How to get an equation for a cubic spline using the spline function?

Say I have two sets of data, x and y, such that

x = [1,2,3,4,5] y = [6,7,8,9,10]

t = linspace(1,5,100) Finding the cubic spline using the function:

splineX = spline(x,y,t);

I have used the command to be able to plot function splineXbut I'm not sure how I can find the actual equation the spline function calculates

(I know that for this data it would simply be a straight line but I only used this to better articulate what I'm trying to find)

Answer 1

[Joshua Long]

When you pass in a third parameter, the "spline" function automatically evaluates the spline for those points using "ppval". If you only pass in two parameters, "spline" returns a struct representing the spline created. The coefficients for the piecewise polynomials can be extracted using the function "unmkpp".

 >> x = [1,2,3,4,5];
 >> y = [6,7,8,9,10];
 >> pp = spline(x, y);
 >> [~, coeffs] = unmkpp(pp);

Each row of "coeffs" has the coefficients for one of the piecewise polynomials at each break.

For example:

 >> coeffs(1, :)

is

 [0, 0, 1, 6]

representing the function "x + 6".

[farouk messaoud]

hey; I have data to fit by cubic B-spline; How can I get the piecewise equations of the curves and the knot vector? thank you sir

[Aissam]

    >> coeffs(1, :)
    [0, 0, 1, 6]
represents
    (x-pp.breaks(1))+6=x+5