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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Wang, R., Zhou, K., Snyder, J. et al. Variational sphere set approximation for solid objects. Visual Comput 22, 612–621 (2006). https://doi.org/10.1007/s00371-006-0052-0
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DOI: https://doi.org/10.1007/s00371-006-0052-0