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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. Ourdoi:10.1007/978-3-7091-6215-6_7 fatcat:b5rreyfhjfdjnizamchmtdum2e