Journal for Geometry and Graphics 10 (2006), No. 1, 073--098
Copyright Heldermann Verlag 2006
Ortho-Circles of Dupin Cyclides
Michael Schrott
Institute of Discrete Mathematics, Technical University, Wiedner Hauptstr. 8-10/113, 1040 Wien, Austria
mschrott@geometrie.tuwien.ac.at
Boris Odehnal
Institute of Discrete Mathematics, Technical University, Wiedner Hauptstr. 8-10/113, 1040 Wien, Austria
odehnal@geometrie.tuwien.ac.at
We study the set of circles which intersect a Dupin cyclide in at least two different points orthogonally. Dupin cyclides can be obtained by inverting a cylinder, or cone of revolution, or by inverting a torus. Since orthogonal intersection is invariant under Möbius transformations we first study the ortho-circles of cylinder/cone of revolution and tori and transfer the results afterwards.
Keywords: Ortho-circle, double normal, Dupin cyclide, torus, inversion.
MSC: 53A05; 51N20, 51N35
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