Numerical Algorithms

, Volume 43, Issue 1, pp 75–98 | Cite as

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

  • G. Casciola
  • E. Franchini
  • L. Romani


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.


trivariate Box-splines recurrence relations exact evaluation tetrahedral Bézier volume decomposition B-net 

Mathematics Subject Classifications (2000)

65D17 68U05 33F99 65D07 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BolognaBolognaItaly
  2. 2.Department of Pure and Applied MathematicsUniversity of PadovaPadovaItaly

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