<s>
Laplacian	B-Algorithm
smoothing	I-Algorithm
is	O
an	O
algorithm	O
to	O
smooth	B-Application
a	O
polygonal	B-Algorithm
mesh	I-Algorithm
.	O
</s>
<s>
For	O
each	O
vertex	O
in	O
a	O
mesh	B-Algorithm
,	O
a	O
new	O
position	O
is	O
chosen	O
based	O
on	O
local	O
information	O
(	O
such	O
as	O
the	O
position	O
of	O
neighbours	O
)	O
and	O
the	O
vertex	O
is	O
moved	O
there	O
.	O
</s>
<s>
In	O
the	O
case	O
that	O
a	O
mesh	B-Algorithm
is	O
topologically	O
a	O
rectangular	O
grid	O
(	O
that	O
is	O
,	O
each	O
internal	O
vertex	O
is	O
connected	O
to	O
four	O
neighbours	O
)	O
then	O
this	O
operation	O
produces	O
the	O
Laplacian	O
of	O
the	O
mesh	B-Algorithm
.	O
</s>
<s>
More	O
formally	O
,	O
the	O
smoothing	B-Application
operation	O
may	O
be	O
described	O
per-vertex	O
as	O
:	O
</s>
