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MathGroup Archive 2003

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Re: Interpolation over an irregular surface

  • To: mathgroup at smc.vnet.net
  • Subject: [mg39247] Re: Interpolation over an irregular surface
  • From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
  • Date: Thu, 6 Feb 2003 03:06:51 -0500 (EST)
  • Organization: Universitaet Leipzig
  • References: <b1q6o9$347$1@smc.vnet.net>
  • Reply-to: kuska at informatik.uni-leipzig.de
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

the easy way would be to edit the delaunay.tm file
and return the adjacence information (as written
in the package comments).

If you don't like this you can make a loop over all
triangles, and append the point list in the triangle
to the adjacence list of every vertex in the triangle,
finaly build the Union[] of the adjacence list for every
vertex and remove the index k of the adjacence list for
vertex k.

Regards
  Jens

Jacob Rome wrote:
> 
> I'm trying to map (interpolate) temperatures from one 2D set of points
> to another for a finite element application.  The initial set of
> points is {x1,y1,t1} and the second set is {X1,Y1,T1}, and I know all
> the values except for T1. I have connectivity data for the new mesh
> {X1,Y1}, but not for the original mesh (x1,y1).
> 
> I have downloaded the ExtendGraphics package, and it has a functions
> (TriangularInterpolate) which should do exactly what I need. No error
> is given when I initially use it
> (interpFunc=TriangularInterpolate[nodeTemp], where nodeTemp is a
> 3-column matrix). However, when I invoke it again (interpFunc[x1,y1]),
> I get a series of errors, primarily about reaching the recursion or
> iteration limits. Could this have to do with the size of the initial
> matrix (~15,000 sets of data), or is there a different problem? It
> only seems to work correctly when the point is outside of the initial
> region, or if all the nearest nodes have the same temperature.
> 
> After this setback, I planned to use the Delaunay function in the same
> package to help write my own interpolation routine. Using this
> function should return three sets of data: the Convex Hull, Adjacency
> Matrix and the Triangles. However, it appears that only the Convex
> Hull and the Triangles are returned; to effectively write an
> interpolation routine, the Adjacency Matrix is crucial. How can I get
> this data from the Delaunay function?
> 
> Any advice on solving this problem is greatly appreciated, whether you
> can suggest an alternative approach or provide a means to use these
> functions more effectively. Thank you.


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