# Voronoi pole

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

## Definition

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

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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