How to define endslopes for spline interpolation for 2-dimensional curves?

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David 2019-3-4

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/448167-how-to-define-endslopes-for-spline-interpolation-for-2-dimensional-curves

While working with splines and trying to define some endslopes, I had some problems:

The example from matlab help worked fine:

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

But after that I wanted to try something like an ellipse:

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

I figured out that I had to change the endslopes to 0.15 to obtain the expected ellipse:

x = pi*[0:.5:2];
y = [0   1   0  -1   0  1    0;
    .15  0  .1   0 -.1  0  .15];
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