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Radial Basis Functions, Discrete Differences, and Bell-Shaped Bases

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Geometric Modelling

Part of the book series: Computing ((COMPUTING,volume 14))

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Abstract

In this paper, we introduce the notion of a normalized radial basis function. In the univariate case, taking these basis functions in combinations determined by certain discrete differences leads to the B-spline basis. In the bivariate case, these combinations lead to a generalization of the B-spline basis to the surface case. Subdivision rules for the resulting basis functions can easily be derived.

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References

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Author information

Authors and Affiliations

  1. Department of Computer Science, Rice University, P.O. Box 1892, Houston, TX, 77251-1892, USA

    J. Warren & H. Weimer

Authors
  1. J. Warren
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  2. H. Weimer
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Editor information

Editors and Affiliations

  1. Fakultät für Informatik, TU Chemnitz, Chemnitz, Germany

    Guido Brunnett

  2. Institut für Informatik und angewandte Mathematik, Universität Bern, Bern, Switzerland

    Hanspeter Bieri

  3. Department of Computer Science and Engineering, Arizona State University, Tempe, AZ, USA

    Gerald Farin

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© 2001 Springer-Verlag Wien

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Warren, J., Weimer, H. (2001). Radial Basis Functions, Discrete Differences, and Bell-Shaped Bases. In: Brunnett, G., Bieri, H., Farin, G. (eds) Geometric Modelling. Computing, vol 14. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6270-5_20

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  • DOI: https://doi.org/10.1007/978-3-7091-6270-5_20

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83603-3

  • Online ISBN: 978-3-7091-6270-5

  • eBook Packages: Springer Book Archive

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