Smooth surfaces from rational bilinear patches

Authors:
Ling Shi;Jun Wang;Helmut Pottmann
Affiliations:
King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia;King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia;King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia and Vienna University of Technology, 1040 Vienna, Austria
Venue:
Computer Aided Geometric Design
Year:
2014

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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 Rorig 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.