<s>
Cone	B-Algorithm
tracing	I-Algorithm
and	O
beam	B-Algorithm
tracing	I-Algorithm
are	O
a	O
derivative	O
of	O
the	O
ray	B-Algorithm
tracing	I-Algorithm
algorithm	O
that	O
replaces	O
rays	O
,	O
which	O
have	O
no	O
thickness	O
,	O
with	O
thick	O
rays	O
.	O
</s>
<s>
In	O
ray	B-Algorithm
tracing	I-Algorithm
,	O
rays	O
are	O
often	O
modeled	O
as	O
geometric	O
ray	O
with	O
no	O
thickness	O
to	O
perform	O
efficient	O
geometric	O
queries	O
such	O
as	O
a	O
ray-triangle	O
intersection	O
.	O
</s>
<s>
In	O
the	O
simplified	O
pinhole	B-Algorithm
camera	I-Algorithm
optics	O
model	O
,	O
the	O
energy	O
reaching	O
the	O
pixel	O
comes	O
from	O
the	O
integral	O
of	O
radiance	O
from	O
the	O
solid	O
angle	O
by	O
which	O
the	O
sensor	O
pixel	O
sees	O
the	O
scene	O
through	O
the	O
pinhole	O
at	O
the	O
focal	O
plane	O
.	O
</s>
<s>
From	O
a	O
signal	O
processing	O
point	O
of	O
view	O
,	O
ignoring	O
the	O
point	O
spread	O
function	O
and	O
approximating	O
the	O
integral	O
of	O
radiance	O
with	O
a	O
single	O
,	O
central	O
sample	O
(	O
through	O
a	O
ray	O
with	O
no	O
thickness	O
)	O
can	O
lead	O
to	O
strong	O
aliasing	B-Error_Name
because	O
the	O
"	O
projected	O
geometric	O
signal	O
"	O
has	O
very	O
high	O
frequencies	O
exceeding	O
the	O
Nyquist-Shannon	O
maximal	O
frequency	O
that	O
can	O
be	O
represented	O
using	O
the	O
uniform	O
pixel	O
sampling	B-Algorithm
rate	O
.	O
</s>
<s>
In	O
practice	O
,	O
techniques	O
such	O
as	O
multisample	B-Algorithm
anti-aliasing	I-Algorithm
estimate	O
this	O
cone-based	O
model	O
by	O
oversampling	O
the	O
signal	O
and	O
then	O
performing	O
a	O
convolution	O
(	O
the	O
reconstruction	O
filter	O
)	O
.	O
</s>
<s>
Note	O
that	O
contrary	O
to	O
intuition	O
,	O
the	O
reconstruction	O
filter	O
should	O
not	O
be	O
the	O
pixel	O
footprint	O
(	O
as	O
the	O
pinhole	B-Algorithm
camera	I-Algorithm
model	O
would	O
suggest	O
)	O
,	O
since	O
a	O
box	O
filter	O
has	O
poor	O
spectral	O
properties	O
.	O
</s>
<s>
Conversely	O
,	O
the	O
ideal	O
sinc	B-Algorithm
function	I-Algorithm
is	O
not	O
practical	O
,	O
having	O
infinite	O
support	O
with	O
possibly	O
negative	O
values	O
which	O
often	O
creates	O
ringing	B-Algorithm
artifacts	I-Algorithm
due	O
to	O
the	O
Gibbs	O
phenomenon	O
.	O
</s>
<s>
A	O
Gaussian	O
or	O
a	O
Lanczos	B-Algorithm
filter	I-Algorithm
are	O
considered	O
good	O
compromises	O
.	O
</s>
<s>
Cone	B-Algorithm
tracing	I-Algorithm
solves	O
certain	O
problems	O
related	O
to	O
sampling	B-Algorithm
and	O
aliasing	B-Error_Name
,	O
which	O
can	O
plague	O
conventional	O
ray	B-Algorithm
tracing	I-Algorithm
.	O
</s>
<s>
However	O
,	O
cone	B-Algorithm
tracing	I-Algorithm
creates	O
a	O
host	O
of	O
problems	O
of	O
its	O
own	O
.	O
</s>
<s>
For	O
this	O
reason	O
,	O
cone	B-Algorithm
tracing	I-Algorithm
has	O
remained	O
mostly	O
unpopular	O
.	O
</s>
<s>
In	O
recent	O
years	O
,	O
increases	O
in	O
computer	O
speed	O
have	O
made	O
Monte	B-Algorithm
Carlo	I-Algorithm
algorithms	O
like	O
distributed	B-Algorithm
ray	I-Algorithm
tracing	I-Algorithm
-	O
i.e.	O
</s>
<s>
stochastic	O
explicit	O
integration	O
of	O
the	O
pixel	O
-	O
much	O
more	O
used	O
than	O
cone	B-Algorithm
tracing	I-Algorithm
because	O
the	O
results	O
are	O
exact	O
provided	O
enough	O
samples	O
are	O
used	O
.	O
</s>
<s>
But	O
the	O
convergence	O
is	O
so	O
slow	O
that	O
even	O
in	O
the	O
context	O
of	O
off-line	O
rendering	O
a	O
huge	O
amount	O
of	O
time	O
can	O
be	O
required	O
to	O
avoid	O
noise	B-Algorithm
.	O
</s>
<s>
MIPmapping	B-Data_Structure
is	O
an	O
approximation	O
of	O
it	O
limited	O
to	O
the	O
integration	O
of	O
the	O
surface	O
texture	O
within	O
a	O
cone	O
footprint	O
.	O
</s>
<s>
Differential	O
ray-tracing	B-Algorithm
extends	O
it	O
to	O
textured	O
surfaces	O
viewed	O
through	O
complex	O
paths	O
of	O
cones	O
reflected	O
or	O
refracted	O
by	O
curved	O
surfaces	O
.	O
</s>
