Re: 2D interpolation

*To*: mathgroup at smc.vnet.net*Subject*: [mg72953] Re: 2D interpolation*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Fri, 26 Jan 2007 06:58:34 -0500 (EST)*Organization*: The University of Western Australia*References*: <ep7cv1$bl5$1@smc.vnet.net>

In article <ep7cv1$bl5$1 at smc.vnet.net>, "Jouvenot, Fabrice" <F.Jouvenot at liverpool.ac.uk> wrote: > 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. n dimensional interpolation using Interpolation requires that the coordinates lie on a structured tensor product grid. The point {1.23, 1.1, -10} is not on the grid formed by x, y = 1, 2, ..., 5, i.e, Outer[List, Range[5], Range[5]] Have a look at the triangular interpolation functionality which is included in the ExtendGraphics Packages available at http://library.wolfram.com/infocenter/Books/3753/ Cheers, Paul _______________________________________________________________________ Paul Abbott Phone: 61 8 6488 2734 School of Physics, M013 Fax: +61 8 6488 1014 The University of Western Australia (CRICOS Provider No 00126G) AUSTRALIA http://physics.uwa.edu.au/~paul