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- W2128846649 abstract "The volume enclosed by subdivision surfaces, such as Doo-Sabin, Catmull-Clark, and Loop has recently been derived. Moments of higher degree d are more challenging computationally because of the growing number of coefficients in the d + 3-linear forms. We account for the intrinsic symmetries of the tensors, and thereby reduce the complexity of the problem formulation. Our framework allows to compute the 4-linear forms that determine the centroid defined by Doo-Sabin, and Loop surfaces, including Loop with sharp creases. For Doo-Sabin surfaces, we also establish the tensors of rank 5 that determine the inertia for valences 3, and 4. When the subdivision weights are rational, the centroid, and inertia are obtained as exact, symbolic values. In practice, the formulas are restricted to meshes with a certain maximum valence of a vertex." @default.
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- W2128846649 date "2014-08-01" @default.
- W2128846649 modified "2023-09-24" @default.
- W2128846649 title "On Moments of Sets Bounded by Subdivision Surfaces" @default.
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