<s>
In	O
geometry	O
,	O
a	O
star-shaped	B-Algorithm
polygon	I-Algorithm
is	O
a	O
polygonal	O
region	O
in	O
the	O
plane	O
that	O
is	O
a	O
star	O
domain	O
,	O
that	O
is	O
,	O
a	O
polygon	O
that	O
contains	O
a	O
point	O
from	O
which	O
the	O
entire	O
polygon	O
boundary	O
is	O
visible	B-Algorithm
.	O
</s>
<s>
The	O
set	O
of	O
all	O
points	O
with	O
this	O
property	O
(	O
that	O
is	O
,	O
the	O
set	O
of	O
points	O
from	O
which	O
all	O
of	O
is	O
visible	B-Algorithm
)	O
is	O
called	O
the	O
kernel	B-Algorithm
of	O
.	O
</s>
<s>
If	O
a	O
star-shaped	B-Algorithm
polygon	I-Algorithm
is	O
convex	O
,	O
the	O
link	O
distance	O
between	O
any	O
two	O
of	O
its	O
points	O
(	O
the	O
minimum	O
number	O
of	O
sequential	O
line	O
segments	O
sufficient	O
to	O
connect	O
those	O
points	O
)	O
is	O
1	O
,	O
and	O
so	O
the	O
polygon	O
's	O
link	O
diameter	O
(	O
the	O
maximum	O
link	O
distance	O
over	O
all	O
pairs	O
of	O
points	O
)	O
is	O
1	O
.	O
</s>
<s>
If	O
a	O
star-shaped	B-Algorithm
polygon	I-Algorithm
is	O
not	O
convex	O
,	O
the	O
link	O
distance	O
between	O
a	O
point	O
in	O
the	O
kernel	B-Algorithm
and	O
any	O
other	O
point	O
in	O
the	O
polygon	O
is	O
1	O
,	O
while	O
the	O
link	O
distance	O
between	O
any	O
two	O
points	O
that	O
are	O
in	O
the	O
polygon	O
but	O
outside	O
the	O
kernel	B-Algorithm
is	O
either	O
1	O
or	O
2	O
;	O
in	O
this	O
case	O
the	O
maximum	O
link	O
distance	O
is	O
2	O
.	O
</s>
<s>
Convex	O
polygons	O
are	O
star	O
shaped	O
,	O
and	O
a	O
convex	O
polygon	O
coincides	O
with	O
its	O
own	O
kernel	B-Algorithm
.	O
</s>
<s>
Regular	O
star	O
polygons	O
are	O
star-shaped	O
,	O
with	O
their	O
center	O
always	O
in	O
the	O
kernel	B-Algorithm
.	O
</s>
<s>
Antiparallelograms	O
and	O
self-intersecting	O
Lemoine	O
hexagons	O
are	O
star-shaped	O
,	O
with	O
the	O
kernel	B-Algorithm
consisting	O
of	O
a	O
single	O
point	O
.	O
</s>
<s>
Visibility	B-Algorithm
polygons	I-Algorithm
are	O
star-shaped	O
as	O
every	O
point	O
within	O
them	O
must	O
be	O
visible	B-Algorithm
to	O
the	O
center	O
by	O
definition	O
.	O
</s>
<s>
Testing	O
whether	O
a	O
polygon	O
is	O
star-shaped	O
,	O
and	O
finding	O
a	O
single	O
point	O
in	O
the	O
kernel	B-Algorithm
,	O
may	O
be	O
solved	O
in	O
linear	O
time	O
by	O
formulating	O
the	O
problem	O
as	O
a	O
linear	B-Algorithm
program	I-Algorithm
and	O
applying	O
techniques	O
for	O
low-dimensional	O
linear	B-Algorithm
programming	I-Algorithm
(	O
see	O
,	O
page	O
16	O
)	O
.	O
</s>
<s>
The	O
kernel	B-Algorithm
of	I-Algorithm
a	I-Algorithm
polygon	I-Algorithm
is	O
the	O
intersection	O
of	O
all	O
its	O
interior	O
half-planes	O
.	O
</s>
<s>
The	O
intersection	O
of	O
an	O
arbitrary	O
set	O
of	O
N	O
half-planes	O
may	O
be	O
found	O
in	O
Θ(N log N )	O
time	O
using	O
the	O
divide	B-Algorithm
and	I-Algorithm
conquer	I-Algorithm
approach	I-Algorithm
.	O
</s>
<s>
However	O
,	O
for	O
the	O
case	O
of	O
kernels	B-Algorithm
of	O
polygons	O
,	O
a	O
faster	O
method	O
is	O
possible	O
:	O
presented	O
an	O
algorithm	O
to	O
construct	O
the	O
kernel	B-Algorithm
in	O
linear	O
time	O
.	O
</s>
