Generating polyhedron vertices

From: Laurence Finston (lfinsto1_at_gwdg.de)
Date: 11/20/04 

Date: 20 Nov 2004 14:33:52 -0800

Hello,

I would like to improve the way I generate polyhedra in a software
package I am writing, namely GNU 3DLDF. Currently, my procedure is
naive. It is the virtual equivalent of folding together a cardboard
model. I create a net of polygons in the x-z plane and rotate them
until the polyhedron is formed. This works, and was simple to
implement, but has a number of disadvantages. In the first place, I
store multiple points for each vertex. The real problem is that,
because of the limited precision of the values returned by the C++
library functions representing the trigonometric functions, the n
points representing a given vertex do not have identical coordinates.
The deviation is too small to have any effect on the visual result (at
least, under normal circumstances), but it bothers me.

Is there a better way of generating vertices for polyhedra? I don't
have a good mathematical background, but I'm trying to learn. Any
help and/or references to relevant literature would be much
appreciated.

Laurence Finston
http://www.gnu.org/software/3dldf/LDF.html