Interpolation on surfaces using minimum norm networks

Helmut Pottmann*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

New methods for interpolating scattered data on a surface are presented. Similar to G. Nielson's minimum norm network technique, this approach is based upon a functional minimization that characterizes the restriction of the final interpolant to curves which form the edges in a triangulation of the domain surface. However, unlike the known minimum norm network methods we do not use only data points as vertices in the triangulation. We also consider minimum norm networks with tension properties. An appropriate method for extending the network data to a final C1 interpolant is described. Both color blended contour regions on the surface and projections of the 4D graph of a function on a surface are used in illustrating examples. Finally, special cases, possible extensions and applications in surface design are addressed.

Original languageEnglish (US)
Pages (from-to)51-67
Number of pages17
JournalComputer Aided Geometric Design
Volume9
Issue number1
DOIs
StatePublished - Jan 1 1992

Keywords

  • Scattered data fitting
  • functional minimization
  • interpolation
  • minimum norm network
  • scientific visualization.
  • surfaces
  • tension
  • triangular interpolant

ASJC Scopus subject areas

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

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