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Re: 3D Curve fitting

  • To: mathgroup at
  • Subject: [mg4035] Re: 3D Curve fitting
  • From: ianc (Ian Collier)
  • Date: Tue, 28 May 1996 01:45:40 -0400
  • Organization: Wolfram Research, Inc.
  • Sender: owner-wri-mathgroup at

In article <4ne6e4$car at>, nishioka at
(Owen Nishioka) wrote:

> I'm not sure if this is a trivial question, but I haven't been able
> to figure it out.  I'm trying to fit a surface through a series of
> points, (similar to Fit, but in z for x and y) and generate an
> equation.  Any ideas on how to do this?
> Thanks,
> Owen
> --

Yes. You can simply use Fit.

Here is a simple example.

    Fit[data, funs, vars] finds a least-squares fit to a list of
       data as a linear combination of the functions funs of
       variables vars. The data can have the form {{x1, y1, ...,
       f1}, {x2, y2, ..., f2}, ...}, where the number of
       coordinates x, y, ... is equal to the number of variables
       in the list vars. The data can also be of the form {f1,
       f2, ...}, with a single coordinate assumed to take values
       1, 2, .... The argument funs can be any list of functions
       that depend only on the objects vars.

    data =  Flatten[
                Table[ {x, y, 
                        2 x + 3 x^3 + 7 y - 2 y^3 + .5 Random[]},
                        {x, 0, 2, .2}, {y, 0, 2, .2}],

    Fit[ data, {x, x^3, y, y^3}, {x, y}]
                         3                       3
    2.18738 x + 2.96728 x  + 7.1637 y - 2.02183 y

Fit is documented in some detail, including an example of 
fitting a set of data to a function of x and y, in section 
3.8.1 of the Mathematica book (pp 672-676) .

If you require further help with this I would suggest that you 
contact Wolfram Research Technical Support (support at

I hope this helps.


Ian Collier
Wolfram Research, Inc.
tel:(217)-398-0700   fax:(217)-398-0747    ianc at
Wolfram Research Home Page:


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