  Mean value interpolation is a method for fitting a smooth function to
piecewise-linear data prescribed on the boundary of a polygon of arbitrary
shape, and has applications in computer graphics and curve and surface
modelling. The method generalizes to transfinite interpolation, i.e., to any
continuous data on the boundary but a mathematical proof that interpolation
always holds has so far been missing. The purpose of this note is to complete
this gap in the theory.
