<s>
Bresenham	B-Algorithm
's	I-Algorithm
line	I-Algorithm
algorithm	I-Algorithm
is	O
a	O
line	B-Algorithm
drawing	I-Algorithm
algorithm	I-Algorithm
that	O
determines	O
the	O
points	O
of	O
an	O
n-dimensional	O
raster	B-Algorithm
that	O
should	O
be	O
selected	O
in	O
order	O
to	O
form	O
a	O
close	O
approximation	O
to	O
a	O
straight	O
line	O
between	O
two	O
points	O
.	O
</s>
<s>
on	O
a	O
computer	B-Device
screen	I-Device
)	O
,	O
as	O
it	O
uses	O
only	O
integer	O
addition	O
,	O
subtraction	O
,	O
and	O
bit	O
shifting	O
,	O
all	O
of	O
which	O
are	O
very	O
cheap	O
operations	O
in	O
commonly	O
used	O
computer	O
instruction	B-General_Concept
sets	I-General_Concept
such	O
as	O
x86_64	B-Device
.	O
</s>
<s>
An	O
extension	B-Algorithm
to	O
the	O
original	O
algorithm	O
may	O
be	O
used	O
for	O
drawing	O
circles	O
.	O
</s>
<s>
While	O
algorithms	O
such	O
as	O
Wu	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
are	O
also	O
frequently	O
used	O
in	O
modern	O
computer	O
graphics	O
because	O
they	O
can	O
support	O
antialiasing	B-Algorithm
,	O
Bresenham	B-Algorithm
's	I-Algorithm
line	I-Algorithm
algorithm	I-Algorithm
is	O
still	O
important	O
because	O
of	O
its	O
speed	O
and	O
simplicity	O
.	O
</s>
<s>
The	O
algorithm	O
is	O
used	O
in	O
hardware	O
such	O
as	O
plotters	B-Operating_System
and	O
in	O
the	O
graphics	B-Architecture
chips	I-Architecture
of	O
modern	O
graphics	B-Device
cards	I-Device
.	O
</s>
<s>
It	O
can	O
also	O
be	O
found	O
in	O
many	O
software	O
graphics	B-Library
libraries	I-Library
.	O
</s>
<s>
Because	O
the	O
algorithm	O
is	O
very	O
simple	O
,	O
it	O
is	O
often	O
implemented	O
in	O
either	O
the	O
firmware	B-Application
or	O
the	O
graphics	B-General_Concept
hardware	I-General_Concept
of	O
modern	O
graphics	B-Device
cards	I-Device
.	O
</s>
<s>
Bresenham	B-Algorithm
's	I-Algorithm
line	I-Algorithm
algorithm	I-Algorithm
is	O
named	O
after	O
Jack	O
Elton	O
Bresenham	O
who	O
developed	O
it	O
in	O
1962	O
at	O
IBM	O
.	O
</s>
<s>
A	O
Calcomp	O
plotter	B-Operating_System
had	O
been	O
attached	O
to	O
an	O
IBM	B-Device
1401	I-Device
via	O
the	O
1407	O
typewriter	O
console	O
.	O
</s>
<s>
Bresenham	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
has	O
been	O
extended	O
to	O
produce	O
circles	O
,	O
ellipses	O
,	O
cubic	O
and	O
quadratic	O
bezier	O
curves	O
,	O
as	O
well	O
as	O
native	O
anti-aliased	O
versions	O
of	O
those	O
.	O
</s>
<s>
Bresenham	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
chooses	O
the	O
integer	O
y	O
corresponding	O
to	O
the	O
pixel	O
center	O
that	O
is	O
closest	O
to	O
the	O
ideal	O
(	O
fractional	O
)	O
y	O
for	O
the	O
same	O
x	O
;	O
on	O
successive	O
columns	O
y	O
can	O
remain	O
the	O
same	O
or	O
increase	O
by	O
1	O
.	O
</s>
<s>
To	O
derive	O
Bresenham	B-Algorithm
's	I-Algorithm
algorithm	I-Algorithm
,	O
two	O
steps	O
must	O
be	O
taken	O
.	O
</s>
<s>
The	O
Bresenham	B-Algorithm
algorithm	I-Algorithm
can	O
be	O
interpreted	O
as	O
slightly	O
modified	O
digital	B-Algorithm
differential	I-Algorithm
analyzer	I-Algorithm
(	O
using	O
0.5	O
as	O
error	O
threshold	O
instead	O
of	O
0	O
,	O
which	O
is	O
required	O
for	O
non-overlapping	O
polygon	O
rasterizing	O
)	O
.	O
</s>
<s>
It	O
is	O
possible	O
to	O
use	O
this	O
technique	O
to	O
calculate	O
the	O
U	O
,	O
V	O
co-ordinates	O
during	O
raster	B-Algorithm
scan	O
of	O
texture	O
mapped	O
polygons	O
.	O
</s>
<s>
The	O
voxel	B-Algorithm
heightmap	O
software-rendering	O
engines	O
seen	O
in	O
some	O
PC	O
games	O
also	O
used	O
this	O
principle	O
.	O
</s>
<s>
An	O
extension	B-Algorithm
to	O
the	O
algorithm	O
that	O
handles	O
thick	O
lines	O
was	O
created	O
by	O
Alan	O
Murphy	O
at	O
IBM	O
.	O
</s>
