An explicit solution for computing the Euclidean d-dimensional Voronoi diagram of spheres in a floating-point arithmetic

Authors:
M. L. Gavrilova
Affiliations:
Dept of Comp. Science, University of Calgary, Calgary, AB, Canada
Venue:
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Year:
2003

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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.