A curvature theory for discrete surfaces based on mesh parallelity
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
Visual Computing Center (VCC)
Date
2009-12-18Preprint Posting Date
2009-01-29Online Publication Date
2009-12-18Print Publication Date
2010-09Permanent link to this record
http://hdl.handle.net/10754/561482
Metadata
Show full item recordAbstract
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.Citation
Bobenko, A. I., Pottmann, H., & Wallner, J. (2009). A curvature theory for discrete surfaces based on mesh parallelity. Mathematische Annalen, 348(1), 1–24. doi:10.1007/s00208-009-0467-9Sponsors
This research was supported by grants P19214-N18, S92-06, and S92-09 of the Austrian Science Foundation (FWF), and by the DFG Research Unit "Polyhedral Surfaces".Publisher
Springer NatureJournal
Mathematische AnnalenarXiv
0901.4620Additional Links
http://arxiv.org/abs/arXiv:0901.4620v1ae974a485f413a2113503eed53cd6c53
10.1007/s00208-009-0467-9