Interpolation and Curve Fitting
Interpolation and Curve Fitting
Interpolation and Curve Fitting
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Hermite <strong>Curve</strong> Formation—<br />
consider x coordinate first<br />
• Cubic polynomial <strong>and</strong> its derivative<br />
3 2<br />
x(<br />
u)<br />
a<br />
u b<br />
u c<br />
u<br />
x'<br />
( u)<br />
• Given x i , x i+1 , x’ i , x’ i+1 , solve for a, b, c, d<br />
• 4 equations are given for 4 unknowns<br />
x<br />
x<br />
x<br />
2<br />
3<br />
a u 2<br />
b<br />
x<br />
x<br />
u c<br />
x<br />
d<br />
x(0)<br />
x i<br />
d x<br />
x(1)<br />
x<br />
i 1<br />
a<br />
x<br />
b<br />
x<br />
c<br />
x<br />
d<br />
x'<br />
(0) x'<br />
i<br />
c x<br />
x (1) x<br />
' <br />
3<br />
a 2<br />
b c<br />
'<br />
i 1<br />
x<br />
x<br />
Numerical Methods © Wen-Chieh Lin 9<br />
x<br />
x<br />
x
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