<s>
A	O
bounding	B-Data_Structure
volume	I-Data_Structure
hierarchy	I-Data_Structure
(	O
BVH	O
)	O
is	O
a	O
tree	B-Data_Structure
structure	I-Data_Structure
on	O
a	O
set	O
of	O
geometric	O
objects	O
.	O
</s>
<s>
All	O
geometric	O
objects	O
,	O
which	O
form	O
the	O
leaf	O
nodes	O
of	O
the	O
tree	O
,	O
are	O
wrapped	O
in	O
bounding	B-Algorithm
volumes	I-Algorithm
.	O
</s>
<s>
These	O
nodes	O
are	O
then	O
grouped	O
as	O
small	O
sets	O
and	O
enclosed	O
within	O
larger	O
bounding	B-Algorithm
volumes	I-Algorithm
.	O
</s>
<s>
These	O
,	O
in	O
turn	O
,	O
are	O
also	O
grouped	O
and	O
enclosed	O
within	O
other	O
larger	O
bounding	B-Algorithm
volumes	I-Algorithm
in	O
a	O
recursive	O
fashion	O
,	O
eventually	O
resulting	O
in	O
a	O
tree	B-Data_Structure
structure	I-Data_Structure
with	O
a	O
single	O
bounding	B-Algorithm
volume	I-Algorithm
at	O
the	O
top	O
of	O
the	O
tree	O
.	O
</s>
<s>
Bounding	B-Data_Structure
volume	I-Data_Structure
hierarchies	I-Data_Structure
are	O
used	O
to	O
support	O
several	O
operations	O
on	O
sets	O
of	O
geometric	O
objects	O
efficiently	O
,	O
such	O
as	O
in	O
collision	O
detection	O
and	O
ray	B-Algorithm
tracing	I-Algorithm
.	O
</s>
<s>
Although	O
wrapping	O
objects	O
in	O
bounding	B-Algorithm
volumes	I-Algorithm
and	O
performing	O
collision	O
tests	O
on	O
them	O
before	O
testing	O
the	O
object	O
geometry	O
itself	O
simplifies	O
the	O
tests	O
and	O
can	O
result	O
in	O
significant	O
performance	O
improvements	O
,	O
the	O
same	O
number	O
of	O
pairwise	O
tests	O
between	O
bounding	B-Algorithm
volumes	I-Algorithm
are	O
still	O
being	O
performed	O
.	O
</s>
<s>
By	O
arranging	O
the	O
bounding	B-Algorithm
volumes	I-Algorithm
into	O
a	O
bounding	B-Data_Structure
volume	I-Data_Structure
hierarchy	I-Data_Structure
,	O
the	O
time	O
complexity	O
(	O
the	O
number	O
of	O
tests	O
performed	O
)	O
can	O
be	O
reduced	O
to	O
logarithmic	O
in	O
the	O
number	O
of	O
objects	O
.	O
</s>
<s>
With	O
such	O
a	O
hierarchy	O
in	O
place	O
,	O
during	O
collision	O
testing	O
,	O
children	O
volumes	O
do	O
not	O
have	O
to	O
be	O
examined	O
if	O
their	O
parent	O
volumes	O
are	O
not	O
intersected	O
(	O
for	O
example	O
,	O
if	O
the	O
bounding	B-Algorithm
volumes	I-Algorithm
of	O
two	O
bumper	O
cars	O
do	O
not	O
intersect	O
,	O
the	O
bounding	B-Algorithm
volumes	I-Algorithm
of	O
the	O
bumpers	O
themselves	O
would	O
not	O
have	O
to	O
be	O
checked	O
for	O
collision	O
)	O
.	O
</s>
<s>
The	O
choice	O
of	O
bounding	B-Algorithm
volume	I-Algorithm
is	O
determined	O
by	O
a	O
trade-off	O
between	O
two	O
objectives	O
.	O
</s>
<s>
On	O
the	O
one	O
hand	O
,	O
we	O
would	O
like	O
to	O
use	O
bounding	B-Algorithm
volumes	I-Algorithm
that	O
have	O
a	O
very	O
simple	O
shape	O
.	O
</s>
<s>
On	O
the	O
other	O
hand	O
,	O
we	O
would	O
like	O
to	O
have	O
bounding	B-Algorithm
volumes	I-Algorithm
that	O
fit	O
the	O
corresponding	O
data	O
objects	O
very	O
tightly	O
.	O
</s>
<s>
One	O
of	O
the	O
most	O
commonly	O
used	O
bounding	B-Algorithm
volumes	I-Algorithm
is	O
an	O
axis-aligned	B-Algorithm
minimum	I-Algorithm
bounding	I-Algorithm
box	I-Algorithm
.	O
</s>
<s>
The	O
axis-aligned	B-Algorithm
minimum	I-Algorithm
bounding	I-Algorithm
box	I-Algorithm
for	O
a	O
given	O
set	O
of	O
data	O
objects	O
is	O
easy	O
to	O
compute	O
,	O
needs	O
only	O
few	O
bytes	O
of	O
storage	O
,	O
and	O
robust	O
intersection	O
tests	O
are	O
easy	O
to	O
implement	O
and	O
extremely	O
fast	O
.	O
</s>
<s>
The	O
sum	O
of	O
all	O
bounding	B-Algorithm
volumes	I-Algorithm
should	O
be	O
minimal	O
.	O
</s>
<s>
Top-down	O
methods	O
proceed	O
by	O
partitioning	O
the	O
input	O
set	O
into	O
two	O
(	O
or	O
more	O
)	O
subsets	O
,	O
bounding	O
them	O
in	O
the	O
chosen	O
bounding	B-Algorithm
volume	I-Algorithm
,	O
then	O
keep	O
partitioning	O
(	O
and	O
bounding	O
)	O
recursively	O
until	O
each	O
subset	O
consists	O
of	O
only	O
a	O
single	O
primitive	O
(	O
leaf	O
nodes	O
are	O
reached	O
)	O
.	O
</s>
<s>
Some	O
recent	O
studies	O
indicate	O
that	O
in	O
low-dimensional	O
space	O
,	O
the	O
construction	O
speed	O
can	O
be	O
largely	O
improved	O
(	O
which	O
matches	O
or	O
outperforms	O
the	O
top-down	O
approaches	O
)	O
by	O
sorting	O
objects	O
using	O
space-filling	B-Algorithm
curve	I-Algorithm
and	O
applying	O
approximate	O
clustering	O
based	O
on	O
this	O
sequential	O
order	O
.	O
</s>
<s>
BVHs	O
are	O
often	O
used	O
in	O
ray	B-Algorithm
tracing	I-Algorithm
to	O
eliminate	O
potential	O
intersection	O
candidates	O
within	O
a	O
scene	O
by	O
omitting	O
geometric	O
objects	O
located	O
in	O
bounding	B-Algorithm
volumes	I-Algorithm
which	O
are	O
not	O
intersected	O
by	O
the	O
current	O
ray	O
.	O
</s>
<s>
Additionally	O
,	O
as	O
common	O
performance	O
optimization	O
,	O
when	O
only	O
closest	O
intersection	O
of	O
the	O
ray	O
is	O
of	O
interest	O
,	O
as	O
the	O
ray	B-Algorithm
tracing	I-Algorithm
traversal	O
algorithm	O
is	O
descending	O
nodes	O
,	O
and	O
multiple	O
child	B-Data_Structure
nodes	I-Data_Structure
are	O
intersecting	O
the	O
ray	O
,	O
traversal	O
algorithm	O
will	O
consider	O
the	O
closer	O
volume	O
first	O
,	O
and	O
if	O
it	O
finds	O
intersection	O
there	O
,	O
which	O
is	O
definitively	O
closer	O
than	O
any	O
possible	O
intersection	O
in	O
second	O
(	O
or	O
other	O
)	O
volume	O
(	O
i.e.	O
</s>
<s>
Additionally	O
,	O
many	O
specialized	O
methods	O
were	O
developed	O
for	O
BVHs	O
,	O
especially	O
ones	O
based	O
on	O
AABB	O
(	O
axis-aligned	B-Algorithm
bounding	I-Algorithm
boxes	I-Algorithm
)	O
,	O
such	O
as	O
parallel	O
building	O
,	O
SIMD	B-Device
accelerated	O
traversal	O
,	O
good	O
split	O
heuristics	O
(	O
SAH	O
-	O
surface-area	O
heuristic	O
is	O
often	O
used	O
in	O
ray	B-Algorithm
tracing	I-Algorithm
)	O
,	O
wide	O
trees	O
(	O
4-ary	O
and	O
16-ary	O
trees	O
provide	O
some	O
performance	O
benefits	O
,	O
both	O
in	O
build	O
and	O
query	O
performance	O
for	O
practical	O
scenes	O
)	O
,	O
and	O
quick	O
structure	O
update	O
(	O
in	O
real	O
time	O
applications	O
objects	O
might	O
be	O
moving	O
or	O
deforming	O
spatially	O
relatively	O
slowly	O
or	O
be	O
still	O
,	O
and	O
same	O
BVH	O
can	O
be	O
updated	O
to	O
be	O
still	O
valid	O
without	O
doing	O
a	O
full	O
rebuild	O
from	O
scratch	O
)	O
.	O
</s>
<s>
BVHs	O
can	O
also	O
be	O
combined	O
with	O
scene	B-Data_Structure
graph	I-Data_Structure
methods	O
,	O
and	O
geometry	B-General_Concept
instancing	I-General_Concept
,	O
to	O
reduce	O
memory	O
usage	O
,	O
improve	O
structure	O
update	O
and	O
full	O
rebuild	O
performance	O
,	O
as	O
well	O
as	O
guide	O
better	O
object	O
or	O
primitive	O
splitting	O
.	O
</s>
