<s>
In	O
computational	O
geometry	O
,	O
a	O
fan	B-Algorithm
triangulation	I-Algorithm
is	O
a	O
simple	O
way	O
to	O
triangulate	B-Algorithm
a	O
polygon	B-General_Concept
by	O
choosing	O
a	O
vertex	O
and	O
drawing	O
edges	O
to	O
all	O
of	O
the	O
other	O
vertices	O
of	O
the	O
polygon	B-General_Concept
.	O
</s>
<s>
Not	O
every	O
polygon	B-General_Concept
can	O
be	O
triangulated	O
this	O
way	O
,	O
so	O
this	O
method	O
is	O
usually	O
only	O
used	O
for	O
convex	O
polygons	B-General_Concept
.	O
</s>
<s>
Aside	O
from	O
the	O
properties	O
of	O
all	O
triangulations	O
,	O
fan	B-Algorithm
triangulations	I-Algorithm
have	O
the	O
following	O
properties	O
:	O
</s>
<s>
All	O
convex	O
polygons	B-General_Concept
,	O
but	O
not	O
all	O
polygons	B-General_Concept
,	O
can	O
be	O
fan	O
triangulated	O
.	O
</s>
<s>
Polygons	B-General_Concept
with	O
only	O
one	O
concave	O
vertex	O
can	O
always	O
be	O
fan	O
triangulated	O
,	O
as	O
long	O
as	O
the	O
diagonals	O
are	O
drawn	O
from	O
the	O
concave	O
vertex	O
.	O
</s>
<s>
It	O
can	O
be	O
known	O
if	O
a	O
polygon	B-General_Concept
can	O
be	O
fan	O
triangulated	O
by	O
solving	O
the	O
Art	O
gallery	O
problem	O
,	O
in	O
order	O
to	O
determine	O
whether	O
there	O
is	O
at	O
least	O
one	O
vertex	O
that	O
is	O
visible	O
from	O
every	O
point	O
in	O
the	O
polygon	B-General_Concept
.	O
</s>
<s>
The	O
triangulation	O
of	O
a	O
polygon	B-General_Concept
with	O
vertices	O
uses	O
diagonals	O
,	O
and	O
generates	O
triangles	O
.	O
</s>
<s>
As	O
such	O
,	O
it	O
is	O
unnecessary	O
to	O
explicitly	O
store	O
the	O
list	O
of	O
triangles	O
,	O
and	O
therefore	O
,	O
many	O
graphical	O
libraries	O
implement	O
primitives	O
to	O
represent	O
polygons	B-General_Concept
based	O
on	O
this	O
triangulation	O
.	O
</s>
