KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
Visual Computing Center (VCC)
Computer Science Program
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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.
SponsorsThis 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.
JournalComputer Aided Geometric Design