<s>
In	O
computer	O
graphics	O
,	O
mipmaps	B-Data_Structure
(	O
also	O
MIP	B-Data_Structure
maps	I-Data_Structure
)	O
or	O
pyramids	B-Algorithm
are	O
pre-calculated	O
,	O
optimized	O
sequences	O
of	O
images	B-Algorithm
,	O
each	O
of	O
which	O
is	O
a	O
progressively	O
lower	O
resolution	B-Algorithm
representation	O
of	O
the	O
previous	O
.	O
</s>
<s>
The	O
height	O
and	O
width	O
of	O
each	O
image	O
,	O
or	O
level	O
,	O
in	O
the	O
mipmap	B-Data_Structure
is	O
a	O
factor	O
of	O
two	O
smaller	O
than	O
the	O
previous	O
level	O
.	O
</s>
<s>
Mipmaps	B-Data_Structure
do	O
not	O
have	O
to	O
be	O
square	O
.	O
</s>
<s>
They	O
are	O
intended	O
to	O
increase	O
rendering	O
speed	O
and	O
reduce	O
aliasing	B-Error_Name
artifacts	O
.	O
</s>
<s>
A	O
high-resolution	B-Algorithm
mipmap	B-Data_Structure
image	O
is	O
used	O
for	O
high-density	O
samples	O
,	O
such	O
as	O
for	O
objects	O
close	O
to	O
the	O
camera	O
;	O
lower-resolution	O
images	B-Algorithm
are	O
used	O
as	O
the	O
object	O
appears	O
farther	O
away	O
.	O
</s>
<s>
This	O
is	O
a	O
more	O
efficient	O
way	O
of	O
downfiltering	O
(	O
minifying	O
)	O
a	O
texture	O
than	O
sampling	O
all	O
texels	O
in	O
the	O
original	O
texture	O
that	O
would	O
contribute	O
to	O
a	O
screen	O
pixel	B-Algorithm
;	O
it	O
is	O
faster	O
to	O
take	O
a	O
constant	O
number	O
of	O
samples	O
from	O
the	O
appropriately	O
downfiltered	O
textures	O
.	O
</s>
<s>
Mipmaps	B-Data_Structure
are	O
widely	O
used	O
in	O
3D	O
computer	O
games	O
,	O
flight	B-Application
simulators	I-Application
,	O
other	O
3D	O
imaging	O
systems	O
for	O
texture	O
filtering	O
,	O
and	O
2D	O
and	O
3D	O
GIS	B-Application
software	I-Application
.	O
</s>
<s>
Their	O
use	O
is	O
known	O
as	O
mipmapping	B-Data_Structure
.	O
</s>
<s>
Since	O
mipmaps	B-Data_Structure
,	O
by	O
definition	O
,	O
are	O
pre-allocated	B-General_Concept
,	O
additional	O
storage	B-General_Concept
space	I-General_Concept
is	O
required	O
to	O
take	O
advantage	O
of	O
them	O
.	O
</s>
<s>
Mipmap	B-Data_Structure
textures	O
are	O
used	O
in	O
3D	O
scenes	O
to	O
decrease	O
the	O
time	O
required	O
to	O
render	O
a	O
scene	O
.	O
</s>
<s>
They	O
also	O
improve	O
image	B-Algorithm
quality	I-Algorithm
by	O
reducing	O
aliasing	B-Error_Name
and	O
Moiré	O
patterns	O
that	O
occur	O
at	O
large	O
viewing	O
distances	O
,	O
at	O
the	O
cost	O
of	O
33%	O
more	O
memory	O
per	O
texture	O
.	O
</s>
<s>
Mipmaps	B-Data_Structure
are	O
used	O
for	O
:	O
</s>
<s>
Improving	O
image	B-Algorithm
quality	I-Algorithm
.	O
</s>
<s>
Speeding	O
up	O
rendering	O
times	O
,	O
either	O
by	O
reducing	O
the	O
number	O
of	O
texels	O
sampled	O
to	O
render	O
each	O
pixel	B-Algorithm
,	O
or	O
increasing	O
the	O
memory	O
locality	O
of	O
the	O
samples	O
taken	O
;	O
</s>
<s>
Reducing	O
stress	O
on	O
the	O
GPU	B-Architecture
or	O
CPU	B-Device
.	O
</s>
<s>
Mipmapping	B-Data_Structure
was	O
invented	O
by	O
Lance	O
Williams	O
in	O
1983	O
and	O
is	O
described	O
in	O
his	O
paper	O
Pyramidal	O
parametrics	O
.	O
</s>
<s>
From	O
the	O
abstract	O
:	O
"	O
This	O
paper	O
advances	O
a	O
'	O
pyramidal	O
parametric	O
 '	O
prefiltering	O
and	O
sampling	O
geometry	O
which	O
minimizes	O
aliasing	B-Error_Name
effects	O
and	O
assures	O
continuity	O
within	O
and	O
between	O
target	O
images.	O
"	O
</s>
<s>
The	O
referenced	O
pyramid	B-Algorithm
can	O
be	O
imagined	O
as	O
the	O
set	O
of	O
mipmaps	B-Data_Structure
stacked	O
in	O
front	O
of	O
each	O
other	O
.	O
</s>
<s>
The	O
origin	O
of	O
the	O
term	O
mipmap	B-Data_Structure
is	O
an	O
initialism	O
of	O
the	O
Latin	O
phrase	O
multum	O
in	O
parvo	O
(	O
"	O
much	O
in	O
a	O
small	O
space	O
"	O
)	O
,	O
and	O
map	O
,	O
modeled	O
on	O
bitmap	O
.	O
</s>
<s>
The	O
term	O
pyramids	B-Algorithm
is	O
still	O
commonly	O
used	O
in	O
a	O
GIS	B-Application
context	O
.	O
</s>
<s>
In	O
GIS	B-Application
software	I-Application
,	O
pyramids	B-Algorithm
are	O
primarily	O
used	O
for	O
speeding	O
up	O
rendering	O
times	O
.	O
</s>
<s>
Each	O
bitmap	O
image	O
of	O
the	O
mipmap	B-Data_Structure
set	O
is	O
a	O
downsized	O
duplicate	O
of	O
the	O
main	O
texture	O
,	O
but	O
at	O
a	O
certain	O
reduced	O
level	O
of	O
detail	O
.	O
</s>
<s>
Although	O
the	O
main	O
texture	O
would	O
still	O
be	O
used	O
when	O
the	O
view	O
is	O
sufficient	O
to	O
render	O
it	O
in	O
full	O
detail	O
,	O
the	O
renderer	O
will	O
switch	O
to	O
a	O
suitable	O
mipmap	B-Data_Structure
image	O
(	O
or	O
in	O
fact	O
,	O
interpolate	B-Algorithm
between	O
the	O
two	O
nearest	O
,	O
if	O
trilinear	O
filtering	O
is	O
activated	O
)	O
when	O
the	O
texture	O
is	O
viewed	O
from	O
a	O
distance	O
or	O
at	O
a	O
small	O
size	O
.	O
</s>
<s>
Rendering	O
speed	O
increases	O
since	O
the	O
number	O
of	O
texture	O
pixels	B-Algorithm
(	O
texels	O
)	O
being	O
processed	O
per	O
display	O
pixel	B-Algorithm
can	O
be	O
much	O
lower	O
for	O
similar	O
results	O
with	O
the	O
simpler	O
mipmap	B-Data_Structure
textures	O
.	O
</s>
<s>
If	O
using	O
a	O
limited	O
number	O
of	O
texture	O
samples	O
per	O
display	O
pixel	B-Algorithm
(	O
as	O
is	O
the	O
case	O
with	O
bilinear	O
filtering	O
)	O
then	O
artifacts	O
are	O
reduced	O
since	O
the	O
mipmap	B-Data_Structure
images	B-Algorithm
are	O
effectively	O
already	O
anti-aliased	B-Algorithm
.	O
</s>
<s>
Scaling	O
down	O
and	O
up	O
is	O
made	O
more	O
efficient	O
with	O
mipmaps	B-Data_Structure
as	O
well	O
.	O
</s>
<s>
If	O
the	O
texture	O
has	O
a	O
basic	O
size	O
of	O
256	O
by	O
256	O
pixels	B-Algorithm
,	O
then	O
the	O
associated	O
mipmap	B-Data_Structure
set	O
may	O
contain	O
a	O
series	O
of	O
8	O
images	B-Algorithm
,	O
each	O
one-fourth	O
the	O
total	O
area	O
of	O
the	O
previous	O
one	O
:	O
128×128	O
pixels	B-Algorithm
,	O
64×64	O
,	O
32×32	O
,	O
16×16	O
,	O
8×8	O
,	O
4×4	O
,	O
2×2	O
,	O
1×1	O
(	O
a	O
single	O
pixel	B-Algorithm
)	O
.	O
</s>
<s>
If	O
,	O
for	O
example	O
,	O
a	O
scene	O
is	O
rendering	O
this	O
texture	O
in	O
a	O
space	O
of	O
40×40	O
pixels	B-Algorithm
,	O
then	O
either	O
a	O
scaled-up	O
version	O
of	O
the	O
32×32	O
(	O
without	O
trilinear	O
interpolation	B-Algorithm
)	O
or	O
an	O
interpolation	B-Algorithm
of	O
the	O
64×64	O
and	O
the	O
32×32	O
mipmaps	B-Data_Structure
(	O
with	O
trilinear	O
interpolation	B-Algorithm
)	O
would	O
be	O
used	O
.	O
</s>
<s>
The	O
simplest	O
way	O
to	O
generate	O
these	O
textures	O
is	O
by	O
successive	O
averaging	O
;	O
however	O
,	O
more	O
sophisticated	O
algorithms	O
(	O
perhaps	O
based	O
on	O
signal	O
processing	O
and	O
Fourier	B-Algorithm
transforms	I-Algorithm
)	O
can	O
also	O
be	O
used	O
.	O
</s>
<s>
The	O
increase	O
in	O
storage	B-General_Concept
space	I-General_Concept
required	O
for	O
all	O
of	O
these	O
mipmaps	B-Data_Structure
is	O
a	O
third	O
of	O
the	O
original	O
texture	O
,	O
because	O
the	O
sum	O
of	O
the	O
areas	O
1/4	O
+	O
1/16	O
+	O
1/64	O
+	O
1/256	O
+	O
⋯	O
converges	O
to	O
1/3	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
an	O
RGB	O
image	O
with	O
three	O
channels	O
stored	O
as	O
separate	O
planes	O
,	O
the	O
total	O
mipmap	B-Data_Structure
can	O
be	O
visualized	O
as	O
fitting	O
neatly	O
into	O
a	O
square	O
area	O
twice	O
as	O
large	O
as	O
the	O
dimensions	O
of	O
the	O
original	O
image	O
on	O
each	O
side	O
(	O
twice	O
as	O
large	O
on	O
each	O
side	O
is	O
four	O
times	O
the	O
original	O
area	O
-	O
one	O
plane	O
of	O
the	O
original	O
size	O
for	O
each	O
of	O
red	O
,	O
green	O
and	O
blue	O
makes	O
three	O
times	O
the	O
original	O
area	O
,	O
and	O
then	O
since	O
the	O
smaller	O
textures	O
take	O
1/3	O
of	O
the	O
original	O
,	O
1/3	O
of	O
three	O
is	O
one	O
,	O
so	O
they	O
will	O
take	O
the	O
same	O
total	O
space	O
as	O
just	O
one	O
of	O
the	O
original	O
red	O
,	O
green	O
,	O
or	O
blue	O
planes	O
)	O
.	O
</s>
<s>
When	O
a	O
texture	O
is	O
viewed	O
at	O
a	O
steep	O
angle	O
,	O
the	O
filtering	O
should	O
not	O
be	O
uniform	O
in	O
each	O
direction	O
(	O
it	O
should	O
be	O
anisotropic	O
rather	O
than	O
isotropic	O
)	O
,	O
and	O
a	O
compromise	O
resolution	B-Algorithm
is	O
required	O
.	O
</s>
<s>
If	O
a	O
higher	O
resolution	B-Algorithm
is	O
used	O
,	O
the	O
cache	B-General_Concept
coherence	I-General_Concept
goes	O
down	O
,	O
and	O
the	O
aliasing	B-Error_Name
is	O
increased	O
in	O
one	O
direction	O
,	O
but	O
the	O
image	O
tends	O
to	O
be	O
clearer	O
.	O
</s>
<s>
If	O
a	O
lower	O
resolution	B-Algorithm
is	O
used	O
,	O
the	O
cache	B-General_Concept
coherence	I-General_Concept
is	O
improved	O
,	O
but	O
the	O
image	O
is	O
overly	O
blurry	O
.	O
</s>
<s>
This	O
would	O
be	O
a	O
tradeoff	O
of	O
MIP	O
level	O
of	O
detail	O
(	O
LOD	O
)	O
for	O
aliasing	B-Error_Name
vs	O
blurriness	O
.	O
</s>
<s>
However	O
anisotropic	O
filtering	O
attempts	O
to	O
resolve	O
this	O
trade-off	O
by	O
sampling	O
a	O
non	O
isotropic	O
texture	O
footprint	O
for	O
each	O
pixel	B-Algorithm
rather	O
than	O
merely	O
adjusting	O
the	O
MIP	O
LOD	O
.	O
</s>
<s>
Summed-area	B-Algorithm
tables	I-Algorithm
can	O
conserve	O
memory	O
and	O
provide	O
more	O
resolutions	O
.	O
</s>
<s>
However	O
,	O
they	O
again	O
hurt	O
cache	B-General_Concept
coherence	I-General_Concept
,	O
and	O
need	O
wider	O
types	O
to	O
store	O
the	O
partial	O
sums	O
,	O
which	O
are	O
larger	O
than	O
the	O
base	O
texture	O
's	O
word	O
size	O
.	O
</s>
