Box splines

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.