This paper offers a general formula for surface subdivision rules for quad meshes by using 2-D Lagrange interpolating polynomial . We also see that the result obtained is equivalent to the tensor product of (2N + 4)-point n-ary interpolating curve scheme for N ≥ 0 and n ≥ 2. The simple interpolatory subdivision scheme for quadrilateral nets with arbitrary topology is presented by L. Kobbelt , which can be directly calculated from the proposed formula. Furthermore, some characteristics and applications of the proposed work are also discussed.
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