       nonlinear fits of parametric equation?

• To: mathgroup at smc.vnet.net
• Subject: [mg18081] nonlinear fits of parametric equation?
• From: Christian Honeker <xian at mpip-mainz.mpg.de>
• Date: Tue, 15 Jun 1999 01:43:37 -0400
• Delivery-date: Tue Jun 15 03:11:23 1999
• Sender: owner-wri-mathgroup at wolfram.com

```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.
Must I have a function of the form y = f(x) in order to use
NonlinearFit? Can the command NonlinearFit accept
the parametric form of an equation as the model?

I realize that the simple form of an ellipse

x^2/a^2 + y^2/b^2 = 1

can be plotted either in two parts:

Plot[{Sqrt[(1-x^2/a^2) b^2], -Sqrt[(1-x^2/a^2) b^2]}, etc. ]

or parametrically

ParametricPlot[{a Cos[theta], b Sin[theta]}, etc. ]

It seems that working with the parametric form is simpler.
However, I would like to be able to fit data which
has the shape of an ellipse, but is not necessarily
centered about the origin nor parallel to one of the
axes. The most general form for an ellipse
can be written:

A x^2 + B xy + C y^2 + D x + E y = 0

But I don't know how to get NonlinearFit to
fit the above function to my data!
Worse yet, I don't know how to reduce the five
constants to the information I need:
center of the ellipse, width of major & minor axes etc.

Any assistence is appreciated!

Christian Honeker

```

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