Variational sphere set approximation for solid objects |
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Authors: | Rui Wang Kun Zhou John Snyder Xinguo Liu Hujun Bao Qunsheng Peng Baining Guo |
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Affiliation: | 2. State Key Lab of CAD & CG, Zhejiang University, Hangzhou, Zhejiang, P.R. China 1. Microsoft Research Asia, Beijing, China 3. Microsoft Research, Redmond, WA, USA
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Abstract: | We approximate a solid object represented as a triangle mesh by a bounding set of spheres having minimal summed volume outside the object. We show how outside volume for a single sphere can be computed using a simple integration over the object’s triangles. We then minimize the total outside volume over all spheres in the set using a variant of iterative Lloyd clustering that splits the mesh points into sets and bounds each with an outside volume-minimizing sphere. The resulting sphere sets are tighter than those of previous methods. In experiments comparing against a state-of-the-art alternative (adaptive medial axis), our method often requires half as many spheres, or fewer, to obtain the same error, under a variety of error metrics including total outside volume, shadowing fidelity, and proximity measurement. |
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