<s>
In	O
applied	O
mathematics	O
,	O
an	O
Akima	B-Algorithm
spline	I-Algorithm
is	O
a	O
type	O
of	O
non-smoothing	O
spline	B-Algorithm
that	O
gives	O
good	O
fits	O
to	O
curves	O
where	O
the	O
second	O
derivative	O
is	O
rapidly	O
varying	O
.	O
</s>
<s>
The	O
Akima	B-Algorithm
spline	I-Algorithm
was	O
published	O
by	O
Hiroshi	O
Akima	O
in	O
1970	O
.	O
</s>
<s>
Given	O
a	O
set	O
of	O
"	O
knot	B-Algorithm
"	O
points	O
,	O
where	O
the	O
are	O
strictly	O
increasing	O
,	O
the	O
Akima	B-Algorithm
spline	I-Algorithm
will	O
go	O
through	O
each	O
of	O
the	O
given	O
points	O
.	O
</s>
<s>
The	O
spline	B-Algorithm
is	O
then	O
defined	O
as	O
the	O
piecewise	O
cubic	O
function	O
whose	O
value	O
between	O
and	O
is	O
the	O
unique	O
cubic	O
polynomial	O
,	O
</s>
<s>
where	O
the	O
coefficients	O
of	O
the	O
polynomial	O
are	O
chosen	O
such	O
that	O
the	O
four	O
conditions	O
of	O
continuity	O
of	O
the	O
spline	B-Algorithm
together	O
with	O
its	O
first	O
derivative	O
are	O
satisfied	O
,	O
</s>
<s>
Due	O
to	O
these	O
conditions	O
the	O
Akima	B-Algorithm
spline	I-Algorithm
is	O
a	O
C1	O
differentiable	O
function	O
,	O
that	O
is	O
,	O
the	O
function	O
itself	O
is	O
continuous	O
and	O
the	O
first	O
derivative	O
is	O
also	O
continuous	O
.	O
</s>
<s>
An	O
advantage	O
of	O
the	O
Akima	B-Algorithm
spline	I-Algorithm
is	O
due	O
to	O
the	O
fact	O
that	O
it	O
uses	O
only	O
values	O
from	O
neighboring	O
knot	B-Algorithm
points	O
in	O
the	O
construction	O
of	O
the	O
coefficients	O
of	O
the	O
interpolation	O
polynomial	O
between	O
any	O
two	O
knot	B-Algorithm
points	O
.	O
</s>
<s>
This	O
means	O
that	O
there	O
is	O
no	O
large	O
system	O
of	O
equations	O
to	O
solve	O
and	O
the	O
Akima	B-Algorithm
spline	I-Algorithm
avoids	O
unphysical	O
wiggles	O
in	O
regions	O
where	O
the	O
second	O
derivative	O
in	O
the	O
underlying	O
curve	O
is	O
rapidly	O
changing	O
.	O
</s>
<s>
A	O
possible	O
disadvantage	O
of	O
the	O
Akima	B-Algorithm
spline	I-Algorithm
is	O
that	O
it	O
has	O
a	O
discontinuous	O
second	O
derivative	O
.	O
</s>
