divided by the device's aspect
ratio, all the parallelogram issues go away (see attached second plot which
was generated like the first plot except for the code change [currently
commented out] to divide lx by the device aspect ratio).

I currently don't understand why this correction works; and the results do
not preserve the aspect ratio of the original (say for -ori 1), have severe
cropping issues, and also have character aspect ratio issues for Hershey
fonts (circles are rendered as ellipses).  So I have commented out the
correction (revision revision 11017).  But I feel I am close to the correct
solution because the second plot looks so much better than the first, and at
least the character aspect ratio issue can be ascribed to an old
experimental correction which likely now needs to be adjusted to be
consistent with this latest fix (once it is uncommented).

Anyhow, I hope that the nice second plot I have attached will inspire
somebody with more knowledge than I have of the various PLplot coordinate
systems to try and understand why this correction works, and to use that
understanding to deal with the other issues that I have observed
with the experimental correction.

Alan
__________________________
Alan W. Irwin

Astronomical research affiliation with Department of Physics and Astronomy,
University of Victoria (astrowww.phys.uvic.ca).

Programming affiliations with the FreeEOS equation-of-state implementation
for stellar interiors (freeeos.sf.net); PLplot scientific plotting software
package (plplot.org); the libLASi project (unifont.org/lasi); the Loads of
Linux Links project (loll.sf.net); and the Linux Brochure Project
(lbproject.sf.net).
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