Smooth surfaces from rational bilinear patches

Ling Shi; Jun Wang; Helmut Pottmann

doi:10.1016/j.cagd.2013.11.001

Smooth surfaces from rational bilinear patches

Ling Shi, Jun Wang, Helmut Pottmann

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1-12
Number of pages	12
Journal	Computer Aided Geometric Design
Volume	31
Issue number	1
DOIs	https://doi.org/10.1016/j.cagd.2013.11.001
State	Published - Jan 2014

ASJC Scopus subject areas

Modeling and Simulation
Computer Graphics and Computer-Aided Design
Automotive Engineering
Aerospace Engineering

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10.1016/j.cagd.2013.11.001

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title = "Smooth surfaces from rational bilinear patches",

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 R{\"o}rig 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. {\textcopyright} 2013 Elsevier B.V.",

author = "Ling Shi and Jun Wang and Helmut Pottmann",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: 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.",

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AU - Pottmann, Helmut

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Smooth surfaces from rational bilinear patches

Abstract

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