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Subject: Re: Data Fitting to Parametric Equations
Date: Wed, 4 Nov 2009 16:01:03 +0000 (UTC)
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"Anthony Mai" <antoniusmae@gmail.com> wrote in message <hcs794$m3p$1@fred.mathworks.com>...
> Hello all,
> I have a data set of (x,y,z) Cartesian values, and the following parametric equations for a skewed tear-dropped ellipsoid:
> X=a0+a1*cos(theta)*sin(phi)
> Y=b0+b1*sin(phi)*sin(theta)
> Z=c0+c1*cos(phi)*exp(d0*phi)
> theta=(0:2*pi)
> phi=(0:pi)
> Is there any way possible to determine these parameters a0, a1, etc.? I have attempted to google every link regarding at surface fitting and have come up empty handed. These equations are weird in that it's in parametric and it's in 3d. The equations are for experimental data obtained from testing antennae strengths. Possibly it could be some type of spheroid also, but again same complexity of equations. Also maybe I could try using the implicit equation instead of using parametric? With that regard I tried finding some implicit data fitting methods and again nothing. Any help or points in some direction would greatly help. Thanks!
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Doesn't seem weird to me. It's almost a linear fitting problem, apart from the parameter d0, which is your only intrinisically non-linear parameter. Check the file exchange for the function fminspleas()