# Applying boundary conditions on a cubic spline interpolation

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Marc Abdel Nour on 4 Nov 2022
Commented: Marc Abdel Nour on 10 Nov 2022
Hello,
I'm trying to implement the function interp1 in my code, as follows:
S=interp1(x,y,xq,'spline')
As output, I'm getting the interpolated value at position xq, using cubic spline interpolation. But interp1 uses not-a-knot as boundary condition, is there any way i can get S using different boundary conditions?like clamped or periodic or ....?
I tried using csape, but the thing is that i couldn't get the interpolated value at the specific location xq.

Santosh Fatale on 10 Nov 2022
Hi Marc,
As you mentioned, you can use “csape” function for different end conditions. Note that “csape” returns interpolants in ppform. You can use “fnval” function to calculate value of interpolant in ppform at the specific location xq.
Marc Abdel Nour on 10 Nov 2022
It works, thank you

Bruno Luong on 10 Nov 2022
You can select periodic bc, natural bc [default]; not-a-knot, or clamping first or second derivative on boundary.
This FEX is written long ago and a little bit out-date, but it still working =.
x=cumsum(rand(1,6));
y=rand(size(x));
xi=linspace(min(x),max(x));
yi_notaknot=interp1(x,y,xi,'spline');
yi_natural=spline1d(x,y,xi,[]);
figure
plot(x,y,'or');
hold on
h1=plot(xi,yi_notaknot,'b');
h2=plot(xi,yi_natural,'r');
legend([h1 h2],'not-a-knot','natural')