Partially blended surfaces are extensively used in the literature for shape preserving interpolation. Most of these shape preserving partially blended surface interpolation is based on the result that "shape-preserving properties on the transfinite interpolating surface follows from shape-preserving properties of the network of boundary curves" which is claimed to be trivial (see, for instance, Rational Interpolants with Tension Parameters by Giulio Casciola and Lucia Romani [PDF Link]).
I do not find this to be trivial. Can anyone shed some light?