Primitives for the manipulation of general subdivisions and the computation of Voronoi

@article{Guibas1985PrimitivesFT,
  title={Primitives for the manipulation of general subdivisions and the computation of Voronoi},
  author={Leonidas J. Guibas and Jorge Stolfi},
  journal={ACM Trans. Graph.},
  year={1985},
  volume={4},
  pages={74-123}
}
The following problem is discussed: given n points in the plane (the sites) and an arbitrary query point q, find the site that is closest to q. This problem can be solved by constructing the Voronoi diagram of the griven sites and then locating the query point inone of its regions. Two algorithms are given, one that constructs the Voronoi diagram in O(n log n) time, and another that inserts a new sit on O(n) time. Both are based on the use of the Voronoi dual, or Delaunay triangulation, and are… 
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