Voronoi pole

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In geometry, the positive and negative Voronoi poles of a cell in a Voronoi diagram are certain vertices of the diagram.

Definition[edit]

Let be the Voronoi cell of the site . If is bounded then its positive pole is the Voronoi vertex in with maximal distance to the sample point . Furthermore, let be the vector from to the positive pole. If the cell is unbounded, then a positive pole is not defined, and is defined to be a vector in the average direction of all unbounded Voronoi edges of the cell.

The negative pole is the Voronoi vertex in with the largest distance to such that the vector and the vector from to make an angle larger than .

Example[edit]

Example of poles in a Voronoi diagram

Here is the positive pole of and its negative. As the cell corresponding to is unbounded only the negative pole exists.

References[edit]