<s>
Curve	B-Algorithm
fitting	I-Algorithm
is	O
the	O
process	O
of	O
constructing	O
a	O
curve	O
,	O
or	O
mathematical	O
function	O
,	O
that	O
has	O
the	O
best	B-Algorithm
fit	I-Algorithm
to	O
a	O
series	O
of	O
data	B-Application
points	I-Application
,	O
possibly	O
subject	O
to	O
constraints	O
.	O
</s>
<s>
Curve	B-Algorithm
fitting	I-Algorithm
can	O
involve	O
either	O
interpolation	B-Algorithm
,	O
where	O
an	O
exact	O
fit	O
to	O
the	O
data	O
is	O
required	O
,	O
or	O
smoothing	B-Algorithm
,	O
in	O
which	O
a	O
"	O
smooth	O
"	O
function	O
is	O
constructed	O
that	O
approximately	O
fits	O
the	O
data	O
.	O
</s>
<s>
Extrapolation	O
refers	O
to	O
the	O
use	O
of	O
a	O
fitted	O
curve	O
beyond	O
the	O
range	B-General_Concept
of	O
the	O
observed	O
data	O
,	O
and	O
is	O
subject	O
to	O
a	O
degree	O
of	O
uncertainty	O
since	O
it	O
may	O
reflect	O
the	O
method	O
used	O
to	O
construct	O
the	O
curve	O
as	O
much	O
as	O
it	O
reflects	O
the	O
observed	O
data	O
.	O
</s>
<s>
For	O
linear-algebraic	O
analysis	O
of	O
data	O
,	O
"	O
fitting	O
"	O
usually	O
means	O
trying	O
to	O
find	O
the	O
curve	O
that	O
minimizes	O
the	O
vertical	O
(	O
y-axis	O
)	O
displacement	O
of	O
a	O
point	O
from	O
the	O
curve	O
(	O
e.g.	O
,	O
ordinary	B-General_Concept
least	I-General_Concept
squares	I-General_Concept
)	O
.	O
</s>
<s>
However	O
,	O
for	O
graphical	O
and	O
image	O
applications	O
,	O
geometric	O
fitting	O
seeks	O
to	O
provide	O
the	O
best	O
visual	O
fit	O
;	O
which	O
usually	O
means	O
trying	O
to	O
minimize	O
the	O
orthogonal	O
distance	O
to	O
the	O
curve	O
(	O
e.g.	O
,	O
total	B-Algorithm
least	I-Algorithm
squares	I-Algorithm
)	O
,	O
or	O
to	O
otherwise	O
include	O
both	O
axes	O
of	O
displacement	O
of	O
a	O
point	O
from	O
the	O
curve	O
.	O
</s>
<s>
Identical	O
end	O
conditions	O
are	O
frequently	O
used	O
to	O
ensure	O
a	O
smooth	O
transition	O
between	O
polynomial	O
curves	O
contained	O
within	O
a	O
single	O
spline	B-Algorithm
.	O
</s>
<s>
The	O
least	B-Algorithm
squares	I-Algorithm
method	I-Algorithm
is	O
one	O
way	O
to	O
compare	O
the	O
deviations	O
.	O
</s>
<s>
The	O
effect	O
of	O
averaging	O
out	O
questionable	O
data	B-Application
points	I-Application
in	O
a	O
sample	O
,	O
rather	O
than	O
distorting	O
the	O
curve	O
to	O
fit	O
them	O
exactly	O
,	O
may	O
be	O
desirable	O
.	O
</s>
<s>
In	O
agriculture	O
the	O
inverted	O
logistic	O
sigmoid	B-Algorithm
function	I-Algorithm
(	O
S-curve	B-Algorithm
)	O
is	O
used	O
to	O
describe	O
the	O
relation	O
between	O
crop	O
yield	O
and	O
growth	O
factors	O
.	O
</s>
<s>
Hence	O
,	O
matching	O
trajectory	O
data	B-Application
points	I-Application
to	O
a	O
parabolic	O
curve	O
would	O
make	O
sense	O
.	O
</s>
<s>
Tides	O
follow	O
sinusoidal	O
patterns	O
,	O
hence	O
tidal	O
data	B-Application
points	I-Application
should	O
be	O
matched	O
to	O
a	O
sine	O
wave	O
,	O
or	O
the	O
sum	O
of	O
two	O
sine	O
waves	O
of	O
different	O
periods	O
,	O
if	O
the	O
effects	O
of	O
the	O
Moon	O
and	O
Sun	O
are	O
both	O
considered	O
.	O
</s>
<s>
For	O
a	O
parametric	O
curve	O
,	O
it	O
is	O
effective	O
to	O
fit	O
each	O
of	O
its	O
coordinates	O
as	O
a	O
separate	O
function	O
of	O
arc	O
length	O
;	O
assuming	O
that	O
data	B-Application
points	I-Application
can	O
be	O
ordered	O
,	O
the	O
chord	O
distance	O
may	O
be	O
used	O
.	O
</s>
<s>
Coope	O
approaches	O
the	O
problem	O
of	O
trying	O
to	O
find	O
the	O
best	O
visual	O
fit	O
of	O
circle	O
to	O
a	O
set	O
of	O
2D	O
data	B-Application
points	I-Application
.	O
</s>
<s>
Many	O
statistical	B-Algorithm
packages	I-Algorithm
such	O
as	O
R	B-Language
and	O
numerical	B-Application
software	I-Application
such	O
as	O
the	O
gnuplot	B-Application
,	O
GNU	B-Application
Scientific	I-Application
Library	I-Application
,	O
MLAB	B-General_Concept
,	O
Maple	B-Language
,	O
MATLAB	B-Language
,	O
TK	O
Solver	O
6.0	O
,	O
Scilab	B-Application
,	O
Mathematica	B-Language
,	O
GNU	B-Language
Octave	I-Language
,	O
and	O
SciPy	B-Application
include	O
commands	O
for	O
doing	O
curve	B-Algorithm
fitting	I-Algorithm
in	O
a	O
variety	O
of	O
scenarios	O
.	O
</s>
<s>
There	O
are	O
also	O
programs	O
specifically	O
written	O
to	O
do	O
curve	B-Algorithm
fitting	I-Algorithm
;	O
they	O
can	O
be	O
found	O
in	O
the	O
lists	B-Algorithm
of	I-Algorithm
statistical	I-Algorithm
and	O
numerical-analysis	B-Application
programs	I-Application
as	O
well	O
as	O
in	O
:Category:Regression	O
and	O
curve	B-Algorithm
fitting	I-Algorithm
software	O
.	O
</s>
