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Interpolating Subdivisions from Approximating Subdivisions

A subdivision surface is a method of representing a smooth, continuous, seamless surface via the specification of a coarser piecewise linear polygon mesh. In this paper, we propose an innovative unified method for constructing interpolating subdivisions. Our algorithm extends the selected approximating subdivision by merging the merits of other different interpolating functions. By using Loop subdivision and Two-point Linear interpolation as specified approximating subdivision and difference interpolating function respectively, the generated interpolating subdivision is modified Butterfly scheme. In addition, the Butterfly subdivision was also used as an instance of corresponding difference interpolating function. A novel interpolating subdivision scheme, which is named Loop-Butterfly scheme and refers to the features of both Loop and Butterfly subdivision, is introduced in this paper. The Loop-Butterfly subdivision scheme can produce more fairing surface than the Butterfly subdivision only using the initial control points for the final interpolation. The results of our experiments reveal that our method utilizes the advantages of both the approximation subdivision method and the difference interpolating function. The convergence analysis verified that the graph of Loop-Butterfly subdivision is a C 1 continuous surface.