Zeitschrift fur angewandte mathematik und mechanik vol:76 pages:147-150
We present an algorithm for smoothing a convex surface to a set of scattered data. As for the approximation functions, Powell-Sabin splines on triangulations are used. These piecewise quadratics with C-1-continuity are expressed as a linear combination of locally supported basis functions (B-splines), which are fairly easy to construct. The necessary and sufficient convexity conditions are translated into a suitable set of constraints. Due to the local support of the B-splines these constraints are sparse, which can be exploited to efficiently solve the problem. A refinement procedure for the triangulation that automatically takes account of the difficulties in the function underlying the data is included.