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.

Casciola, G., Franchini, E., & Romani, L. (2006). The mixed directional difference–summation algorithm for generating the Bézier net of a trivariate four-direction Box-spline. NUMERICAL ALGORITHMS, 43(1), 75-98 [10.1007/s11075-006-9042-6].

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

ROMANI, LUCIA
2006-11

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.
Articolo in rivista - Articolo scientifico
Scientifica
Trivariate Box-splines; Recurrence relations; Exact evaluation; Tetrahedral Bézier volume decomposition; B-net
English
75
98
Casciola, G., Franchini, E., & Romani, L. (2006). The mixed directional difference–summation algorithm for generating the Bézier net of a trivariate four-direction Box-spline. NUMERICAL ALGORITHMS, 43(1), 75-98 [10.1007/s11075-006-9042-6].
Casciola, G; Franchini, E; Romani, L
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/7676
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