<s>
A	O
min/max	B-Data_Structure
kd-tree	I-Data_Structure
is	O
a	O
k-d	B-Data_Structure
tree	I-Data_Structure
with	O
two	O
scalar	O
values	O
-	O
a	O
minimum	O
and	O
a	O
maximum	O
-	O
assigned	O
to	O
its	O
nodes	O
.	O
</s>
<s>
Min/max	B-Data_Structure
kd-trees	I-Data_Structure
may	O
be	O
constructed	O
recursively	O
.	O
</s>
<s>
The	O
min/max	B-Data_Structure
kdtree	I-Data_Structure
has	O
-	O
besides	O
the	O
properties	O
of	O
an	O
kd-tree	B-Data_Structure
-	O
the	O
special	O
property	O
that	O
an	O
inner	O
node	O
's	O
min/max	O
values	O
coincide	O
each	O
with	O
a	O
min/max	O
value	O
of	O
either	O
one	O
child	O
.	O
</s>
<s>
The	O
resulting	O
memory	O
reduction	O
is	O
not	O
minor	O
,	O
as	O
the	O
leaf	O
nodes	O
of	O
full	O
binary	O
kd-trees	B-Data_Structure
are	O
one	O
half	O
of	O
the	O
tree	O
's	O
nodes	O
.	O
</s>
<s>
Min/max	B-Data_Structure
kd-trees	I-Data_Structure
are	O
used	O
for	O
ray	B-Algorithm
casting	I-Algorithm
isosurfaces/MIP	O
(	O
maximum	B-Application
intensity	I-Application
projection	I-Application
)	O
.	O
</s>
<s>
Isosurface	O
ray	B-Algorithm
casting	I-Algorithm
only	O
traverses	O
nodes	O
for	O
which	O
the	O
chosen	O
isovalue	O
lies	O
between	O
the	O
min/max	O
values	O
of	O
the	O
current	O
node	O
.	O
</s>
<s>
The	O
favorable	O
visualization	O
complexity	O
of	O
ray	B-Algorithm
casting	I-Algorithm
allows	O
to	O
ray	B-Algorithm
cast	I-Algorithm
(	O
and	O
even	O
change	O
the	O
isosurface	O
for	O
)	O
very	O
large	O
scalar	O
fields	O
at	O
interactive	O
framerates	O
on	O
commodity	O
PCs	O
.	O
</s>
<s>
Especially	O
implicit	B-Data_Structure
max	B-Data_Structure
kd-trees	I-Data_Structure
are	O
an	O
optimal	O
choice	O
for	O
visualizing	O
scalar	O
fields	O
defined	O
on	O
rectilinear	O
grids	O
(	O
see	O
)	O
.	O
</s>
<s>
Similarly	O
an	O
implicit	B-Data_Structure
min/max	B-Data_Structure
kd-tree	I-Data_Structure
may	O
be	O
used	O
to	O
efficiently	O
evaluate	O
queries	O
such	O
as	O
terrain	O
line	O
of	O
sight	O
.	O
</s>
