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    Smooth surfaces from rational bilinear patches

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    Type
    Article
    Authors
    Shi, Ling
    Wang, Jun
    Pottmann, Helmut cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Visual Computing Center (VCC)
    Computer Science Program
    Date
    2014-01
    Permanent link to this record
    http://hdl.handle.net/10754/563316
    
    Metadata
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    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.
    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.2013.11.001
    Sponsors
    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 BV
    Journal
    Computer Aided Geometric Design
    DOI
    10.1016/j.cagd.2013.11.001
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.cagd.2013.11.001
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer Science Program; Visual Computing Center (VCC); Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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