A curvature theory for discrete surfaces based on mesh parallelity

A.I. Bobenko, H. Pottmann, J. Wallner
Mathematische Annalen, volume 348, issue 1, pp. 1-24, (2010)

A curvature theory for discrete surfaces based on mesh parallelity

Keywords

Mesh parallelity

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.

Code

DOI: 10.1007/s00208-009-0467-9

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