An Explicit Solution for Computing the Euclidean d-dimensional Voronoi Diagram of Spheres in a Floating-Point Arithmetic

  • M. L. Gavrilova
Conference paper

DOI: 10.1007/3-540-44842-X_84

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2669)
Cite this paper as:
Gavrilova M.L. (2003) An Explicit Solution for Computing the Euclidean d-dimensional Voronoi Diagram of Spheres in a Floating-Point Arithmetic. In: Kumar V., Gavrilova M.L., Tan C.J.K., L’Ecuyer P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg

Abstract

The problem of computing a d-dimensional Euclidean Voronoi diagram of spheres is relevant to many areas, including computer simulation, motion planning, CAD, and computer graphics. This paper presents a new algorithm based on the explicit computation of the coordinates and radii of Euclidean Voronoi diagram vertices for a set of spheres. The algorithm is further applied to compute the Voronoi diagram with a specified precision in a fixed length floating-point arithmetic. The algorithm is implemented using the ECLibrary (Exact Computation Library) and tested on the example of a 3-dimensional Voronoi diagram of a set of spheres.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • M. L. Gavrilova
    • 1
  1. 1.Dept of Comp. ScienceUniversity of CalgaryCalgaryCanada

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