Barycentric coordinates and transfinite interpolation

Recent generalizations of barycentric coordinates to polygons and polyhedra, such as Wachspress and mean value coordinates, have been used to construct smooth mappings that are easier to compute than harmonic amd conformal mappings, and have been applied to curve and surface modelling.

We will summarize some of these developments and then discuss how these coordinates naturally lead to smooth transfinite interpolants over curved domains, and how one can also match derivative data on the domain boundary.