# Voronoi pole

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Given a point set and the corresponding Voronoi diagram, then for each cell at most two poles are defined, namely the *positive* and *negative* poles.

## Definition

Let be the corresponding cell of the point . 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

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

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