Systems and methods for computing three-dimensional (3D) Euclidean Voronoi diagrams are disclosed. For some embodiments, a set of 3D objects is accessed, in which each 3D object is mathematically defined. Thereafter, a Voronoi region associated with each of the 3D objects is computed, thereby resulting in a complete Euclidean Voronoi diagram of the set of 3D objects. In some embodiments, the 3D objects are spheres, each of which is defined by a center and a radius. For other embodiments, the 3D objects are convex objects, each of which is mathematically-definable (e.g., cylinders, sphero-cylinders, etc.). Unlike prior approaches that suggested using a numerical approach to computing the Voronoi diagram, the present disclosure employs mathematical approaches for computing the Euclidean Voronoi diagram, thereby improving efficiency in the computation of the Euclidean Voronoi diagram.
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