The Visual Computer

, Volume 3, Issue 6, pp 323–328

Computing the volume of the union of spheres

  • David Avis
  • Binay K. Bhattacharya
  • Hiroshi Imai
Article

DOI: 10.1007/BF01901190

Cite this article as:
Avis, D., Bhattacharya, B.K. & Imai, H. The Visual Computer (1988) 3: 323. doi:10.1007/BF01901190

Abstract

OnO(n2) 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.

Key words

Union of SpheresVolumesLaguerre Voronoid diagramPower diagram

Copyright information

© Springer-Verlag 1988

Authors and Affiliations

  • David Avis
    • 1
  • Binay K. Bhattacharya
    • 2
  • Hiroshi Imai
    • 3
  1. 1.School of Computer ScienceMcGill UniversityMontrealCanada
  2. 2.School of Computer ScienceSimon Fraser UniversityBurnabyCanada
  3. 3.Department of Computer Science and Communication EngineeringKyushu UniversityFukuokaJapan