<s>
Minimizing	O
the	O
exact	O
thin	B-Algorithm
plate	I-Algorithm
energy	I-Algorithm
functional	I-Algorithm
would	O
result	O
in	O
a	O
system	O
of	O
non-linear	O
equations	O
.	O
</s>
<s>
The	O
approximate	O
thin	B-Algorithm
plate	I-Algorithm
energy	I-Algorithm
functional	I-Algorithm
can	O
be	O
used	O
to	O
fit	O
B-spline	B-Algorithm
surfaces	I-Algorithm
to	O
scattered	O
1D	O
data	O
on	O
a	O
2D	O
grid	O
(	O
for	O
example	O
,	O
digital	O
terrain	O
model	O
data	O
)	O
.	O
</s>
<s>
The	O
following	O
images	O
illustrate	O
the	O
results	O
of	O
fitting	O
a	O
B-spline	B-Algorithm
surface	I-Algorithm
to	O
some	O
terrain	O
data	O
using	O
this	O
method	O
.	O
</s>
<s>
The	O
thin	O
plate	O
smoothing	O
spline	O
also	O
minimizes	O
equation	O
(	O
)	O
,	O
but	O
it	O
is	O
much	O
more	O
expensive	O
to	O
compute	O
than	O
a	O
B-spline	B-Algorithm
and	O
not	O
as	O
smooth	O
(	O
it	O
is	O
only	O
at	O
the	O
"	O
centers	O
"	O
and	O
has	O
unbounded	O
second	O
derivatives	O
there	O
)	O
.	O
</s>
