<s>
Newest	B-Algorithm
Vertex	I-Algorithm
Bisection	I-Algorithm
is	O
an	O
algorithmic	O
method	O
to	O
locally	O
refine	O
triangulations	B-Algorithm
.	O
</s>
<s>
It	O
is	O
widely	O
used	O
in	O
computational	O
science	O
,	O
numerical	B-Application
simulation	I-Application
,	O
and	O
computer	O
graphics	O
.	O
</s>
<s>
The	O
advantage	O
of	O
newest	B-Algorithm
vertex	I-Algorithm
bisection	I-Algorithm
is	O
that	O
it	O
allows	O
local	O
refinement	O
of	O
triangulations	B-Algorithm
without	O
degenerating	O
the	O
shape	O
of	O
the	O
triangles	O
after	O
repeated	O
usage	O
.	O
</s>
<s>
In	O
newest	B-Algorithm
vertex	I-Algorithm
bisection	I-Algorithm
,	O
whenever	O
a	O
triangle	O
is	O
to	O
be	O
split	O
into	O
smaller	O
triangles	O
,	O
it	O
will	O
be	O
bisected	O
by	O
drawing	O
a	O
line	O
from	O
the	O
newest	O
vertex	O
to	O
the	O
midpoint	O
of	O
the	O
edge	O
opposite	O
to	O
that	O
vertex	O
.	O
</s>
<s>
One	O
can	O
show	O
that	O
repeating	O
this	O
procedure	O
for	O
a	O
given	O
triangulation	B-Algorithm
leads	O
to	O
triangles	O
that	O
belong	O
to	O
only	O
a	O
finite	O
number	O
of	O
similarity	O
classes	O
.	O
</s>
<s>
Generalizations	O
of	O
newest	B-Algorithm
vertex	I-Algorithm
bisection	I-Algorithm
to	O
dimension	O
three	O
and	O
higher	O
are	O
known	O
.	O
</s>
<s>
Newest	B-Algorithm
vertex	I-Algorithm
bisection	I-Algorithm
is	O
used	O
in	O
local	O
mesh	O
refinement	O
for	O
adaptive	O
finite	B-Application
element	I-Application
methods	I-Application
,	O
where	O
it	O
is	O
an	O
alternative	O
to	O
red-green	O
refinement	O
and	O
uniform	O
mesh	O
refinement	O
.	O
</s>
