<s>
In	O
computer	O
graphics	O
,	O
the	O
centripetal	B-Algorithm
Catmull	I-Algorithm
–	I-Algorithm
Rom	I-Algorithm
spline	I-Algorithm
is	O
a	O
variant	O
form	O
of	O
the	O
Catmull	O
–	O
Rom	O
spline	O
,	O
originally	O
formulated	O
by	O
Edwin	O
Catmull	O
and	O
Raphael	O
Rom	O
,	O
which	O
can	O
be	O
evaluated	O
using	O
a	O
recursive	O
algorithm	O
proposed	O
by	O
Barry	O
and	O
Goldman	O
.	O
</s>
<s>
For	O
a	O
curve	O
segment	O
defined	O
by	O
points	O
and	O
knot	O
sequence	O
,	O
the	O
centripetal	B-Algorithm
Catmull	I-Algorithm
–	I-Algorithm
Rom	I-Algorithm
spline	I-Algorithm
can	O
be	O
produced	O
by	O
:	O
</s>
<s>
For	O
centripetal	B-Algorithm
Catmull	I-Algorithm
–	I-Algorithm
Rom	I-Algorithm
spline	I-Algorithm
,	O
the	O
value	O
of	O
is	O
.	O
</s>
<s>
Centripetal	B-Algorithm
Catmull	I-Algorithm
–	I-Algorithm
Rom	I-Algorithm
spline	I-Algorithm
has	O
several	O
desirable	O
mathematical	O
properties	O
compared	O
to	O
the	O
original	O
and	O
the	O
other	O
types	O
of	O
Catmull-Rom	O
formulation	O
.	O
</s>
<s>
In	O
computer	B-Application
vision	I-Application
,	O
centripetal	B-Algorithm
Catmull-Rom	I-Algorithm
spline	I-Algorithm
has	O
been	O
used	O
to	O
formulate	O
an	O
active	O
model	O
for	O
segmentation	O
.	O
</s>
<s>
The	O
model	O
is	O
devised	O
on	O
the	O
basis	O
of	O
active	B-General_Concept
shape	I-General_Concept
model	I-General_Concept
,	O
but	O
uses	O
centripetal	B-Algorithm
Catmull-Rom	I-Algorithm
spline	I-Algorithm
to	O
join	O
two	O
successive	O
points	O
(	O
active	B-General_Concept
shape	I-General_Concept
model	I-General_Concept
uses	O
simple	O
straight	O
line	O
)	O
,	O
so	O
that	O
the	O
total	O
number	O
of	O
points	O
necessary	O
to	O
depict	O
a	O
shape	O
is	O
less	O
.	O
</s>
<s>
The	O
use	O
of	O
centripetal	B-Algorithm
Catmull-Rom	I-Algorithm
spline	I-Algorithm
makes	O
the	O
training	O
of	O
a	O
shape	O
model	O
much	O
simpler	O
,	O
and	O
it	O
enables	O
a	O
better	O
way	O
to	O
edit	O
a	O
contour	O
after	O
segmentation	O
.	O
</s>
<s>
The	O
following	O
is	O
an	O
implementation	O
of	O
the	O
Catmull	O
–	O
Rom	O
spline	O
in	O
Python	B-Language
that	O
produces	O
the	O
plot	O
shown	O
beneath	O
.	O
</s>
