In geometry, the positive and negative Voronoi poles of a cell in a Voronoi diagram are certain vertices of the diagram.
Let V p be the Voronoi cell of the site p ∈ P . If V p is bounded then its positive pole is the Voronoi vertex in V p with maximal distance to the sample point p . Furthermore, let u ¯ be the vector from p to the positive pole. If the cell is unbounded, then a positive pole is not defined, and u ¯ 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 v in V p with the largest distance to p such that the vector u ¯ and the vector from p to v make an angle larger than π 2 .
Here x is the positive pole of V p and y its negative. As the cell corresponding to q is unbounded only the negative pole z exists.
