Smooth surfaces from rational bilinear patches

Ling Shi, Jun Wang, Helmut Pottmann

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)1-12
Number of pages12
JournalComputer Aided Geometric Design
Volume31
Issue number1
DOIs
StatePublished - Jan 2014

ASJC Scopus subject areas

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

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