How can I obtain the analytical expression (polynomial) of the spline curve from a curve fitting?

I have extracted data from some graphs (images) and then I curve fitted that data to obtain some spline curves. What I need is the polynomial of those spline, the f(x) that draw the initial graphs, the function that relates the x and y points. How can I do that? Thanks!

[KSSV]

pp = spline(x,y)

In the above pp has the information you want.

[Mathieu NOE]

hi

see :

finding the equation of spline in matlab - (mathworks.com)

[Radu Andrei Matei]

Thanks, after reading the answers to this question I could understand the ones for that question better.

Answer 1

[David Goodmanson]

Hi Radu,

x = 1:10;
y = sin(x).^3;
a = interp1(x,y,'spline','pp')

a = 

  struct with fields:

      form: 'pp'
    breaks: [1 2 3 4 5 6 7 8 9 10]
     coefs: [9×4 double]
    pieces: 9
     order: 4
       dim: 1
    orient: 'first'

>> a.coefs

ans =

    0.3050   -1.3676    1.2186    0.5958
    0.3050   -0.4525   -0.6016    0.7518
   -0.3075    0.4626   -0.5914    0.0028
    0.6000   -0.4598   -0.5886   -0.4335
   -0.7723    1.3403    0.2920   -0.8818
    0.6265   -0.9767    0.6556   -0.0218
   -0.7998    0.9029    0.5818    0.2836
    0.6101   -1.4966   -0.0119    0.9684
    0.6101    0.3337   -1.1748    0.0700

each row is a polynomial in standard Matlab notation, coefficient of x^3 first, coefficient of x^0 last.

a = spline(x,y) does the same thing.

[Radu Andrei Matei]

Hi, thanks a lot for your answer, it is exactly what I asked for. The problem is that I probably didn't ask for exactly what I wanted and don't know how to manage the information you have provided. This might be one of those "don't expect people to make your work" type of questions but anyway, I don't exactly know what to do with those polynomials, I have somewhere around 40 of them. Is this like a piecewise function where each of the polynomials describes my spline for a given little range? Is my f(x) described by polynomials bit by bit? Is there any matlab way to use those polynomials so that if I give an X value a function or something gives back the associated y=f(x) value back for the entire spline? Or do I have to know the exact range that each polynomial describes so that I can create a big piecewise expression that gives me f(x)?

[Radu Andrei Matei]

Hi, I think I found it. I think using ppval I can find the f(x) value for a given x in the entire spline. Correct me if I'm wrong please.

[David Goodmanson]

Hello Radu,

Yes, each polynomial describes the function for a given little range. Also each polynomial is local in the sense that x = 0 effectively restarts at the beginning of each range. And you are correct, ppval will reconstruct the whole works.

Answer 2

[Matt J]

What I need is the polynomial of those spline

A spline consists of many polynomials stuck together, not just one.Also, there are a number of different forms in which spline fits can exist in Matlab, and we don't know which ones you have. If you really need to break down a spline, and it is in the form of a pp structure you could use unmkpp. More likely, you used cftool, in which case you have a cfit object.

Regardless, there is a reason that Matlab doesn't provide you with an analytical form for the spline. It's because far better tools are provided to post-process a fit,

https://www.mathworks.com/help/curvefit/fit-postprocessing.html?searchHighlight=fit%20post&s_tid=srchtitle_fit%20post_2

[Radu Andrei Matei]

Hi, thank you for your answer, but as I am a big matlab noob I could understand David Goodmanson's answer better.