EMAIL: mgrady@mindspring.com
NAME: Michael James Grady
TOPIC: Glass
COPYRIGHT: I SUBMIT TO THE STANDARD RAYTRACING COMPETITION COPYRIGHT.
TITLE: Klein Bottle
COUNTRY: USA
WEBPAGE: http://www.cs.gsu.edu/~matmjg/surfaces
RENDERER USED: povray 3.0 beta
TOOLS USED: Mathematica
RENDER TIME: 30 minutes
HARDWARE USED: Pentium 133

IMAGE DESCRIPTION:

The Klein bottle is a fundamental surface in topology, and is quite 
beautiful in its own right. PovRay allows one to model exquisite reflections and refractions, and in this case the Klein bottle is actually reflecting a second Klein bottle. 
     
DESCRIPTION OF HOW THIS IMAGE WAS CREATED:

To obtain this image of the Klein bottle, I used the parametric description given by Stewart Dickson in his Mathematica notebook "Klein.ma". After Mathematica computed the necessary graphics primitives the file was converted to DXF format using an efficient converter written by John Novak. This was then converted to a pov file using the converter dxf2pov. Alternatively, one could use the package written by Roman Maeder in his book on Mathematica Programming. PovRay users should consult his chapter on Ray Tracing. The geometry file is about a megabyte, and is not included. Interested parties should send me e-mail at this address: matmjg@cs.gsu.edu