Darboux cyclides and webs from circles

Details Darboux cyclides and webs from circles Darboux cyclides and webs from circles

2011-06-07

arxiv.org/abs/1106.1354v1

Computer Aided Geom. Design 29:1 (2012), 77-97

Mathematics

Algebraic Geometry

34 pages, 20 figures

Scientific paper

10.1016/j.cagd.2011.10.002

Motivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order a most 4 are a superset of Dupin cyclides and quadrics, and they carry up to six real families of circles. Revisiting the classical approach to these surfaces based on the spherical model of 3D Moebius geometry, we provide computational tools for the identification of circle families on a given cyclide and for the direct design of those. In particular, we show that certain triples of circle families may be arranged as so-called hexagonal webs, and we provide a complete classification of all possible hexagonal webs of circles on Darboux cyclides.

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