       Re: 3D Curve fitting

• To: mathgroup at smc.vnet.net
• 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 wolfram.com

```In article <4ne6e4\$car at dragonfly.wolfram.com>, nishioka at nntp1.best.com
(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.

In:=
?Fit
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.

In:=
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}],
1];

In:=
Fit[ data, {x, x^3, y, y^3}, {x, y}]
Out=
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 wolfram.com)
directly.

I hope this helps.

--Ian

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