Box splines

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

Abstract

Box splines are density functions of the shadows of higher dimensional polyhe-dra, namely boxes. For example, B-splines with equidistant knots are special univariate box splines, and the surfaces obtained by the averaging algorithm described in Section 15.7 are box spline surfaces over a regular triangular grid. This chapter (an abbreviated version of [Prautzsch & Boehm ′02]) provides a brief introduction to general box splines. It also covers half-box splines. Symmetric half-box splines of degree 3n are more suitable than box splines for the construction of arbitrary G2n-1 free-form surfaces with triangular patches than box splines.

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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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