Slime wrote:
> 
> Hmm, what's the formula for a klein bottle?
> 
I do not think there is. First there is not such a thing as 
_the_ Klein bottle. It is a general description for objects
that have a finite surface, that do not have discontinuities,
and where there for every point on the surface a path that
gets you to the other surface.
Second because for every point on the surface the normal 
points both in and out, I do not think there is an analitic
formula for any Klein bottle.

In the construction of this bottle I followed the approach
of Denise L. Chen in the Matlab demo's here is what she sais
%   A Klein bottle is a nonorientable surface in 
%   four-dimensional space. It is formed by attaching two 
%   Mobius strips along their common boundary.
%
%   Klein bottles cannot be constructed without intersection 
%   in three-space. The figure shown is an example of such a 
%   self-intersecting Klein bottle. 
%
%   Thanks to Davide Cervone, University of Minnesota.

%   Denise L. Chen  7-6-93
%   Copyright (c) 1984-98 by The MathWorks, Inc.
%   $Revision: 1.22 $  $Date: 1997/11/21 23:27:39 $
I do not think this makes any sense but this is what was in
the description.
Construction is as follows: make two objects
- the bulb, essentially a surface of recolution
- the handle, shaped like an inverted question mark (without the dot)
and merge them together.

Attached is another image that shows the construction better
note that there is some tension in the glass where the 
handle attached to the bulb at the lower point.

I used a mesh for this image, I think now with the new features 
I would use the sphere_sweep for the handle (although we do 
have this problem with the inverse of the sphere sweep)

	Andrel





> - Slime
> [ http://www.slimeland.com/ ]
> [ http://www.slimeland.com/images/ ]

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