Multivariate B-splines and Delaunay Configurations

In this expository talk we will review the theory of multivariate B-splines. These are analogs of the classical univariate B-splines that are built from simplex splines. The presented construction uses the so-called Delaunay configurations. We will survey this area of approximation theory and discuss a number of unresolved issues. We will also sketch an algorithm to compute Delaunay configurations effectively and then apply it to a construction of spline spaces using bivariate B-splines.