Loop Subdivision Surface Based Progressive Interpolation

A new method for constructing interpolating Loop subdivision surfaces ispresented. The new method is an extension of the progressiveinterpolation technique for B-splines. Given a triangular mesh M, theidea is to iteratively upgrade the vertices of M to generate a newcontrol mesh \ovM such that limit surface of \ovM wouldinterpolate M. It can be shown that the iterative process isconvergent for Loop subdivision surfaces. Hence, the method iswell-defined. The new method has the advantages of both a local methodand a global method, i.e., it can handle meshes of any size and anytopology while generating smooth interpolating subdivision surfaces thatfaithfully resemble the shape of the given meshes. The meshes consideredhere can be open or closed.