Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
Visual Computing Center (VCC)
Computer Science Program
Date
2014-01Permanent link to this record
http://hdl.handle.net/10754/563316
Metadata
Show full item recordAbstract
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.Citation
Shi, L., Wang, J., & Pottmann, H. (2014). Smooth surfaces from rational bilinear patches. Computer Aided Geometric Design, 31(1), 1–12. doi:10.1016/j.cagd.2013.11.001Sponsors
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.Publisher
Elsevier BVJournal
Computer Aided Geometric Designae974a485f413a2113503eed53cd6c53
10.1016/j.cagd.2013.11.001