<s>
A	O
quad-edge	B-Algorithm
data	I-Algorithm
structure	I-Algorithm
is	O
a	O
computer	O
representation	O
of	O
the	O
topology	B-Architecture
of	O
a	O
two-dimensional	O
or	O
three-dimensional	O
map	O
,	O
that	O
is	O
,	O
a	O
graph	O
drawn	O
on	O
a	O
(	O
closed	O
)	O
surface	O
.	O
</s>
<s>
It	O
is	O
a	O
variant	O
of	O
the	O
earlier	O
winged	B-Algorithm
edge	I-Algorithm
data	B-General_Concept
structure	I-General_Concept
.	O
</s>
<s>
The	O
fundamental	O
idea	O
behind	O
the	O
quad-edge	B-Algorithm
structure	O
is	O
the	O
recognition	O
that	O
a	O
single	O
edge	O
,	O
in	O
a	O
closed	O
polygonal	B-Algorithm
mesh	I-Algorithm
topology	B-Architecture
,	O
sits	O
between	O
exactly	O
two	O
faces	O
and	O
exactly	O
two	O
vertices	O
.	O
</s>
<s>
The	O
quad-edge	B-Algorithm
data	I-Algorithm
structure	I-Algorithm
represents	O
an	O
edge	O
,	O
along	O
with	O
the	O
edges	O
it	O
is	O
connected	O
to	O
around	O
the	O
adjacent	O
vertices	O
and	O
faces	O
to	O
encode	O
the	O
topology	B-Architecture
of	O
the	O
graph	O
.	O
</s>
<s>
Each	O
quad-edge	B-Algorithm
contains	O
four	O
references	O
to	O
adjacent	O
quad-edges	B-Algorithm
.	O
</s>
<s>
Each	O
quad-edge	B-Algorithm
reference	O
points	O
to	O
a	O
quad-edge	B-Algorithm
and	O
the	O
rotation	O
(	O
from	O
0	O
to	O
3	O
)	O
of	O
the	O
'	O
arm	O
 '	O
it	O
points	O
at	O
.	O
</s>
<s>
Due	O
to	O
this	O
representation	O
,	O
the	O
quad-edge	B-Algorithm
:	O
</s>
<s>
The	O
quad-edge	B-Algorithm
structure	O
gets	O
its	O
name	O
from	O
the	O
general	O
mechanism	O
by	O
which	O
they	O
are	O
stored	O
.	O
</s>
<s>
Much	O
like	O
Winged	B-Algorithm
Edge	I-Algorithm
,	O
quad-edge	B-Algorithm
structures	O
are	O
used	O
in	O
programs	O
to	O
store	O
the	O
topology	B-Architecture
of	O
a	O
2D	O
or	O
3D	O
polygonal	B-Algorithm
mesh	I-Algorithm
.	O
</s>
<s>
The	O
mesh	B-Algorithm
itself	O
does	O
not	O
need	O
to	O
be	O
closed	O
in	O
order	O
to	O
form	O
a	O
valid	O
quad-edge	B-Algorithm
structure	O
.	O
</s>
<s>
Using	O
a	O
quad-edge	B-Algorithm
structure	O
,	O
iterating	O
through	O
the	O
topology	B-Architecture
is	O
quite	O
easy	O
.	O
</s>
<s>
Often	O
,	O
the	O
interface	O
to	O
quad-edge	B-Algorithm
topologies	B-Architecture
is	O
through	O
directed	O
edges	O
.	O
</s>
