How to obtain the piecewise expressions of spline fit obtained using MATLAB's command spapi?

I am working on fitting the data using B-form splines. I am using "spapi" command in MATLAB. Here is my code:

x = [0.0 0.3 0.5 0.6 1.0 1.0 0.0 0.2 0.6 0.8];
y = [1.0 0.5 0.9 0.8 0.0 1.0 0.0 0.1 0.2 0.7];
[yy,xx] = meshgrid(y,x); z = sin(xx+yy);
sp = spapi({3,5},{x,y},z) 
fnplt(sp) 
fnval(sp,[x;y])

I want to obtain the piece wise expressions of the splines. I tried see the documentation of spapi but they haven't mentioned any formulations for those. The function fnval only provide the value at some points, but i want to obtain the expression and calculate it derivatives further.

Answer 1

[Steven Lord]

i want to obtain the expression and calculate it derivatives further.

Do you need the actual expression, or do you just want to be able to evaluate and differentiate it?

To evaluate it, use fnval. To differentiate it, use fnder.

load census
S = spapi(2, cdate, pop);
S2 = fnder(S);
[minYear, maxYear] = bounds(cdate);
Y = minYear:5:maxYear;
plot(cdate, pop, 'o', Y, fnval(S, Y), '-+')

figure
plot(Y, fnval(S2, Y), 'x--')

[Muhammad Adeel Ahsan Awan]

How can i get the piecewise expressions of splines on different intervals?