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MathGroup Archive 2001

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SplineFit - Parametrization ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg31289] SplineFit - Parametrization ?
  • From: Justus Heimann <Heimann at ism.tu-berlin.de>
  • Date: Fri, 26 Oct 2001 04:28:44 -0400 (EDT)
  • Organization: Technical University Berlin, Germany
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

I got a question concerning the "SplineFit[DATA, Cubic]" function of the
NumericalMath`SplineFit` Package.

My problem is to fit a cubic spline to a set of numerical 2d data. E.g.
using simply x,y-data like:

DATA := Table[{1.*i^2, Random[Real, {-1., 1.}]}, {i, 10}];
splinefit := SplineFit[DATA, Cubic];
splinefit[u=f(x,y)][[1]] =! x ???

I found that SplineFit works much more accurate like e.g. the function
Interpolation. That's why I switched from Interpolation to SplineFit. 

The problem is, that using SplineFit (in contrast to Interpolation),
specfific data along the curve only can be identified by the curve
parameter value. But actually I'm interested to explicitly get a curve
value f(x) as function of x! Is this possible with SplineFit ? In case
not, does anybody know how are the parameter values linked to the x, y
values ?

It seems that the parameter, say "u=f(x,y)", is running like
U=[0,1,2,...,Length[DATA]-1] along the data points, somehow a uniform
(integer) curve parametrization. But what happens with the parameter  in
between data points ?

Thanks alot,
Justus


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