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Re: Re: Multidimensional Splines/Interpolation ?

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  • Subject: [mg20810] Re: [mg20763] Re: Multidimensional Splines/Interpolation ?
  • From: "Dr. Christopher Purcell" <purcell at>
  • Date: Sun, 14 Nov 1999 18:13:58 -0500 (EST)
  • References: <80aur6$>
  • Sender: owner-wri-mathgroup at

I can't give you the code, but I can give you a hint - You can use
Interpolation, (or ListInterpolation in V3.0+ ), and simply apply it
multiple times simultaneously, one for each axis in your multidimensional
space. This works from Version 2.2 onwards. I routinely fit splined space
curves, surfaces and solids to as many arbitrary points on and in weirdly
shaped 3D objects as I need, and it works fine. Takes maybe a dozen lines
lines of code to do this and no special packages are needed.

>you are looking for an interpolation over an irregular grid
>you may try DiscreteMath`ComputationalGeometry`TriangularSurfacePlot
>or the ExtendGraphics packages from Tom Wickham-Jones on MathSource.
>A spline over an irregular triangle mesh is a current research topic
>and I don't expect that you will find a solution in Mathematica.
>  Jens
>Volker Hilsenstein wrote:
>> Hello everyone,
>> I'm looking for something like multidimensional Splines/Interpolation.
>> This is what I want to do: Given some  points of a height field h(x,y)
>>  (water surface; mountain range etc) I want to have a good interpolation
>> f
>> or the points in between (the surface is smooth, no discontinuieties)..
>> I figure something like multidimensional splines is what I want, but
>> I'm not sure whether something like this exists. There's some examples
>> for multidimensional interpolation in the Mathamatica Book but in those
>> examples you have to provide h(x,y) for all points of a grid. I have
>> discrete
>> Data, but I only can provide  h(x_i,_y_i) for some points (x_i,y_i) that
>> don't fill the grid ...
>> Any ideas would be greatly appreciated !
>> Cheers,
>> Volker

Dr. Christopher J. Purcell
DREA, 9 Grove St. Dartmouth NS B2Y3Z7

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