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Localized Radial Basis Methods Using Rational Triangle Patches

  • Conference paper
Book cover Geometric Modelling

Part of the book series: Computing Supplement ((COMPUTING,volume 10))

Abstract

Two of the most effective methods for interpolating scattered data are the multiquadric method and the thin plate spline method. A negative aspect of these radial basis methods is that they are not local and they are computationally expensive and unstable if there are a large number of data points. We present a localized interpolation method that involves partitioning the data into arbitrary overlapping triangular regions based on arbitrary points, forming local radial basis interpolants to the data in each region, and then blending the local interpolants with rational triangle patches so that the resulting function is a locally defined C 1 interpolant. When the triangular regions form a triangulation of the scattered data locations, the resulting interpolant can be considered as a new local triangle patch method that generally has effective derivatives at the vertices and cross-boundary derivatives along the edges of the triangulation.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, Arizona State University, Tempe, AZ, 85287-5406, USA

    Dr. T. A. Foley & Dr. S. Dayanand

  2. Informatik Department, Universität Kaiserslautern, D-67653, Kaiserslautern, Federal Republic of Germany

    Dr. D. Zeckzer

Authors
  1. Dr. T. A. Foley
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  2. Dr. S. Dayanand
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  3. Dr. D. Zeckzer
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Editor information

Editors and Affiliations

  1. Fachbereich Informatik, Universität Kaiserslautern, Federal Republic of Germany

    H. Hagen

  2. Department of Computer Science, Arizona State University, Tempe, USA

    G. Farin

  3. Lehrstuhl für Informatik I, Universität Würzburg, Federal Republic of Germany

    H. Noltemeier

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© 1995 Springer-Verlag/Wien

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Foley, T.A., Dayanand, S., Zeckzer, D. (1995). Localized Radial Basis Methods Using Rational Triangle Patches. In: Hagen, H., Farin, G., Noltemeier, H. (eds) Geometric Modelling. Computing Supplement, vol 10. Springer, Vienna. https://doi.org/10.1007/978-3-7091-7584-2_11

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  • DOI: https://doi.org/10.1007/978-3-7091-7584-2_11

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82666-9

  • Online ISBN: 978-3-7091-7584-2

  • eBook Packages: Springer Book Archive

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