Filling an N-sided hole using combined subdivision schemes

A new algorithm is presented for filling n-sided holes. The algorithm generates a subdivision surface which connects smoothly (G) with the surface around the hole. The data to the algorithm consists of n boundary curves and cross boundary derivatives, given in any parametric form. The algorithm is based on Sabin’s variant of CatmullClark scheme [1], which operates in the surface interior. Near the boundary we introduce new subdivision rules that involve the given boundary curves and crossboundary derivatives. The generated subdivision surface is G-continuous except at one extraordinary point. In the neighborhood of this point the surface curvature is bounded. The proposed subdivision scheme falls into the category of combined subdivision schemes, which combine operations on control points with operations on functions. The theory of combined subdivision schemes is used to derive the scheme and to establish its properties.