<s>
In	O
computational	O
geometry	O
,	O
a	O
sweep	B-Algorithm
line	I-Algorithm
algorithm	I-Algorithm
or	O
plane	B-Algorithm
sweep	I-Algorithm
algorithm	O
is	O
an	O
algorithmic	B-Algorithm
paradigm	I-Algorithm
that	O
uses	O
a	O
conceptual	O
sweep	B-Algorithm
line	I-Algorithm
or	O
sweep	O
surface	O
to	O
solve	O
various	O
problems	O
in	O
Euclidean	O
space	O
.	O
</s>
<s>
Geometric	O
operations	O
are	O
restricted	O
to	O
geometric	O
objects	O
that	O
either	O
intersect	O
or	O
are	O
in	O
the	O
immediate	O
vicinity	O
of	O
the	O
sweep	B-Algorithm
line	I-Algorithm
whenever	O
it	O
stops	O
,	O
and	O
the	O
complete	O
solution	O
is	O
available	O
once	O
the	O
line	O
has	O
passed	O
over	O
all	O
objects	O
.	O
</s>
<s>
This	O
approach	O
may	O
be	O
traced	O
to	O
scanline	B-Algorithm
algorithms	I-Algorithm
of	O
rendering	O
in	O
computer	O
graphics	O
,	O
followed	O
by	O
exploiting	O
this	O
approach	O
in	O
early	O
algorithms	O
of	O
integrated	O
circuit	O
layout	O
design	O
,	O
in	O
which	O
a	O
geometric	O
description	O
of	O
an	O
IC	O
was	O
processed	O
in	O
parallel	O
strips	O
because	O
the	O
entire	O
description	O
could	O
not	O
fit	O
into	O
memory	O
.	O
</s>
<s>
Application	O
of	O
this	O
approach	O
led	O
to	O
a	O
breakthrough	O
in	O
the	O
computational	B-General_Concept
complexity	I-General_Concept
of	O
geometric	O
algorithms	O
when	O
Shamos	O
and	O
Hoey	O
presented	O
algorithms	O
for	O
line	O
segment	O
intersection	O
in	O
the	O
plane	O
,	O
and	O
in	O
particular	O
,	O
they	O
described	O
how	O
a	O
combination	O
of	O
the	O
scanline	O
approach	O
with	O
efficient	O
data	O
structures	O
(	O
self-balancing	B-Data_Structure
binary	I-Data_Structure
search	I-Data_Structure
trees	I-Data_Structure
)	O
makes	O
it	O
possible	O
to	O
detect	O
whether	O
there	O
are	O
intersections	O
among	O
segments	O
in	O
the	O
plane	O
in	O
time	O
complexity	O
of	O
.	O
</s>
<s>
The	O
closely	O
related	O
Bentley	B-Algorithm
–	I-Algorithm
Ottmann	I-Algorithm
algorithm	I-Algorithm
uses	O
a	O
sweep	B-Algorithm
line	I-Algorithm
technique	O
to	O
report	O
all	O
intersections	O
among	O
any	O
segments	O
in	O
the	O
plane	O
in	O
time	O
complexity	O
of	O
and	O
space	O
complexity	O
of	O
.	O
</s>
<s>
Since	O
then	O
,	O
this	O
approach	O
has	O
been	O
used	O
to	O
design	O
efficient	O
algorithms	O
for	O
a	O
number	O
of	O
problems	O
,	O
such	O
as	O
the	O
construction	O
of	O
the	O
Voronoi	B-Architecture
diagram	I-Architecture
(	O
Fortune	O
's	O
algorithm	O
)	O
and	O
the	O
Delaunay	B-Algorithm
triangulation	I-Algorithm
or	O
boolean	B-Algorithm
operations	I-Algorithm
on	I-Algorithm
polygons	I-Algorithm
.	O
</s>
<s>
Topological	O
sweeping	O
is	O
a	O
form	O
of	O
plane	B-Algorithm
sweep	I-Algorithm
with	O
a	O
simple	O
ordering	O
of	O
processing	O
points	O
,	O
which	O
avoids	O
the	O
necessity	O
of	O
completely	O
sorting	O
the	O
points	O
;	O
it	O
allows	O
some	O
sweep	B-Algorithm
line	I-Algorithm
algorithms	I-Algorithm
to	O
be	O
performed	O
more	O
efficiently	O
.	O
</s>
<s>
The	O
rotating	B-Algorithm
calipers	I-Algorithm
technique	O
for	O
designing	O
geometric	O
algorithms	O
may	O
also	O
be	O
interpreted	O
as	O
a	O
form	O
of	O
the	O
plane	B-Algorithm
sweep	I-Algorithm
,	O
in	O
the	O
projective	O
dual	O
of	O
the	O
input	O
plane	O
:	O
a	O
form	O
of	O
projective	O
duality	O
transforms	O
the	O
slope	O
of	O
a	O
line	O
in	O
one	O
plane	O
into	O
the	O
x-coordinate	O
of	O
a	O
point	O
in	O
the	O
dual	O
plane	O
,	O
so	O
the	O
progression	O
through	O
lines	O
in	O
sorted	O
order	O
by	O
their	O
slope	O
as	O
performed	O
by	O
a	O
rotating	B-Algorithm
calipers	I-Algorithm
algorithm	O
is	O
dual	O
to	O
the	O
progression	O
through	O
points	O
sorted	O
by	O
their	O
x-coordinates	O
in	O
a	O
plane	B-Algorithm
sweep	I-Algorithm
algorithm	O
.	O
</s>
