Loop, CharlesRoberto Scopigno and Denis Zorin2014-01-292014-01-2920043-905673-13-41727-8384https://doi.org/10.2312/SGP/SGP04/169-178Catmull & Clark subdivision is now a standard for smooth free-form surface modeling. These surfaces are everywhere curvature continuous except at points corresponding to vertices not incident on four edges. While the surface has a continuous tangent plane at such a point, the lack of curvature continuity presents a severe problem for many applications. Topologically, each n-valent extraordinary vertex of a Catmull & Clark limit surface corresponds to an n-sided hole in the underlying 2-manifold represented by the control mesh. The problem we address here is: How to fill such a hole in a Catmull & Clark surface with exactly n tensor product patches that meet the surrounding bicubic patch network and each other with second order continuity. We convert the problem of filling the hole with n tensor product patches in the spatial domain into the problem of filling the hole in the n frequency modes with a single bidegree 7 tensor product patch.Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Curve, surface, solid, and object representations