Shape-preserving quasi-interpolation and interpolation by box spline surfaces (Q1116262)

The authors study shape-preserving approximation and interpolation of functions by box-spline surfaces on three and four directional meshes. They restrict the attention to the bivariate setting since one objective of this paper is to obtain relatively sharp estimates and the higher dimensional setting seems amenable to the same techniques but only at a cost of much more complexity. The properties of positivity, monotonicity and convexity are studied.