From: "j.e.mebius" Subject: Re: Dupin cyclides Date: Fri, 12 Feb 1999 17:16:00 +0100 Newsgroups: sci.math To: badidi 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