Handbook of Computer Aided Geometric Design

Chapter 10

Box Splines

Hartmut Prautzsch and Wolfgang Boehm

This chapter provides a brief introduction to box and half-box splines with particular focus on triangular splines and surface design. A particular example of box splines are the B-splines with equidistant knots. In general, box splines consist of regularly arranged polynomial pieces and they have a useful geometric interpretation. Namely they can be viewed as density functions of the shadows of higher dimensional boxes and half-boxes. Of particular interest for Geometric Design are box spline surfaces that consist of triangular polynomial pieces. These box spline surfaces have planar domains, but it is quite simple to construct arbitrary two-dimensional surfaces, i.e., manifolds, ...