A new method for constructing interpolating Loop subdivision surfaces is presented. The new method is an extension of the progressive interpolation technique for B-splines. Given a triangular mesh
, the idea is to iteratively upgrade the vertices of
to generate a new control mesh
such that limit surface of
. It can be shown that the iterative process is convergent for Loop subdivision surfaces. Hence, the method is well-defined. The new method has the advantages of both a local method and a global method, i.e., it can handle meshes of any size and any topology while generating smooth interpolating subdivision surfaces that faithfully resemble the shape of the given meshes.