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


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 Spheres Volumes Laguerre Voronoid diagram Power diagram 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations