       Re: Question about interpolation and ListPlot3D

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1492] Re: Question about interpolation and ListPlot3D
• From: roth at sunny.mpimf-heidelberg.mpg.de (Arnd Roth)
• Date: Mon, 19 Jun 1995 01:16:10 -0400
• Organization: Max-Planck-Institut fuer Medizinische Forschung

```In article <3rn543\$acd at news0.cybernetics.net>
zwiener at lehman.com (Zvi Wiener) writes:

>   I have an array representing 3 dimensional points
> in a form of their Eucledean coordinates:
> arr = {{x1,y1,z1}, ... ,{xN,yN,zN}};
> (they were generated from a very smooth function).
>
> 1. I wish to generate a 3D plot of this surface (approximately),
> but format of ListPlot3D does not permit it, since my points
> {xi, yi} do not form a regular grid.
> How I can draw the surface?

The function TriangularSurfacePlot[] in the package
DiscreteMath`ComputationalGeometry` is what you need:

In:= <<DiscreteMath`ComputationalGeometry`

In:= ?TriangularSurfacePlot
TriangularSurfacePlot[{{x1, y1, z1},... ,{xn, yn, zn}}] plots
the zi according to the planar Delaunay triangulation
established by the {xi, yi}. (...)

However you should condition your set of points such that
no two points {x1, y1, z1} and {x2, y2, z2} are very very
close (compared to the average distance) or even identical.

> 2. I would like to find value of this function at another point
> {x, y}, the answer obviously depend on the way the function was
> interpolated (extrapolated), but I am interested in any way, as
> simple as possible.
> How to extract the Interpolating Function's value at {x, y} ?

You can use the resulting set of triangles (TriangularSurfacePlot
returns Graphics3D[{Polygon[{{..., ..., ...}, ..., ...}], ...}]
objects) to linearly interpolate your function. However at the
moment I do not have a function ready that does this. It should
not be too difficult to write one.

Sincerely,

Arnd Roth
Abteilung Zellphysiologie
Max-Planck-Institut fuer Medizinische Forschung
Postfach 10 38 20, D-69028 Heidelberg, Germany
http://sunny.mpimf-heidelberg.mpg.de/people/roth/ArndRoth.html

```

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