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Voronoi Diagram Distances

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Encyclopedia of Distances

Abstract

Given a finite set A of objects A i in a space S, computing the Voronoi diagram of A means partitioning the space S into Voronoi regions V(A i ) in such a way that V(A i ) contains all points of S that are “closer” to A i than to any other object A j in A.

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References

  1. Aichholzer O., Aurenhammer F., Chen D.Z., Lee D.T., Mukhopadhyay A. and Papadopoulou E. Voronoi Diagrams for Direction-Sensitive Distances, in Proc. 13th Symposium on Computational Geometry, ACM Press, New York, 1997

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  2. Klein R. Concrete and Abstract Voronoi Diagrams, Lecture Notes in Computer Science, Springer, Berlin, 1989.

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  3. Nishida T. and Sugihara K. FEM-Like Fast Marching Method for the Computation of the Boat–Sail Distance and the Associated Voronoi Diagram, Technical Reports, METR 2003-45, Dept. Math. Informatics, The University of Tokyo, 2003.

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  4. Okabe A., Boots B. and Sugihara K. Spatial Tessellation: Concepts and Applications of Voronoi Diagrams, Wiley, New York, 1992

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Deza, M.M., Deza, E. (2013). Voronoi Diagram Distances. In: Encyclopedia of Distances. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30958-8_20

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