Spline coordinates from spap2

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?

[Torsten]

What are the "orthogonal coordinates" ?

[Biraj Khanal]

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]

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]

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.

Answer 1

[Torsten]

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

[Biraj Khanal]

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]

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.