       Re: nonlinear fits of parametric equation?

• To: mathgroup at smc.vnet.net
• Subject: [mg18111] Re: [mg18081] nonlinear fits of parametric equation?
• From: Christian Honeker <xian at mpip-mainz.mpg.de>
• Date: Thu, 17 Jun 1999 12:26:43 -0400
• References: <001101beb79a\$e6178420\$70b7fdd0@d.parks>
• Sender: owner-wri-mathgroup at wolfram.com

```My thanks go to David!
His example was exactly what I needed to get what I wanted!

Christian

David Park wrote:

> >Dear Mathematica Users!
> >
> >I would like to fit (x,y) points which are arranged in the shape of an
> >ellipse
> >using the equation of an ellipse.
>
> Christian,
>
> I have attached a Mathematica notebook which shows how to do part of your problem.
> For a standard ellipse this is the trick. Your function is:
> f[x, y] == x^2/a^2 + y^2/b^2 == 1. So modify each {x, y} data point to {x, y, 1} and
> use NonlinearFit.
>
> In the notebook I have generated a random set of data and then fitted it with a
> standard ellipse. It seemed to work all right.
>
> I have a ConicSections package which I think will help you with the more general
> problem. It has routines such as ReduceConic which will find a rotation and shift of
> origin which will reduce a conic expression to a standard form equation. There is
> also a routine which will take an expression and then generate the new expression
> under a rotation and shift. So I think what will be needed is to generate the
> equation with parameters {a,b,x0,y0,theta} and then make a fit to that.
>
>   ------------------------------------------------------------------------
>                         Name: HonekerExample.nb
>    HonekerExample.nb    Type: application/mathematica (application/mathematica)
>                     Encoding: 7bit

```

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