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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: a cubic fitting curve in a set of (x, y, z) data ?
Date: Thu, 21 Mar 2013 21:41:06 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
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"Kuo-Hsien" wrote in message <kifjqt$qq6$1@newscl01ah.mathworks.com>...
> "Torsten" wrote in message <kied7n$oom$1@newscl01ah.mathworks.com>...
> > "Kuo-Hsien" wrote in message <kidpp3$440$1@newscl01ah.mathworks.com>...
> > > Dear all,
> > > 
> > > I have a set of scatter data (x, y, z).
> > > 
> > > How to add a cubic fitting curve in this 3d plot?
> > > 
> > > Thanks for the hint.
> > > 
> > > Michael
> > 
> > A curve for 3d data ?
> > 
> > Best wishes
> > Torsten.
> 
> Hi Torsten,
> 
> Yes. the 3d dataset looks like a narrow galaxy band (scatters) across the xyz plot. I'd like to just add a cubic fitting line to stand for this narrow band scatters.
> 
> Any ideas?

Essentially, it sounds like you wish to fit a "cubic" model to data
with noise in all three variables. So a cubic errors in variables
model. Not at all trivial.

Worse, a "cubic" curve makes essentially little sense anyway
in three dimensions. What model are you posing? What is a 
function of what? When you say cubic, this has to mean
something in terms of mathematics.

It sounds like what you really want is some general curve that
follows through the center of your curvilinear cloud, in itself
not a trivial task either.

I'd suggest grouping your points by averaging into a relatively
few points, spaced apart. Now use a tool that can interpolate
a curve through those points in three dimensions. cscvn is
such a tool, or my own interparc from the file exchange.

John