A curvature theory for discrete surfaces based on mesh parallelity

Alexander Ivanovich Bobenko, Helmut Pottmann, Johannes Wallner

Research output: Contribution to journalArticlepeer-review

47 Scopus citations

Abstract

We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards. © 2009 Springer-Verlag.
Original languageEnglish (US)
Pages (from-to)1-24
Number of pages24
JournalMathematische Annalen
Volume348
Issue number1
DOIs
StatePublished - Dec 18 2009

ASJC Scopus subject areas

  • Mathematics(all)

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