This article introduces a procedure for progressively increasing the density of an initial point set that can be used as a basis for interpolating surfaces of variable resolution from sparse samples of data sites. The procedure uses the Simple Recursive Point Voronoi Diagram in which Voronoi concepts are used to tessellate space with respect to a given set of generator points. The construction is repeated every time with a new generator set, which comprises members selected from the previous generator set plus features of the current tessellation. We show how this procedure can be implemented in Arc/Info and present an illustration of its application using three known surfaces and alternative generator point configurations. Initial results suggest that the procedure has considerable potential and we discuss further methods for evaluating and extending it.