Multivariate splines

  • Hartmut Prautzsch
  • Wolfgang Boehm
  • Marco Paluszny
Part of the Mathematics and Visualization book series (MATHVISUAL)


De Boor’s algorithm is a generalization of de Casteljau’s and univariate B-splines are a generalization of Bernstein polynomials. Analogously, it is possible to generalize de Casteljau’s algorithm for multivariate polynomials to multivariate splines. The underlying basis functions of this generalized algorithm are simplex splines forming a partition of unity. These simplex splines are proper generalizations of the univariate B-splines and many properties of the univariate B-splines also hold for these multivariate simplex splines.


Control Point Recurrence Relation Directional Derivative Recurrence Formula Polar Form 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Hartmut Prautzsch
    • 1
  • Wolfgang Boehm
    • 2
  • Marco Paluszny
    • 3
  1. 1.Geometrische DatenverarbeitungUniversität Karlruhe (TH)KarlsruheGermany
  2. 2.Angewandte Geometrie und ComputergraphikTechnische Universität BraunschweigBraunschweigGermany
  3. 3.Escuela de Matematicas, Facultad de CienciasUniversidad Central de VenezuelaCaracasVenezuela

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