Abstract
This paper develops new refinement rules for non-uniform Catmull-Clark surfaces that produce G 1 extraordinary points whose blending functions have a single local maximum. The method consists of designing an "eigen polyhedron" in R 2 for each extraordinary point, and formulating refinement rules for which refinement of the eigen polyhedron reduces to a scale and translation. These refinement rules, when applied to a non-uniform Catmull-Clark control mesh in R 3 , yield a G 1 extraordinary point.
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