MATLAB: Unexpected interpolation result when using scatteredInterpolant or TriScatteredInterp

MATLABunexpected interpolation scatteredinterpolant triscatteredinterp bug?

I'm usuing scatteredInterpolant to linearly interpolate scattered data. The Z values (samples) in my data-set range from 0.005 to 15.26 and the point that I'm interpolating to is fully enclosed by avaialble points, so interpolation is possible.

I would expect a value of about 0.04, but both scatteredInterpolant and TriScatteredInterp return values of -85.8, which doesn't make sense at all.. Using 'natural' or 'nearest' does produce realistic results.

All required data to reproduce this issue is attached and given below. Any help is greatly appriciated.

top view, blue points are available data, red dot is requested point

same plot in 3d

Code (required .mat file is attached)

close all; clear all; clc;
load('debugData');
% Since we're using linear interpolation, we would expect a result 
% between the minimum and maximum of zz
min(zz)
max(zz)
temp = scatteredInterpolant(real(xx),real(yy),real(zz),'linear','none');
% linear interpolation
% no extrapolation
howcanthisbe = temp(rx,ry) % would exepect 0.04 but gives -85
% trying the old method
old = TriScatteredInterp(xx,yy,zz);
oldResult = old(rx,ry) % same result
% top view
figure;
plot(xx,yy,'b.');
hold on;
plot(rx,ry,'r.');
% and 3d
figure;
t = delaunay(xx,yy);
defaultFaceColor  = [0.6875 0.8750 0.8984];
trimesh(t,xx,yy, zz, ...
    'EdgeColor','b','FaceColor',defaultFaceColor,'FaceAlpha',0.5)
hold on;
scatter3(xx,yy,zz);
hold on;
scatter3(rx,ry,howcanthisbe,'r.');

Best Answer

Some of the sample-points are very close (machine precision) to eachother. This caused the algorithm to some up with the wrong solution.

Thanks to the people from Mathworks for coming up with the solution via email.

Related Solutions

MATLAB: Does interp3 (with linear option) perform trilinear interpolation

Both interp2 and interp3 use n-dimensional tensor product linear interpolation, thus respectively bilinear and trilinear interpolation.

Interp2 uses bilinear interpolation.

Interp3 uses trilinear interpolation.

How do I know this? Both tools use griddedInterpolant, when called with the 'linear' option.

In the help for griddedInterpolant, we see the statement:

    %   The Method is one of the following:
    %     'linear'   - (default) linear, bilinear, trilinear,... interpolation

Just to be painfully sure, I checked. Both interp2 and interp3 produce a characteristic NONLINEAR interpolation, when applied along the diagonal of the corresponding 2-d and 3-d hypercubes. This is a known fact about bilinear and trilinear interpolation, that bilinear interpolation when applied through the main diagonal of a square produces a characteristic quadratic function along the path where X==Y. Likewise, a trilinear interpolant produces a characteristic cubic polynomial along the corresponding diagonal path where X==Y==Z.

Ok, I said this behavior is a known fact. I did not say it was a well known fact. Not difficult to prove though. Just for kicks, in case you might not believe me...

Vq = interp2(0:1,0:1,[0 1;1 0],0:.1:1,0:.1:1,'linear')
Vq =
          0         0.18         0.32         0.42         0.48          0.5         0.48         0.42         0.32         0.18            0
plot(Vq)

You can do a similar test for interp3, generating a very pretty cubic curve.

Note that the nonlinear behavior of bilinear and trilinear interpolation along that diagonal are in fact a reason why other interpolation methods are sometimes chosen, when a linear interpolant is required. However, it is also true that any variety of "linear" interpolant will exhibit similarly interesting artifacts if you push them. And yes, there is at least one alternative method one can choose that also produces an interpolant that is arguably "linear".

MATLAB: TriScatteredInterp and ScatteredInterpolant functions produce different results

The 'TriScatteredInterp' function does not perform any extrapolation, whereas the 'scatteredInterpolant' function performs extrapolation by default.

Specifically, the 'scatteredInterpolant' function defaults to the extrapolation method of 'linear' when the interpolation method is 'linear' or 'natural' and the extrapolation method of 'nearest' when the interpolation method is 'nearest,' as described in the documentation found below under 'ExtrapolationMethod':

https://www.mathworks.com/help/matlab/ref/scatteredinterpolant.html

This can be resolved by manually setting the extrapolation method to 'none' in the call to 'scatteredInterpolant.' For example, the following lines of code should produce the same result for vectors x, y, and v:

>>scatteredInterpolant(x, y, v, 'linear', 'none')
>>TriScatteredInterp(x, y, v, 'linear')

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