University of Lugano

In this talk I will focus on the method of barycentric interpolation, which ties up to the ideas that August Ferdinand Möbius published in his seminal work "Der barycentrische Calcül" in 1827. For univariate data, this gives a special kind of rational interpolant which is guaranteed to have no poles and favourable approximation properties.

I further discuss how to extend this idea to bivariate data, where it leads to the concept of generalized barycentric coordinates and to an efficient method for interpolating data given at the vertices of an arbitrary polygon.