Bézier and B-Spline Techniques

Part of the series Mathematics and Visualization pp 239-258

Box splines

  • Hartmut PrautzschAffiliated withGeometrische Datenverarbeitung, Universität Karlruhe (TH)
  • , Wolfgang BoehmAffiliated withAngewandte Geometrie und Computergraphik, Technische Universität Braunschweig
  • , Marco PalusznyAffiliated withEscuela de Matematicas, Facultad de Ciencias, Universidad Central de Venezuela

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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 G 2n-1 free-form surfaces with triangular patches than box splines.