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dc.contributor.authorShi, Ling
dc.contributor.authorWang, Jun
dc.contributor.authorPottmann, Helmut
dc.date.accessioned2015-08-03T11:45:33Z
dc.date.available2015-08-03T11:45:33Z
dc.date.issued2014-01
dc.identifier.issn01678396
dc.identifier.doi10.1016/j.cagd.2013.11.001
dc.identifier.urihttp://hdl.handle.net/10754/563316
dc.description.abstractSmooth freeform skins from simple panels constitute a challenging topic arising in contemporary architecture. We contribute to this problem area by showing how to approximate a negatively curved surface by smoothly joined rational bilinear patches. The approximation problem is solved with help of a new computational approach to the hyperbolic nets of Huhnen-Venedey and Rörig and optimization algorithms based on it. We also discuss its limits which lie in the topology of the input surface. Finally, freeform deformations based on Darboux transformations are used to generate smooth surfaces from smoothly joined Darboux cyclide patches; in this way we eliminate the restriction to surfaces with negative Gaussian curvature. © 2013 Elsevier B.V.
dc.description.sponsorshipThis research was supported in part by the DFG-Collaborative Research Center, TRR 109, Discretization in Geometry and Dynamics, through grant I 706-N26 of the Austrian Science Fund (FWF). We thank Udo Hertrich-Jeromin and Johannes Wallner for stimulating discussions and the reviewers for their excellent comments and suggestions.
dc.publisherElsevier BV
dc.subjectArchitectural geometry
dc.subjectAsymptotic net
dc.subjectDarboux cyclide
dc.subjectDarboux transformation
dc.subjectDiscrete differential geometry
dc.subjectFabrication-aware design
dc.subjectHyperbolic net
dc.subjectRational bilinear patch
dc.titleSmooth surfaces from rational bilinear patches
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentVisual Computing Center (VCC)
dc.contributor.departmentComputer Science Program
dc.identifier.journalComputer Aided Geometric Design
dc.contributor.institutionVienna University of Technology, 1040 Vienna, Austria
kaust.personShi, Ling
kaust.personWang, Jun
kaust.personPottmann, Helmut


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