Abstract
OnO(n 2) exact algorithm is given for computing the volume of a set ofn spheres in space. The algorithm employs the Laguerre Voronoi (power) diagram and a method for computing the volume of the intersection of a simplex and a sphere exactly. We give a new proof of a special case of a conjecture, popularized by Klee, concerning the change in volume as the centres of the spheres become further apart.
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Avis, D., Bhattacharya, B.K. & Imai, H. Computing the volume of the union of spheres. The Visual Computer 3, 323–328 (1988). https://doi.org/10.1007/BF01901190
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DOI: https://doi.org/10.1007/BF01901190