polygon problem in 3D

*To*: mathgroup at yoda.physics.unc.edu*Subject*: polygon problem in 3D*From*: James King <king at math.washington.edu>*Date*: Thu, 21 May 92 10:26:25 -0700

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. For example, tri3 = { {1,0,0}, {1, 1, 1}, {-2, -1, -1}} gtri3 = Graphics3D[Polygon[tri3]] Show[gtri3, ViewPoint->{2,1,2}] draws a triangle in 3-space but if we change the viewpoint, Show[gtri3, ViewPoint->{2,1,1}] instead of drawing a line or nothing, this will produce this message: The PostScript text in this cell did not contain any drawing commands, or contained an error before the first valid drawing command. The same message results, if the Graphics3D object consists of this triangle along with another triangle in general position. In contrast, with 2D graphics, there is no error is one uses Polygon to draw a triangle made of 3 points which happen to be collinear. This 3D bug is a problem if you deliberately want to show a figure with some flat piece edge-on or if you happen to create such a view by varying some parameter when creating an animation. Can anyone suggest a convenient work-around (or is this fixed in some newer version of Mathematica? James King Dept of Math GN-50 University of Washington Seattle, WA 98195 king at math.washington.edu