Re: Re: Multidimensional Splines/Interpolation ?
- To: mathgroup at smc.vnet.net
- Subject: [mg20810] Re: [mg20763] Re: Multidimensional Splines/Interpolation ?
- From: "Dr. Christopher Purcell" <purcell at drea.dnd.ca>
- Date: Sun, 14 Nov 1999 18:13:58 -0500 (EST)
- References: <email@example.com>
- Sender: owner-wri-mathgroup at wolfram.com
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. >Hi, > >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. > >Regards > 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