A curvature theory for discrete surfaces based on mesh parallelity

Handle URI:
http://hdl.handle.net/10754/561482
Title:
A curvature theory for discrete surfaces based on mesh parallelity
Authors:
Bobenko, Alexander Ivanovich; Pottmann, Helmut ( 0000-0002-3195-9316 ) ; Wallner, Johannes
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.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Applied Mathematics and Computational Science Program; Visual Computing Center (VCC)
Publisher:
Springer Nature
Journal:
Mathematische Annalen
Issue Date:
18-Dec-2009
DOI:
10.1007/s00208-009-0467-9
ARXIV:
arXiv:0901.4620
Type:
Article
ISSN:
00255831
Sponsors:
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".
Additional Links:
http://arxiv.org/abs/arXiv:0901.4620v1
Appears in Collections:
Articles; Applied Mathematics and Computational Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBobenko, Alexander Ivanovichen
dc.contributor.authorPottmann, Helmuten
dc.contributor.authorWallner, Johannesen
dc.date.accessioned2015-08-02T09:12:28Zen
dc.date.available2015-08-02T09:12:28Zen
dc.date.issued2009-12-18en
dc.identifier.issn00255831en
dc.identifier.doi10.1007/s00208-009-0467-9en
dc.identifier.urihttp://hdl.handle.net/10754/561482en
dc.description.abstractWe 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.en
dc.description.sponsorshipThis 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".en
dc.publisherSpringer Natureen
dc.relation.urlhttp://arxiv.org/abs/arXiv:0901.4620v1en
dc.titleA curvature theory for discrete surfaces based on mesh parallelityen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalMathematische Annalenen
dc.contributor.institutionInstitut für Mathematik, TU Berlin, Straße des 17. Juni 136, 10623 Berlin, Germanyen
dc.contributor.institutionGeometric Modeling and Industrial Geometry, TU Wien, Vienna, Austriaen
dc.contributor.institutionInstitut für Geometrie, TU Graz, Kopernikusgasse 24, 8010 Graz, Austriaen
dc.identifier.arxividarXiv:0901.4620en
kaust.authorPottmann, Helmuten
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