Curvature Smoothness of Subdivision Surfaces
نویسنده
چکیده
We examine the smoothness properties of the principal curvatures of subdivision surfaces near extraordinary points. In particular we give an estimate of their Lp class based on the eigen structure of the subdivision matrix. As a result we can show that the popular Loop and Catmull-Clark schemes (among many others) have square integrable principal curvatures justifying their use as shape functions in FEM treatments of the thin shell equations.
منابع مشابه
A Degree Estimate for PolynomialSubdivision Surfaces of Higher RegularitybyUlrich
Subdivision algorithms can be used to construct smooth surfaces from control meshes of arbitrary topological structure. However, in contrast to tangent plane continuity, which is well understood, very little is known about the generation of subdivision surfaces of higher regularity. This work presents an estimate for piecewise polynomial subdivision surfaces by pointing out that curvature conti...
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