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  • From: "Arthur Ogawa" <ogawa at>
  • Date: Mon, 25 May 92 04:23:22 -0700

You write:

> I have encountered what seems to be a bug when using
> Polygon in 3D-graphics.  I am running Mathematica 2.03
> Enhanced on a Mac IIci.

> The problem is that if a polygon is viewed "edge-on", 
> Mathematica gives a Postscript error message instead
> of rendering the graphic.

Welcome to the club. I've encountered the same problem in Mathematica
and reported it to Wolfram himself, and to Tom Wickham-Jones, who
has to do with the implementation of Mathematica's graphics capabilities.

Neither has replied to my note. Perhaps by publicising this problem
on math-group, wri will be made to feel pressure from users...

You've hit upon a way of making Mathematica generate internal PostScript
code that it cannot render, simply by viewing an Edge from an edge-on
viewpoint. The basic problem in Mathematica is that an Edge is not 
presented in anything like a realistic way to the renderer.
In particluar, an Edge has the same apparent thickness regardless
of the angle of view with respect to the Polygon that the Edge belongs
to. In addition, the thickness of an Edge is also independent of the
distance of the viewpoint to the edge. 

Let's say you create a very large planar figure consisting of
Polygons, and view it in such a way as to create a "horizon" of sorts at the
far edge. Because of both the abovementioned features, the "horizon" will
appear black, which is, of course, ludicrously wrong.

Lacking a fix to this limitation from WRI, one can redefine Polygon in
terms that present it as a collection of filled regions (Edge-less
Polygons), one of which would be the interior, and the remainder
constituting the edges.  Such an approach would then be rendered
accurately, but would suffer from the disadvantage of occupying
considerably more space in Mathematica's memory.

In an article in the Mathematica Journal, Vol 1, Issue 1, p32-33, Cameron
Smith and Paul Abbott detail code that could be modified to accomplish
this workaround.

Arthur Ogawa        Internet: ogawa at  Ph: 1/415/691-1126
TeX consultant      AppleLink: ogawa                    FAX:1/415/962-1969
STEPS Project      1101 San Antonio Rd. #413, MOUNTAIN VIEW, CA 94043-1002

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