Three-dimensional convex hull as a fruitful source of diagrams

The relationship between a three-dimensional convex hull and many important two-dimensional diagrams is surveyed, and a unifying approach to robust software for those diagrams is proposed. In this approach, instead of implementing individual algorithms, we first construct a robust algorithm for the three-dimensional convex hull, and next use it as an oracle for computing the other diagrams. The diagrams computable by this approach include the Voronoi diagram and its farthest-point versions both on the plane and on the sphere, the Laguerre Voronoi diagram and its farthest-point version both on the plane and on the sphere, and the intersection of half-spaces.

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