Modified multiquadric methods for scattered data interpolation over a sphere

Helmut Pottmann*, Matthias Eck

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

Given arbitrary points on a sphere and associated real values, we address the problem of constructing a smooth function defined over the sphere which interpolates the given data. Several methods which are appropriate modifications of Hardy's planar multiquadric method are described and compared: the restriction of trivariate multiquadric interpolation to the sphere, spherical multiquadric interpolation due to Hardy and Goepfert and a scheme called 'elliptic multiquadric interpolation'. Following Franke's ideas, localized versions of these global techniques can be derived.

Original languageEnglish (US)
Pages (from-to)313-321
Number of pages9
JournalComputer Aided Geometric Design
Volume7
Issue number1-4
DOIs
StatePublished - Jan 1 1990

Keywords

  • Interpolation
  • multiquadric surfaces
  • scattered data fitting
  • spherical domain

ASJC Scopus subject areas

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

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