The kernel of a freeform surface and its duality with the convex hull of its tangential surface

Gershon Elber, John K. Johnstone, Myung Soo Kim, Joon Kyung Seong

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We present algorithms for computing the kernel of a closed freeform rational surface. The kernel computation is reformulated as a problem of finding the zero-sets of polynomial equations; using these zero-sets we characterize developable surface patches and planar patches that belong to the boundary of the kernel. Using a plane-point duality, this paper also explores a duality relationship between the kernel of a closed surface and the convex hull of its tangential surface.

Original languageEnglish
Pages (from-to)129-142
Number of pages14
JournalInternational Journal of Shape Modeling
Volume12
Issue number2
DOIs
Publication statusPublished - 2006 Dec

Keywords

  • B-spline
  • Convex hull
  • Freeform rational surface
  • Gamma-kernel
  • Kernel
  • Symbolic computation
  • Zero-set finding

ASJC Scopus subject areas

  • Software
  • Modelling and Simulation
  • Computer Vision and Pattern Recognition
  • Computer Science Applications
  • Geometry and Topology
  • Applied Mathematics

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