Dupin Cyclides

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It is worth searching the web for the fascinating properties of a particular type of cyclide named after Charles Dupin in his dissertation of 1803. They are currently used as tools in computer-aided geometric design (CAGD). Most striking is that their curvature lines are all circles, extended to infinity in the parabolic case.

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Darboux studied the nonparabolic polynomial set to zero. It depends on three parameters , , and . It is usual to speak of ring cyclides for , horn cyclides for , and spindle cyclides for .

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Contributed by: Claude Fabre (March 2011)
Open content licensed under CC BY-NC-SA


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