<s>
A	O
face	O
of	O
a	O
polyhedron	O
is	O
a	O
planar	O
polygon	B-General_Concept
bounded	O
by	O
straight	O
line	O
segments	O
,	O
called	O
edges	O
.	O
</s>
<s>
Curved	O
surfaces	O
are	O
usually	O
approximated	O
by	O
a	O
polygon	B-Algorithm
mesh	I-Algorithm
.	O
</s>
<s>
Computer	O
programs	O
for	O
line	B-Algorithm
drawings	I-Algorithm
of	O
opaque	O
objects	O
must	O
be	O
able	O
to	O
decide	O
which	O
edges	O
or	O
which	O
parts	O
of	O
the	O
edges	O
are	O
hidden	O
by	O
an	O
object	O
itself	O
or	O
by	O
other	O
objects	O
,	O
so	O
that	O
those	O
edges	O
can	O
be	O
clipped	B-Algorithm
during	O
rendering	O
.	O
</s>
<s>
This	O
problem	O
is	O
known	O
as	O
hidden-line	B-Algorithm
removal	I-Algorithm
.	O
</s>
<s>
Problem	O
number	O
seven	O
was	O
"	O
hidden-line	B-Algorithm
removal	I-Algorithm
"	O
.	O
</s>
<s>
in	O
computer-aided	B-Application
design	I-Application
,	O
can	O
have	O
thousands	O
or	O
millions	O
of	O
edges	O
.	O
</s>
<s>
Problem	O
sizes	O
for	O
hidden-line	B-Algorithm
removal	I-Algorithm
are	O
the	O
total	O
number	O
of	O
the	O
edges	O
of	O
the	O
model	O
and	O
the	O
total	O
number	O
of	O
the	O
visible	O
segments	O
of	O
the	O
edges	O
.	O
</s>
<s>
In	O
1988	O
Devai	O
proposed	O
an	O
O(log n )	O
-time	O
parallel	O
algorithm	O
using	O
n2	O
processors	O
for	O
the	O
hidden-line	O
problem	O
under	O
the	O
concurrent	B-Operating_System
read	I-Operating_System
,	I-Operating_System
exclusive	I-Operating_System
write	I-Operating_System
(	O
CREW	O
)	O
parallel	B-Operating_System
random-access	I-Operating_System
machine	I-Operating_System
(	O
PRAM	O
)	O
model	O
of	O
computation	O
.	O
</s>
<s>
Hidden-surface	O
algorithms	O
can	O
be	O
used	O
for	O
hidden-line	B-Algorithm
removal	I-Algorithm
,	O
but	O
not	O
the	O
other	O
way	O
around	O
.	O
</s>
<s>
Reif	O
and	O
Sen	O
proposed	O
an	O
O(log4 n )	O
-time	O
algorithm	O
for	O
the	O
hidden-surface	O
problem	O
,	O
using	O
O( ( n	O
+	O
v	O
)	O
/log	O
n	O
)	O
CREW	B-Operating_System
PRAM	I-Operating_System
processors	O
for	O
a	O
restricted	O
model	O
of	O
polyhedral	O
terrains	O
,	O
where	O
v	O
is	O
the	O
output	O
size	O
.	O
</s>
<s>
The	O
hidden-surface	O
algorithm	O
,	O
using	O
n2/log	O
n	O
CREW	B-Operating_System
PRAM	I-Operating_System
processors	O
,	O
is	O
work-optimal	O
.	O
</s>
<s>
The	O
hidden-line	O
algorithm	O
uses	O
n2	O
exclusive	B-Operating_System
read	I-Operating_System
,	I-Operating_System
exclusive	I-Operating_System
write	I-Operating_System
(	O
EREW	B-Operating_System
)	O
PRAM	O
processors	O
.	O
</s>
<s>
The	O
EREW	B-Operating_System
model	O
is	O
the	O
PRAM	O
variant	O
closest	O
to	O
real	O
machines	O
.	O
</s>
