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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© 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
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