Students' Work: Dupin Cyclides

The cyclides of Dupin arise from cones of revolution, cylinders of revolution, and tori under the inversion with respect to a sphere. Any cyclide is a channel surface (envelope of a one-parameter family of spheres) in two different ways. All their curvature lines are circles (or lines). The image depicts a cyclide that is homeomorphic to a torus together with its curvature lines.
(Courtesy of Boris Odehnal.)

Created by Matthias Budil (2007) using POV-Ray - The Persistance of Vision Raytracer.