<s>
A	O
bounding	B-Data_Structure
interval	I-Data_Structure
hierarchy	I-Data_Structure
(	O
BIH	O
)	O
is	O
a	O
partitioning	O
data	B-General_Concept
structure	I-General_Concept
similar	O
to	O
that	O
of	O
bounding	B-Data_Structure
volume	I-Data_Structure
hierarchies	I-Data_Structure
or	O
kd-trees	B-Data_Structure
.	O
</s>
<s>
Bounding	B-Data_Structure
interval	I-Data_Structure
hierarchies	I-Data_Structure
can	O
be	O
used	O
in	O
high	O
performance	O
(	O
or	O
real-time	O
)	O
ray	B-Algorithm
tracing	I-Algorithm
and	O
may	O
be	O
especially	O
useful	O
for	O
dynamic	O
scenes	O
.	O
</s>
<s>
Bounding	B-Data_Structure
interval	I-Data_Structure
hierarchies	I-Data_Structure
(	O
BIH	O
)	O
exhibit	O
many	O
of	O
the	O
properties	O
of	O
both	O
bounding	B-Data_Structure
volume	I-Data_Structure
hierarchies	I-Data_Structure
(	O
BVH	O
)	O
and	O
kd-trees	B-Data_Structure
.	O
</s>
<s>
Whereas	O
the	O
construction	O
and	O
storage	O
of	O
BIH	O
is	O
comparable	O
to	O
that	O
of	O
BVH	O
,	O
the	O
traversal	O
of	O
BIH	O
resemble	O
that	O
of	O
kd-trees	B-Data_Structure
.	O
</s>
<s>
Furthermore	O
,	O
BIH	O
are	O
also	O
binary	O
trees	O
just	O
like	O
kd-trees	B-Data_Structure
(	O
and	O
in	O
fact	O
their	O
superset	O
,	O
BSP	O
trees	O
)	O
.	O
</s>
<s>
The	O
key	O
feature	O
of	O
the	O
BIH	O
is	O
the	O
storage	O
of	O
2	O
planes	O
per	O
node	O
(	O
as	O
opposed	O
to	O
1	O
for	O
the	O
kd	B-Data_Structure
tree	I-Data_Structure
and	O
6	O
for	O
an	O
axis	O
aligned	O
bounding	B-Algorithm
box	I-Algorithm
hierarchy	O
)	O
,	O
which	O
allows	O
for	O
overlapping	O
children	O
(	O
just	O
like	O
a	O
BVH	O
)	O
,	O
but	O
at	O
the	O
same	O
time	O
featuring	O
an	O
order	O
on	O
the	O
children	O
along	O
one	O
dimension/axis	O
(	O
as	O
it	O
is	O
the	O
case	O
for	O
kd	B-Data_Structure
trees	I-Data_Structure
)	O
.	O
</s>
<s>
It	O
is	O
also	O
possible	O
to	O
just	O
use	O
the	O
BIH	O
data	B-General_Concept
structure	I-General_Concept
for	O
the	O
construction	O
phase	O
but	O
traverse	O
the	O
tree	O
in	O
a	O
way	O
a	O
traditional	O
axis	O
aligned	O
bounding	B-Algorithm
box	I-Algorithm
hierarchy	O
does	O
.	O
</s>
<s>
This	O
enables	O
some	O
simple	O
speed	O
up	O
optimizations	O
for	O
large	O
ray	O
bundles	O
while	O
keeping	O
memory/cache	O
usage	O
low	O
.	O
</s>
<s>
Some	O
general	O
attributes	O
of	O
bounding	B-Data_Structure
interval	I-Data_Structure
hierarchies	I-Data_Structure
(	O
and	O
techniques	O
related	O
to	O
BIH	O
)	O
as	O
described	O
by	O
are	O
:	O
</s>
<s>
To	O
construct	O
any	O
space	B-Algorithm
partitioning	I-Algorithm
structure	O
some	O
form	O
of	O
heuristic	B-Algorithm
is	O
commonly	O
used	O
.	O
</s>
<s>
For	O
this	O
the	O
surface	O
area	O
heuristic	B-Algorithm
,	O
commonly	O
used	O
with	O
many	O
partitioning	O
schemes	O
,	O
is	O
a	O
possible	O
candidate	O
.	O
</s>
<s>
Another	O
,	O
more	O
simplistic	O
heuristic	B-Algorithm
is	O
the	O
"	O
global	O
"	O
heuristic	B-Algorithm
which	O
only	O
requires	O
an	O
axis-aligned	B-Algorithm
bounding	I-Algorithm
box	I-Algorithm
,	O
rather	O
than	O
the	O
full	O
set	O
of	O
primitives	O
,	O
making	O
it	O
much	O
more	O
suitable	O
for	O
a	O
fast	O
construction	O
.	O
</s>
<s>
Potential	O
heuristics	B-Algorithm
for	O
the	O
split	O
plane	O
candidate	O
search	O
:	O
</s>
<s>
Surface	O
area	O
heuristic	B-Algorithm
:	O
calculate	O
the	O
surface	O
area	O
and	O
number	O
of	O
objects	O
for	O
both	O
children	O
,	O
over	O
the	O
set	O
of	O
all	O
possible	O
split	O
plane	O
candidates	O
,	O
then	O
choose	O
the	O
one	O
with	O
the	O
lowest	O
costs	O
(	O
claimed	O
to	O
be	O
optimal	O
,	O
though	O
the	O
cost	O
function	O
poses	O
unusual	O
demands	O
to	O
proof	O
the	O
formula	O
,	O
which	O
can	O
not	O
be	O
fulfilled	O
in	O
real	O
life	O
.	O
</s>
<s>
For	O
the	O
third	O
case	O
,	O
depending	O
on	O
the	O
ray	O
direction	O
(	O
negative	O
or	O
positive	O
)	O
of	O
the	O
component	O
(	O
x	O
,	O
y	O
or	O
z	O
)	O
equalling	O
the	O
split	O
axis	O
of	O
the	O
current	O
node	O
,	O
the	O
traversal	O
continues	O
first	O
with	O
the	O
left	O
(	O
positive	O
direction	O
)	O
or	O
the	O
right	O
(	O
negative	O
direction	O
)	O
child	O
and	O
the	O
other	O
one	O
is	O
pushed	O
onto	O
a	O
stack	B-Application
for	O
deferred	O
potential	O
traversal	O
.	O
</s>
<s>
After	O
intersecting	O
the	O
objects	O
in	O
the	O
leaf	O
,	O
the	O
next	O
traversal	O
element	O
is	O
popped	O
from	O
the	O
stack	B-Application
.	O
</s>
<s>
If	O
the	O
stack	B-Application
is	O
empty	O
,	O
the	O
nearest	O
intersection	O
of	O
all	O
pierced	O
leaves	O
is	O
returned	O
.	O
</s>
<s>
Thus	O
no	O
triangle	O
clipping	O
has	O
to	O
be	O
done	O
as	O
it	O
is	O
the	O
case	O
with	O
kd-trees	B-Data_Structure
and	O
which	O
can	O
become	O
a	O
problem	O
for	O
triangles	O
that	O
just	O
slightly	O
intersect	O
a	O
node	O
.	O
</s>
