<s>
In	O
mathematics	O
,	O
the	O
variation	B-Algorithm
diminishing	I-Algorithm
property	I-Algorithm
of	O
certain	O
mathematical	O
objects	O
involves	O
diminishing	O
the	O
number	O
of	O
changes	O
in	O
sign	O
(	O
positive	O
to	O
negative	O
or	O
vice	O
versa	O
)	O
.	O
</s>
<s>
The	O
variation	B-Algorithm
diminishing	I-Algorithm
property	I-Algorithm
of	O
Bézier	O
curves	O
is	O
that	O
they	O
are	O
smoother	O
than	O
the	O
polygon	O
formed	O
by	O
their	O
control	O
points	O
.	O
</s>
<s>
Using	O
the	O
above	O
points	O
,	O
we	O
say	O
that	O
since	O
the	O
Bézier	O
curve	O
B	O
is	O
the	O
limit	O
of	O
these	O
polygons	O
as	O
r	O
goes	O
to	O
,	O
it	O
will	O
have	O
fewer	O
intersections	O
with	O
a	O
given	O
plane	O
than	O
Ri	O
for	O
all	O
i	O
,	O
and	O
in	O
particular	O
fewer	O
intersections	O
that	O
the	O
original	O
control	O
polygon	O
R	O
.	O
This	O
is	O
the	O
statement	O
of	O
the	O
variation	B-Algorithm
diminishing	I-Algorithm
property	I-Algorithm
.	O
</s>
<s>
The	O
variation	B-Algorithm
diminishing	I-Algorithm
property	I-Algorithm
of	I-Algorithm
totally	I-Algorithm
positive	I-Algorithm
matrices	I-Algorithm
is	O
a	O
consequence	O
of	O
their	O
decomposition	O
into	O
products	O
of	O
Jacobi	O
matrices	O
.	O
</s>
<s>
The	O
blocks	O
of	O
Dirichlet-to-Neumann	O
maps	O
of	O
planar	O
graphs	O
have	O
the	O
variation	B-Algorithm
diminishing	I-Algorithm
property	I-Algorithm
.	O
</s>
