angular data spline interpolation

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mukesh bisht
mukesh bisht on 22 Aug 2021
Commented: darova on 23 Aug 2021
Hi, I have the following query using spline interpolation for angular data. The code attached below is from matlab documentation:
x = pi*[0:.5:2];
y = [0 1 0 -1 0 1 0;
1 0 1 0 -1 0 1];
pp = spline(x,y);
yy = ppval(pp, linspace(0,2*pi,101));
plot(yy(1,:),yy(2,:),'-b',y(1,2:5),y(2,2:5),'or')
axis equal
This code gives the closed piecewise polynomial for circle of radius 1unit. Now if I calculate the value of plynomial for a given query point, it doesnt give me the correct answer. why??
For ex: xq = 0; yq = ppval(pp,xq);
It gives yq = [1;0] but it should be yq = [1,-1];
  1 Comment
Julius Muschaweck
Julius Muschaweck on 23 Aug 2021
If you think my answer is correct, please make it the "accepted answer".Thanks

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Accepted Answer

Julius Muschaweck
Julius Muschaweck on 22 Aug 2021
Your x has five values, your y has seven values. This is a mismatch.
I think you should use
y = [0 1 0 -1 0;
1 0 -1 0 1];
and when you do that,
xq = 0; yq = ppval(pp,xq);
gives you [0;1] as it should. Your "circle" looks more triangular, but that's ok since the sine is badly approximated by the spline with only 5 support points.
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