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We provide a method for improving the parameterization of patching schemes that approximate Catmull-Clark subdivision surfaces, such that the new parameterization conforms better to that of the original subdivision surface. We create this reparameterization in real-time using a method that only depends on the topology of the surface and is independent of the surface's geometry. Our method can handle patches with more than one extraordinary vertex and avoids the combinatorial increase in both complexity and storage associated with multiple extraordinary vertices. Moreover, the reparameterization function is easy to implement and fast. © 2012 Wiley Periodicals, Inc.