Re: Multidimensional Interpolation

• To: mathgroup at smc.vnet.net
• Subject: [mg12806] Re: Multidimensional Interpolation
• From: David Annetts <dannetts at laurel.ocs.mq.edu.au>
• Date: Fri, 12 Jun 1998 04:05:37 -0400
• Organization: CRCAMET/Macquarie University
• References: <6llb5r\$da3@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Hi Sean

Sean Ross wrote:

> While attempting to make some nice 3D plots of {x,y,z} data for a
> friend, I ran into the strangest behavior I am hoping someone can shed
> light on.  First, some background:
>
> Interpolation[{{x1,y1,f1},{x2,y2,f2},...}]
>
> usually requires a square number of data points.  If you give it 48 data
> points, it will come back with an error message saying that the number
> of points n in dimension 2 is not 7, since somehow Interpolation has
> decided that there ought to be 49 points in the set.
>
> The data supplied to me by my friend had 441 data points, which is 21^2.
> Interpolation came back and told me that the number of points in
> dimension 2 was not 2 ???!, so it couldn't do anything.  As a test, I
> generated sample data with Table that also had 441 {x,y,z} data points
> of the same format and Interpolation had no problem with the canned
> data, but 8 sets of real data supplied by my friend gave the same
> problem, where Interpolation thought that there should be 2^2 rather
> than 21^2 data points in the set.
>
> Can anyone shed some light on how Interpolation determines its subsets
> and what I might look for in the data set?  Perhaps I might re-order
> the data somehow if I understood what Interpolation was looking for.
> If anyone is interested, I can send you the original data.

I'm not sure about shedding light on the subject, but experience with
Interpolation has taught me that the data shouldbe on a rectangular
grid. Interpolation[{Random[], Random[], Random[]}] tends not to work.

Triangulation, either via "ComputationalGeometry' or Wickham-Jones'
"ExtendGraphics' Package does not suffer this restriction, and is
probably what you're after.  The ExtendGraphics package is probably the
way to go because of its speed.

I think this has been a failure of Interpolation from Day 1.  Why can we
not Interpolate randomly positioned data like other programs in
Mathematica?

--
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