Interpolation and Curve Fitting
Interpolation and Curve Fitting
Interpolation and Curve Fitting
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• From<br />
Solving for B-spline Coefficients<br />
B ( u)<br />
• We can obtain<br />
B<br />
B<br />
i<br />
(0)<br />
<br />
i<br />
d i<br />
(1) a<br />
B'<br />
B'<br />
i<br />
(0)<br />
i<br />
<br />
i<br />
B'<br />
i<br />
c i<br />
i<br />
b<br />
( u)<br />
i<br />
a u<br />
c<br />
(1) 3<br />
a 2<br />
b<br />
i<br />
i<br />
3<br />
i<br />
b u<br />
i<br />
2<br />
c u d<br />
2<br />
3<br />
a u 2<br />
b u c<br />
i<br />
i<br />
d<br />
c<br />
i<br />
i<br />
• We can solve a set of 4 equations for a, b, c, d<br />
i<br />
i<br />
i<br />
i<br />
Then plug in the followings<br />
pi<br />
4<br />
pi<br />
1<br />
p<br />
i<br />
Bi<br />
1) B<br />
i1<br />
(0) <br />
6<br />
pi<br />
1<br />
4<br />
pi<br />
p<br />
i1<br />
Bi<br />
( 0) <br />
6<br />
p<br />
i<br />
p<br />
i2<br />
B' i<br />
(1) B<br />
'<br />
i1<br />
(0) <br />
2<br />
p<br />
i1 p<br />
i1<br />
B' i<br />
(0) <br />
2<br />
2<br />
(<br />
Numerical Methods © Wen-Chieh Lin 23
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