Subdivision surfaces for scattered-data approximation

We propose a modified Loop subdivision surface scheme for the approximation of scattered data in the plane. Starting with a triangulated set of scattered data with associated function values, our scheme applies linear, stationary subdivision rules resulting in a hierarchy of triangulations that converge rapidly to a smooth limit surface. The novelty of our scheme is that it applies subdivision only to the ordinates of control points, whereas the triangulated mesh in the plane is fixed. Our subdivision scheme defines locally supported, bivariate basis functions and provides multiple levels of approximation with triangles. We use our subdivision scheme for terrain modeling.