Multivariate refinable interpolating functions

Multivariate Refinable Interpolating Functions play an important role in the construction of multiresolution analyses and associated wavelet bases. They are also often used in computer aided geometric design, in particular in subdivision schemas and iterative interpolation processes. ^ We present several algorithms for the construction of arbitrary smooth refinable interpolating functions with compact support. We give examples and make the link to a translation invariant multiresolution analysis. We also make a connection to Bernstein polynomials and discuss the asymptotic behaviour of the constructed families of refinable interpolating functions.