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dc.contributor.authorBobenko, Alexander I.
dc.contributor.authorPottmann, Helmut
dc.contributor.authorRörig, Thilo
dc.date.accessioned2019-08-06T13:56:07Z
dc.date.available2019-08-06T13:56:07Z
dc.date.issued2019-05-28
dc.identifier.citationBobenko, A. I., Pottmann, H., & Rörig, T. (2019). Multi-Nets. Classification of Discrete and Smooth Surfaces with Characteristic Properties on Arbitrary Parameter Rectangles. Discrete & Computational Geometry. doi:10.1007/s00454-019-00101-1
dc.identifier.doi10.1007/s00454-019-00101-1
dc.identifier.urihttp://hdl.handle.net/10754/656384
dc.description.abstractWe investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on arbitrary parameter rectangles. For discrete planar quadrilateral nets, circular nets, Q∗-nets and conical nets we obtain a characterization of the corresponding discrete multi-nets. In the limit these discrete nets lead to some classical classes of smooth surfaces. Furthermore, we propose to use the characterized discrete nets as discrete extensions for the nets to obtain structure preserving subdivision schemes.
dc.description.sponsorshipWe would like to thank Wolfgang Schief and Jan Techter for many fruitful discussions. This research was supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics.” – www.discretization.de. Helmut Pottmann was supported through Grant I 2978-N35 of the Austrian Science Fund (FWF).
dc.publisherSpringer Nature
dc.relation.urlhttp://link.springer.com/10.1007/s00454-019-00101-1
dc.relation.urlhttp://arxiv.org/pdf/1802.05063
dc.rightsArchived with thanks to Springer Science and Business Media LLC
dc.subjectDiscrete differential geometry
dc.subjectProjective geometry
dc.subjectDiscrete conjugate nets (Q-nets)
dc.subjectCircular nets
dc.subjectConical nets
dc.subjectInterpolatory subdivision
dc.titleMulti-Nets. Classification of Discrete and Smooth Surfaces with Characteristic Properties on Arbitrary Parameter Rectangles
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentVisual Computing Center (VCC)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalDiscrete and Computational Geometry
dc.rights.embargodate2020-01-01
dc.eprint.versionPre-print
dc.contributor.institutionInstitute of Mathematics, TU Berlin, Secr. MA 8-4, 10623, Berlin, Germany
dc.contributor.institutionGeometric Modeling and Industrial Geometry, TU Wien, 1040, Vienna, Austria
dc.identifier.arxivid1802.05063
kaust.personPottmann, Helmut
refterms.dateFOA2019-12-09T12:20:44Z
dc.date.published-online2019-05-28
dc.date.published-print2020-04


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