<s>
In	O
solid	O
modeling	O
and	O
computer-aided	B-Application
design	I-Application
,	O
the	O
Euler	B-Algorithm
operators	I-Algorithm
modify	O
the	O
graph	O
of	O
connections	O
to	O
add	O
or	O
remove	O
details	O
of	O
a	O
mesh	B-Algorithm
while	O
preserving	O
its	O
topology	O
.	O
</s>
<s>
He	O
chose	O
a	O
set	O
of	O
operators	O
sufficient	O
to	O
create	O
useful	O
meshes	B-Algorithm
,	O
some	O
lose	O
information	O
and	O
so	O
are	O
not	O
invertible	O
.	O
</s>
<s>
The	O
boundary	B-Algorithm
representation	I-Algorithm
for	O
a	O
solid	O
object	O
,	O
its	O
surface	O
,	O
is	O
a	O
polygon	B-Algorithm
mesh	I-Algorithm
of	O
vertices	O
,	O
edges	O
and	O
faces	O
.	O
</s>
<s>
A	O
given	O
mesh	B-Algorithm
may	O
actually	O
contain	O
multiple	O
unconnected	O
shells	O
(	O
or	O
bodies	O
)	O
;	O
each	O
body	O
may	O
be	O
partitioned	O
into	O
multiple	O
connected	O
components	O
each	O
defined	O
by	O
their	O
edge	O
loop	O
boundary	O
.	O
</s>
<s>
The	O
Euler	B-Algorithm
operators	I-Algorithm
preserve	O
this	O
characteristic	O
.	O
</s>
<s>
Euler	B-Algorithm
operators	I-Algorithm
modify	O
the	O
mesh	B-Algorithm
's	O
graph	O
creating	O
or	O
removing	O
faces	O
,	O
edges	O
and	O
vertices	O
according	O
to	O
simple	O
rules	O
while	O
preserving	O
the	O
overall	O
topology	O
thus	O
maintaining	O
a	O
valid	O
boundary	O
(	O
i.e.	O
</s>
