| The Visual Computer manuscript No. (will be inserted by the editor) (2008) | |||||||||||||||
Abstract | |||||||||||||||
| 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 which 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 or fewer as many spheres to obtain the same error, under a variety of error metrics including total outside volume, shadowing fidelity, and proximity measurement. 1 | |||||||||||||||
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