Darboux cyclides and webs from circles

Helmut Pottmann, Ling Shi, Mikhail Skopenkov

Research output: Contribution to journalArticlepeer-review

28 Scopus citations

Abstract

Motivated by potential applications in architecture, we study Darboux cyclides. These algebraic surfaces of order ≤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 Möbius 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. © 2011 Elsevier B.V. All rights reserved.
Original languageEnglish (US)
Pages (from-to)77-97
Number of pages21
JournalComputer Aided Geometric Design
Volume29
Issue number1
DOIs
StatePublished - Jan 2012

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computer Graphics and Computer-Aided Design
  • Automotive Engineering
  • Aerospace Engineering

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