Re: 2D interpolation

• To: mathgroup at smc.vnet.net
• Subject: [mg72910] Re: 2D interpolation
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 25 Jan 2007 06:15:19 -0500 (EST)
• Organization: The Open University, Milton Keynes, UK
• References: <ep7cv1\$bl5\$1@smc.vnet.net>

```Jouvenot, Fabrice wrote:
> Hello,
>
> I try to have a 2 dimensional interpolation of points {x, y, f(x,y)}.
> After some try, I wrote these lines (as an exemple of what I want to do)
> that works :
> ________________________________________
>
> data = {{1, 1, -10}, {1, 2, 2}, {1, 3, 3}, {1, 4, 4}, {1, 5, 5}, {2, 1,
> 2}, {2, 2, 4}, {2, 3, 6}, {2, 4, 8}, {2, 5, 10}, {3., 1, -9}, {3, 2, 6},
> {3, 3, 90}, {3, 4, 12}, {3, 5, 15}, {4, 1, 4}, {4, 2, 8}, {4, 3, 12},
> {4, 4, 16}, {4, 5, 20}, {5, 1, 5}, {5, 2, 10}, {5, 3, 15}, {5, 4, 20},
> {5, 5, 40.5}};
>
> MatrixForm[data]
>
> test[x_, y_] := Interpolation[data][x, y];
>
> test[1.5, 1.5]
>
> Plot[test[x, 1], {x, 1, 5}];
>
> Plot[test[x, x], {x, 1, 5}];
>
> Plot3D[test[x, y], {x, 1, 5}, {y, 1, 5}];
>
> ________________________________________
>
>
> The problem is that when I want to use a point with a real x or y like
> {1.23, 1.1, -10}, nothing works anymore.
> I think that I miss something essential and fundamental, but I don'y
> know why...
> Cheers,
>
> Fabrice.
>

Hi Fabrice,

ListInterpolation should be better suited to the task:

"ListInterpolation is similar to Interpolation, but provides a more
convenient interface for data that does not include coordinates and for
multidimensional data."

See http://documents.wolfram.com/mathematica/functions/ListInterpolation

Regards,
Jean-Msrc

```

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