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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Voronoi Automata
verfasst von : Andrew Adamatzky
Erschienen in: Reaction-Diffusion Automata: Phenomenology, Localisations, Computation
Verlag: Springer Berlin Heidelberg
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Let
P
be a nonempty finite set of planar points. A planar Voronoi diagram [253] of the set
P
is a partition of the plane into such regions, that for any element of
P
, a region corresponding to a unique point
p
contains all those points of the plane which are closer to
p
than to any other node of
P
. A unique region
vor
(
p
) = {
z
∈
R
2
:
d
(
p
,
z
) <
d
(
p
,
m
) ∀
m
∈
R
2
,
m
≠
z
} assigned to point
p
is called a Voronoi cell of the point
p
[211]. The boundary ∂
vor
(
p
) of the Voronoi cell of a point
p
is built of segments of bisectors separating pairs of geographically closest points of the given planar set
P
. A union of
VD
(
P
) = ∪
p
∈
P
∂
vor
(
p
) all boundaries of the Voronoi cells determines the planar Voronoi diagram [211]. A variety of Voronoi diagrams and algorithms of their construction can be found in [162, 206].