From: "j.e.mebius" <j.e.mebius@twi.tudelft.nl>
Subject: Re: Dupin cyclides
Date: Fri, 12 Feb 1999 17:16:00 +0100
Newsgroups: sci.math
To: badidi <badidi@ese-metz.fr>
Keywords: Dupin's cyclides (surfaces)

Delft - February 12th 1999

Dear mr Badini,

For Pierre Dupin see URL

http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Dupin.html

and follow the References link to A.E.Hirst's paper. 

Dupin's cyclides are a class of 4th-degree surfaces in Euclidean 3D
space. Cyclides are generated by moving a circle through 3D space in
a certain way, which I do not know by heart in its full generality.
Anyhow, the familiar torus surface is a cyclide. 
If I remember well, a cyclide is defined as a 4th-degree surface in
3D complex projective space that contains the absolute circle at 
infinity x1^2 + x2^2 + x3^2 = 0 as a double curve.
I guess that any cyclide may be obtained from the torus by an inversion
of 3D space (3D transformation by reciprocical radii), but this too
I do not know for sure.
As indicated in Hirst's paper, cyclides play an important in 3D CAD/CAM
as blending surfaces. You guess in what sense: to connect two circles
in arbitrary relative location in 3D space.
Good luck - FrGr: Johan E. Mebius (j.e.mebius@twi.tudelft.nl)

=========== reply to ============

badidi wrote:
> 
> Hello all;
> I am doing a report for school on Dupin cyclides.  I would appreciate if
> 
> anyone could give me information about this.
> 
> Thanks,
> 
> abdel