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.
