<s>
Beam	B-Algorithm
tracing	I-Algorithm
is	O
an	O
algorithm	O
to	O
simulate	O
wave	O
propagation	O
.	O
</s>
<s>
Beam	B-Algorithm
tracing	I-Algorithm
is	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
beams	O
.	O
</s>
<s>
Beam	B-Algorithm
tracing	I-Algorithm
was	O
first	O
proposed	O
by	O
Paul	O
Heckbert	O
and	O
Pat	O
Hanrahan	O
.	O
</s>
<s>
In	O
beam	B-Algorithm
tracing	I-Algorithm
,	O
a	O
pyramidal	O
beam	O
is	O
initially	O
cast	O
through	O
the	O
entire	O
viewing	B-General_Concept
frustum	I-General_Concept
.	O
</s>
<s>
This	O
initial	O
viewing	O
beam	O
is	O
intersected	O
with	O
each	O
polygon	B-General_Concept
in	O
the	O
environment	O
,	O
typically	O
from	O
nearest	O
to	O
farthest	O
.	O
</s>
<s>
Each	O
polygon	B-General_Concept
that	O
intersects	O
with	O
the	O
beam	O
must	O
be	O
visible	O
,	O
and	O
is	O
removed	O
from	O
the	O
shape	O
of	O
the	O
beam	O
and	O
added	O
to	O
a	O
render	O
queue	O
.	O
</s>
<s>
When	O
a	O
beam	O
intersects	O
with	O
a	O
reflective	O
or	O
refractive	O
polygon	B-General_Concept
,	O
a	O
new	O
beam	O
is	O
created	O
in	O
a	O
similar	O
fashion	O
to	O
ray-tracing	B-Algorithm
.	O
</s>
<s>
A	O
variant	O
of	O
beam	B-Algorithm
tracing	I-Algorithm
casts	O
a	O
pyramidal	O
beam	O
through	O
each	O
pixel	B-Algorithm
of	O
the	O
image	B-General_Concept
plane	I-General_Concept
.	O
</s>
<s>
This	O
sort	O
of	O
implementation	O
is	O
rarely	O
used	O
,	O
as	O
the	O
geometric	O
processes	O
involved	O
are	O
much	O
more	O
complex	O
and	O
therefore	O
expensive	O
than	O
simply	O
casting	O
more	O
rays	O
through	O
the	O
pixel	B-Algorithm
.	O
</s>
<s>
Cone	B-Algorithm
tracing	I-Algorithm
is	O
a	O
similar	O
technique	O
using	O
a	O
cone	O
instead	O
of	O
a	O
complex	O
pyramid	O
.	O
</s>
<s>
Beam	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
approaches	O
.	O
</s>
<s>
Since	O
beam	B-Algorithm
tracing	I-Algorithm
effectively	O
calculates	O
the	O
path	O
of	O
every	O
possible	O
ray	O
within	O
each	O
beam	O
(	O
which	O
can	O
be	O
viewed	O
as	O
a	O
dense	O
bundle	O
of	O
adjacent	O
rays	O
)	O
,	O
it	O
is	O
not	O
as	O
prone	O
to	O
under-sampling	O
(	O
missing	O
rays	O
)	O
or	O
over-sampling	O
(	O
wasted	O
computational	O
resources	O
)	O
.	O
</s>
<s>
In	O
recent	O
years	O
,	O
Monte	B-Algorithm
Carlo	I-Algorithm
algorithms	O
like	O
distributed	B-Algorithm
ray	I-Algorithm
tracing	I-Algorithm
(	O
and	O
Metropolis	B-Algorithm
light	I-Algorithm
transport	I-Algorithm
?	O
)	O
</s>
<s>
A	O
'	O
backwards	O
 '	O
variant	O
of	O
beam	B-Algorithm
tracing	I-Algorithm
casts	O
beams	O
from	O
the	O
light	O
source	O
into	O
the	O
environment	O
.	O
</s>
<s>
Similar	O
to	O
photon	B-Application
mapping	I-Application
,	O
backwards	O
beam	B-Algorithm
tracing	I-Algorithm
may	O
be	O
used	O
to	O
efficiently	O
model	O
lighting	O
effects	O
such	O
as	O
caustics	O
.	O
</s>
<s>
Recently	O
the	O
backwards	O
beam	B-Algorithm
tracing	I-Algorithm
technique	O
has	O
also	O
been	O
extended	O
to	O
handle	O
glossy	O
to	O
diffuse	O
material	O
interactions	O
(	O
glossy	O
backward	O
beam	B-Algorithm
tracing	I-Algorithm
)	O
such	O
as	O
from	O
polished	O
metal	O
surfaces	O
.	O
</s>
<s>
Beam	B-Algorithm
tracing	I-Algorithm
has	O
been	O
successfully	O
applied	O
to	O
the	O
fields	O
of	O
acoustic	O
modelling	O
and	O
electromagnetic	O
propagation	O
modelling	O
.	O
</s>
<s>
Beam	B-Algorithm
tracing	I-Algorithm
is	O
related	O
in	O
concept	O
to	O
cone	B-Algorithm
tracing	I-Algorithm
.	O
</s>
