<s>
Marching	B-Algorithm
tetrahedra	I-Algorithm
is	O
an	O
algorithm	O
in	O
the	O
field	O
of	O
computer	O
graphics	O
to	O
render	O
implicit	B-Algorithm
surfaces	I-Algorithm
.	O
</s>
<s>
It	O
clarifies	O
a	O
minor	O
ambiguity	O
problem	O
of	O
the	O
marching	B-Algorithm
cubes	I-Algorithm
algorithm	I-Algorithm
with	O
some	O
cube	O
configurations	O
.	O
</s>
<s>
While	O
the	O
original	O
marching	B-Algorithm
cubes	I-Algorithm
algorithm	I-Algorithm
was	O
protected	O
by	O
a	O
software	O
patent	O
,	O
marching	B-Algorithm
tetrahedrons	I-Algorithm
offered	O
an	O
alternative	O
algorithm	O
that	O
did	O
not	O
require	O
a	O
patent	O
license	O
.	O
</s>
<s>
More	O
than	O
20	O
years	O
have	O
passed	O
from	O
the	O
patent	O
filing	O
date	O
(	O
June	O
5	O
,	O
1985	O
)	O
,	O
and	O
the	O
marching	B-Algorithm
cubes	I-Algorithm
algorithm	I-Algorithm
can	O
now	O
be	O
used	O
freely	O
.	O
</s>
<s>
Optionally	O
,	O
the	O
minor	O
improvements	O
of	O
marching	B-Algorithm
tetrahedrons	I-Algorithm
may	O
be	O
used	O
to	O
correct	O
the	O
aforementioned	O
ambiguity	O
in	O
some	O
configurations	O
.	O
</s>
<s>
In	O
marching	B-Algorithm
tetrahedra	I-Algorithm
,	O
each	O
cube	O
is	O
split	O
into	O
six	O
irregular	O
tetrahedra	O
by	O
cutting	O
the	O
cube	O
in	O
half	O
three	O
times	O
,	O
cutting	O
diagonally	O
through	O
each	O
of	O
the	O
three	O
pairs	O
of	O
opposing	O
faces	O
.	O
</s>
<s>
Just	O
like	O
in	O
marching	B-Algorithm
cubes	I-Algorithm
,	O
the	O
intersections	O
of	O
these	O
edges	O
with	O
the	O
isosurface	O
are	O
approximated	O
by	O
linearly	O
interpolating	O
the	O
values	O
at	O
the	O
grid	O
points	O
.	O
</s>
<s>
Marching	B-Algorithm
tetrahedra	I-Algorithm
computes	O
up	O
to	O
nineteen	O
edge	O
intersections	O
per	O
cube	O
,	O
where	O
marching	B-Algorithm
cubes	I-Algorithm
only	O
requires	O
twelve	O
.	O
</s>
<s>
The	O
number	O
of	O
configurations	O
,	O
determining	O
the	O
size	O
of	O
the	O
commonly	O
used	O
lookup	B-Data_Structure
tables	I-Data_Structure
,	O
is	O
much	O
smaller	O
,	O
since	O
only	O
four	O
rather	O
than	O
eight	O
separate	O
vertices	O
are	O
involved	O
per	O
tetrahedron	O
.	O
</s>
<s>
The	O
downside	O
is	O
that	O
the	O
tessellation	B-Algorithm
of	O
a	O
cube	O
with	O
tetrahedra	O
requires	O
a	O
choice	O
regarding	O
the	O
orientation	O
of	O
the	O
tetrahedra	O
,	O
which	O
may	O
produce	O
artificial	O
"	O
bumps	O
"	O
in	O
the	O
isosurface	O
because	O
of	O
interpolation	O
along	O
the	O
face	O
diagonals	O
.	O
</s>
