Problem using TriScatteredInterp with highly constrained triangulations

Question

lsailer 2011-10-17

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/18452-problem-using-triscatteredinterp-with-highly-constrained-triangulations

Hello,

I've been having a problem with TriScatteredInterp in version R2009a where I erratically obtain NaN values for my output value. I'm wondering if anyone else has had problems using constrained 2D Delaunay triangulations to create TriScatteredInterp objects, and if anyone has a suggested work-around.

To set up the problem a little, I have an scattered data set [X1,Y1] with point values V, which I need to interpolate into a different scattered data set [X2,Y2]. I also know the Delaunay triangulation of my data set, as calculated by MatLab when calling DelaunayTri, is not a very good triangulation for interpolating with, i.e. there are a lot of long, skinny triangles. Luckily, I know beforehand a better triangulation scheme, which I apply as a constraint into a Delaunay triangulation, which I then use as the triangulation for my interpolation object, like so:

% Data set [X1,Y1] with known values [V1], and known triangulation scheme [TRI]
  trTri = TriRep(TRI,X1,Y1);
  C = edges(trTri);
  dTri = DelaunayTri(X1,Y1,C);
  vInterp = TriScatteredInterp(dTri,V1,'linear');
  V2 = vInterp(X2,Y2);

The points contained in the data set [X2,Y2] are all WITHIN the convex hull of the scattered data [X1,Y1]. However, I often will obtain NaN values in V2. Occasionally, all values in V2 are NaN. Also on occasion, if I try the interpolation a second time, i.e., I re-type the command: V2 = vInterp(X2,Y2), the interpolation will work fine: no NaN values at all. This is even the case if I interpolate each point one at a time through a FOR loop as such:

for n=1:length(X2)
    V2(n) = vInterp(X2(n),Y2(n))
end

Ultimately, the performance of the interpolation object is extremely erratic. I initially chose to use TriScatteredInterp because it allowed me to constrain my interpolation object, and because I am interpolating FROM a scattered data set TO a scattered data set. I absolutely must constrain my triangulation, due to the DelaunayTri's non-ideal triangulation: the values returned by a TriScatteredInterp object created without the constraint C are complete garbage.

If anyone has any insight or potential work-around, I appreciate it in advance.

Cheers, Logan