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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.[more]
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 .[less]
Contributed by: Claude Fabre (March 2011)
Open content licensed under CC BY-NC-SA
Wolfram Demonstrations Project
Published: March 7 2011