Abstract Voronoi diagram in 3-space

Constructing the Exact Voronoi Diagram of Arbitrary Lines in Space

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Space Allocation of Educational Centers Using Multiplicatively Weighted Voronoi Diagram

The main problem of educational centers in a mega city like Tehran, capital of Iran, is that no enforced service areas exist to guide school selection or allow students to make the most convenient commutes to the nearest schools. Without the defined school service areas, parents seeking better and more reputable schools often have no choice but to send children to schools outside the local area...

Time - Based Voronoi Diagram ∗

We consider a variation of Voronoi diagram, or time-based Voronoi diagram, for a set S of points in the presence of transportation lines or highways in the plane. A shortest time-distance path from a query point to any given point in S is a path that takes the least travelling time. The travelling speeds and hence travelling times of the subpaths along the highways and in the plane are differen...

Rounding Voronoi Diagram

Computational geometry classically assumes real-number arithmetic which does not exist in actual computers. A solution consists in using integer coordinates for data and exact arithmetic for computations. This approach implies that if the results of an algorithm are the input of another, these results must be rounded to match this hypothesis of integer coordinates. In this paper, we treat the c...

On the Expected Complexity of the 3-dimensional Voronoi Diagram