Spline coordinates from spap2

2022 6 29
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更新时间：2022 7 1
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I am trying to get third order spline approximation for a given set of points.
p=[..;..];
spline=spap2(knots,3,p(1,:),p(2,:));
This works and I can use fnplt to plot the curve. Howver, I am not sure how I can get the orthogonal coordinates.
For cscvn, fnval would return a 2D matrix of coordinates. However, it does not work here. Is there any solution to this?

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Torsten
Torsten 2022-6-29
What are the "orthogonal coordinates" ?
Biraj Khanal
Biraj Khanal 2022-6-29
This was a mistake. Thank you! I am triying to find the spline coordinates using the knots as it can be done with breaks in cscvn.
Torsten
Torsten 2022-6-29
编辑：Torsten 2022-6-29
You mean the spline coefficients in the different intervals ?
Maybe you can give an example with cscvn of what you want to get.
Biraj Khanal
Biraj Khanal 2022-6-29
okay. i might be getting the terms wrong. but here is what i mean with cscvn.
p=[..;..];
c=cscvn(p);
p_new=fnval(c,linspace(c.breaks(1),c.breaks(end),50));
Here, p_new would be a 2D matrix which I can use to plot and get the similar curve as p.
My idea is to use spap2 to matrix like p and get a p_new with the specific number of points ( which is from the knots as I understand) . Say P is a 2X500 matrix. I am trying to get the approximate curve with the a lower number of points using the approximation.

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Torsten
Torsten 2022-6-29
编辑：Torsten 2022-6-29
Ran in:

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Ran in:
x = -2:.2:2;
y=-1:.25:1;
[xx, yy] = ndgrid(x,y);
z = exp(-(xx.^2+yy.^2));
sp = spap2({augknt([-2:2],3),2},[3 4],{x,y},z);
xyq = [1.8;0];
value = fnval(sp,xyq)
value = 0.0178
exp(-xyq.'*xyq)
ans = 0.0392

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Biraj Khanal
Biraj Khanal 2022-7-1
编辑：Biraj Khanal 2022-7-1
I understand your solution. Here is what I was trying to do:
p = [..;..];
p1=spap2(40,3,p(1,:),p(2,:)); %for 40 knots and third order approximation
x=p1.knots.
y=fnval(p1,p1.knots)
p_approx = [x;y];
I just wanted to get p_approx for further steps. But, can you help me understand what the coefficients are in the structure?
Torsten
Torsten 2022-7-1
编辑：Torsten 2022-7-1
p1.coefs
give you the coefficients of the B-spline. My guess is that these are the coefficients a_ij in the representation of the spline
s(x,y) = sum_i sum_j a_ij * B_i(x) * B_j(y)
But you should read the documentation if this is correct.

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