TITLE: Klein Bottle

NAME: Michael James Grady

COUNTRY: USA

EMAIL: mgrady@mindspring.com

WEBPAGE: http://www.cs.gsu.edu/~matmjg/surfaces

TOPIC: Glass

COPYRIGHT: I SUBMIT TO THE STANDARD RAYTRACING COMPETITION COPYRIGHT.

JPGFILE: klein.jpg

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



