Smooth surfaces from rational bilinear patches
dc.contributor.author | Shi, Ling | |
dc.contributor.author | Wang, Jun | |
dc.contributor.author | Pottmann, Helmut | |
dc.date.accessioned | 2015-08-03T11:45:33Z | |
dc.date.available | 2015-08-03T11:45:33Z | |
dc.date.issued | 2014-01 | |
dc.identifier.issn | 01678396 | |
dc.identifier.doi | 10.1016/j.cagd.2013.11.001 | |
dc.identifier.uri | http://hdl.handle.net/10754/563316 | |
dc.description.abstract | Smooth 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.sponsorship | This 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.publisher | Elsevier BV | |
dc.subject | Architectural geometry | |
dc.subject | Asymptotic net | |
dc.subject | Darboux cyclide | |
dc.subject | Darboux transformation | |
dc.subject | Discrete differential geometry | |
dc.subject | Fabrication-aware design | |
dc.subject | Hyperbolic net | |
dc.subject | Rational bilinear patch | |
dc.title | Smooth surfaces from rational bilinear patches | |
dc.type | Article | |
dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | |
dc.contributor.department | Applied Mathematics and Computational Science Program | |
dc.contributor.department | Visual Computing Center (VCC) | |
dc.contributor.department | Computer Science Program | |
dc.identifier.journal | Computer Aided Geometric Design | |
dc.contributor.institution | Vienna University of Technology, 1040 Vienna, Austria | |
kaust.person | Shi, Ling | |
kaust.person | Wang, Jun | |
kaust.person | Pottmann, Helmut |
This item appears in the following Collection(s)
-
Articles
-
Applied Mathematics and Computational Science Program
For more information visit: https://cemse.kaust.edu.sa/amcs -
Computer Science Program
For more information visit: https://cemse.kaust.edu.sa/cs -
Visual Computing Center (VCC)
-
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
For more information visit: https://cemse.kaust.edu.sa/