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
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.