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The mixed directional difference–summation algorithm for generating the Bézier net of a trivariate four-direction Box-spline

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Abstract

Trivariate Box-splines lack an efficient and general exact evaluation technique. This paper presents one possible and underexploited approach to solving this problem. The algorithm we propose is based on mixed directional differences and summations for computing the Bézier net coefficients of all trivariate four-direction Box-splines of any degree over tetrahedral tessellations of the domain. A Matlab package, called MDDS, for computing the Bézier net both in the trivariate and bivariate cases, is also provided.

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Authors and Affiliations

  1. Department of Mathematics, University of Bologna, P.zza di Porta San Donato 5, 40127, Bologna, Italy

    G. Casciola & L. Romani

  2. Department of Pure and Applied Mathematics, University of Padova, Via G. Belzoni 7, 35131, Padova, Italy

    E. Franchini

Authors
  1. G. Casciola
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  2. E. Franchini
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  3. L. Romani
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Correspondence to L. Romani.

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Casciola, G., Franchini, E. & Romani, L. The mixed directional difference–summation algorithm for generating the Bézier net of a trivariate four-direction Box-spline. Numer Algor 43, 75–98 (2006). https://doi.org/10.1007/s11075-006-9042-6

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  • DOI: https://doi.org/10.1007/s11075-006-9042-6

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