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Network Splines

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Abstract

A multivariate interpolant to scattered data is developed by generalizing (weighted) bivariate network splines to an n-dimensional setting. A graph joining the data points serves to define a set of edges over which an interpolating curve network is constructed subject to smoothness and minimal energy constraints. A subsequent extension of the curve network to the convex hull of the data points defines a smooth interpolating surface. The problems of existence and uniqueness are investigated and some examples of interpolants to rapidly varying data in ℝ3 and ℝ4 are presented.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada, T2N 1N4

    L. P. Bos & D. Holland

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  1. L. P. Bos
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  2. D. Holland
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Bos, L.P., Holland, D. Network Splines. Results. Math. 30, 228–258 (1996). https://doi.org/10.1007/BF03322193

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