<s>
In	O
mathematics	O
,	O
a	O
weighted	B-Application
Voronoi	I-Application
diagram	I-Application
in	O
n	O
dimensions	O
is	O
a	O
generalization	O
of	O
a	O
Voronoi	B-Architecture
diagram	I-Architecture
.	O
</s>
<s>
The	O
Voronoi	B-Architecture
cells	I-Architecture
in	O
a	O
weighted	B-Application
Voronoi	I-Application
diagram	I-Application
are	O
defined	O
in	O
terms	O
of	O
a	O
distance	O
function	O
.	O
</s>
<s>
In	O
weighted	B-Application
Voronoi	I-Application
diagrams	I-Application
,	O
each	O
site	O
has	O
a	O
weight	O
that	O
influences	O
the	O
distance	O
computation	O
.	O
</s>
<s>
The	O
idea	O
is	O
that	O
larger	O
weights	O
indicate	O
more	O
important	O
sites	O
,	O
and	O
such	O
sites	O
will	O
get	O
bigger	O
Voronoi	B-Architecture
cells	I-Architecture
.	O
</s>
<s>
In	O
a	O
multiplicatively	O
weighted	B-Application
Voronoi	I-Application
diagram	I-Application
,	O
the	O
distance	O
between	O
a	O
point	O
and	O
a	O
site	O
is	O
divided	O
by	O
the	O
(	O
positive	O
)	O
weight	O
of	O
the	O
site	O
.	O
</s>
<s>
In	O
the	O
plane	O
under	O
the	O
ordinary	O
Euclidean	O
distance	O
,	O
the	O
multiplicatively	O
weighted	B-Application
Voronoi	I-Application
diagram	I-Application
is	O
also	O
called	O
circular	O
Dirichlet	B-Architecture
tessellation	I-Architecture
and	O
its	O
edges	O
are	O
circular	O
arcs	O
and	O
straight	O
line	O
segments	O
.	O
</s>
<s>
A	O
Voronoi	B-Architecture
cell	I-Architecture
may	O
be	O
non-convex	O
,	O
disconnected	O
and	O
may	O
have	O
holes	O
.	O
</s>
<s>
Since	O
crystals	O
may	O
grow	O
in	O
empty	O
space	O
only	O
and	O
are	O
continuous	O
objects	O
,	O
a	O
natural	O
variation	O
is	O
the	O
crystal	O
Voronoi	B-Architecture
diagram	I-Architecture
,	O
in	O
which	O
the	O
cells	O
are	O
defined	O
somewhat	O
differently	O
.	O
</s>
<s>
In	O
an	O
additively	O
weighted	B-Application
Voronoi	I-Application
diagram	I-Application
,	O
weights	O
are	O
subtracted	O
from	O
the	O
distances	O
.	O
</s>
<s>
In	O
the	O
plane	O
under	O
the	O
ordinary	O
Euclidean	O
distance	O
this	O
diagram	O
is	O
also	O
known	O
as	O
the	O
hyperbolic	O
Dirichlet	B-Architecture
tessellation	I-Architecture
and	O
its	O
edges	O
are	O
arcs	O
of	O
hyperbolas	O
and	O
straight	O
line	O
segments	O
.	O
</s>
<s>
The	O
power	B-Application
diagram	I-Application
is	O
defined	O
when	O
weights	O
are	O
subtracted	O
from	O
the	O
squared	O
Euclidean	O
distance	O
.	O
</s>
