If you run

examples/c/x16c -dev xwin -exclude -nx 20 -ny 20

a smooth donut is excluded from the 5th page (as expected, since years ago
Rafael modified the defined algorithm for plshade(s) to give smooth edges
using some sort of iterative technique). However, if you use
coarser resolutions, e.g.,

examples/c/x16c -dev xwin -exclude -nx 10 -ny 10

Rafael's iteration sometimes still gives reasonably good results (some edges
of the donut are smooth) at coarser resolutions but also sometimes gives
horrible results (the edges of the donut are extremely misplaced or missing
altogether). I interpret these results as a numerical robustness issue (a
starting solution that is so bad that it cannot converge, or a convergence
criterion that stops the iteration before it has converged).

I also just ran into the same problem with the software fallback (using
plshades) for plgradient. 2x2 points should perfectly determine the plane
representing the gradient, but the edge of the defined region was completely
erratic at that resolution, and I had to use a severely redundant 20x20
resolution to get robust smooth results for the edges of the defined region
represented by a polygon.

In the interests of speed I far prefer using 2x2 resolution to represent the
gradient plane for the plgradient plshades fallback so I will look into this
numerical robustness issue.  If I can solve it, I expect to get smooth edge
results at 2x2 resolution not only for example 16, but also for the plshades
fallback for plgradient.

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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