how to reconstruct piecewise polynomial splines?

I am trying to reconstruct and evaluate multivariate pp splines that are made in MATLAB in C, using coefficients that are provided when I built them in MATLAB. However, I could not understand what is the form of these multivariate polynomial, and how can assign the coefficients in different intervals. Can you tell me how to reconstruct these multivariate PPs, or what is their form?

[Walter Roberson]

Which routine did you use to build them in MATLAB?

[Behnam]

I am making B-form splines using spapi and then convert B-form to pp using fn2fm.

Answer 1

[Sreeja Banerjee]

Hi Behnam,

At the end of the documentation page for function SPAPI and FN2FM, you can see that there is a "More About" section which talks about the algorithms the functions use.

• SPAPI: http://www.mathworks.com/help/curvefit/spapi.html
• FN2FM: http://www.mathworks.com/help/curvefit/fn2fm.html

You can also use the following commands at the MATLAB command line to look at the implementation of the algorithms:

>> edit spapi
>> edit fn2fm

[Behnam]

Hi Sreeja, I have looked at those, but they do not provide info about the form of multivariate polynomials. what I am interested in is to know which form of polynomial are those coefficients belong to. So using those coefficients I would be able to evaluate the polynomial's value at arbitrary data points in my code in C.