<s>
The	O
doubly	B-Data_Structure
connected	I-Data_Structure
edge	I-Data_Structure
list	I-Data_Structure
(	O
DCEL	B-Data_Structure
)	O
,	O
also	O
known	O
as	O
half-edge	B-Data_Structure
data	I-Data_Structure
structure	I-Data_Structure
,	O
is	O
a	O
data	B-General_Concept
structure	I-General_Concept
to	O
represent	O
an	O
embedding	B-Algorithm
of	O
a	O
planar	O
graph	O
in	O
the	O
plane	O
,	O
and	O
polytopes	O
in	O
3D	O
.	O
</s>
<s>
This	O
data	B-General_Concept
structure	I-General_Concept
provides	O
efficient	O
manipulation	O
of	O
the	O
topological	O
information	O
associated	O
with	O
the	O
objects	O
in	O
question	O
(	O
vertices	O
,	O
edges	O
,	O
faces	O
)	O
.	O
</s>
<s>
For	O
example	O
,	O
a	O
Voronoi	B-Architecture
diagram	I-Architecture
is	O
commonly	O
represented	O
by	O
a	O
DCEL	B-Data_Structure
inside	O
a	O
bounding	O
box	O
.	O
</s>
<s>
This	O
data	B-General_Concept
structure	I-General_Concept
was	O
originally	O
suggested	O
by	O
Muller	O
and	O
Preparata	O
for	O
representations	O
of	O
3D	O
convex	O
polyhedra	O
.	O
</s>
<s>
Later	O
,	O
a	O
somewhat	O
different	O
data	B-General_Concept
structure	I-General_Concept
was	O
suggested	O
,	O
but	O
the	O
name	O
"	O
DCEL	B-Data_Structure
"	O
was	O
retained	O
.	O
</s>
<s>
For	O
simplicity	O
,	O
only	O
connected	O
graphs	O
are	O
considered	O
,	O
however	O
the	O
DCEL	B-Data_Structure
structure	O
may	O
be	O
extended	O
to	O
handle	O
disconnected	O
graphs	O
as	O
well	O
by	O
introducing	O
dummy	O
edges	O
between	O
disconnected	O
components	O
.	O
</s>
<s>
DCEL	B-Data_Structure
is	O
more	O
than	O
just	O
a	O
doubly	B-Data_Structure
linked	I-Data_Structure
list	I-Data_Structure
of	O
edges	O
.	O
</s>
<s>
In	O
the	O
general	O
case	O
,	O
a	O
DCEL	B-Data_Structure
contains	O
a	O
record	O
for	O
each	O
edge	O
,	O
vertex	O
and	O
face	O
of	O
the	O
subdivision	O
.	O
</s>
<s>
If	O
the	O
vertices	O
or	O
faces	O
do	O
not	O
hold	O
any	O
interesting	O
information	O
,	O
there	O
is	O
no	O
need	O
to	O
store	O
them	O
,	O
thus	O
saving	O
space	O
and	O
reducing	O
the	O
data	B-General_Concept
structure	I-General_Concept
's	O
complexity	O
.	O
</s>
