angular data spline interpolation

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mukesh bisht 2021-8-22

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https://ww2.mathworks.cn/matlabcentral/answers/1438384-angular-data-spline-interpolation

评论： darova 2021-8-23

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];

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Julius Muschaweck 2021-8-23

If you think my answer is correct, please make it the "accepted answer".Thanks

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Julius Muschaweck 2021-8-22

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https://ww2.mathworks.cn/matlabcentral/answers/1438384-angular-data-spline-interpolation#answer_772204

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.