ScatteredInterpolant is giving NaN as an answer when using 'natural' method.

Hello,

I'm using scatteredIntepolant to interpolate an electric field. when using 'linear' as a method to interpolate the field, I get an answer and all is fine but precision wise it's not so great. For that, I decided to use the 'natural' method, as it is stated to be more accurate, though for whatever reason, I keep getting NaN as an answer.

To interpolate the field, I create an interpolant as follows:

interpE = scatteredInterpolant(Xout(:),Yout(:),Zout(:),Ex_Field_out(:),'natural');

then I interpolate the field at a position (x0,y0,z0) using interpE(x0,y0,z0) for any x0 y0 z0 falling into the zone of interpolation, i.e., within the range of positions of Xout, Yout and Zout.

The answer, for some reason, is always NaN, unless it was calculated over the same data points, i.e., interpE(Xout(1),Yout(1),Zout(1)) will give basically the correct answer, as that was basically the input.

I tried also to interpolate only the real or imag part of Ex_Field_out, although I think that is already done internally in the function, but yet even with that, it still gives NaN.

Any help? Thank you.

[Stephen23]

@Mhamad Hantro: please provide a sample point which returns NaN but you think is inside the hull ("zone of interpolation").

[Walter Roberson]

I do not seem to get exactly that result, but it does look sparser than I would expect.

load xyz_Ex.mat
whos

  Name              Size                Bytes  Class     Attributes

  Ex_Field_out      1x17873            285968  double    complex   
  Xout              1x17873            142984  double              
  Yout              1x17873            142984  double              
  Zout              1x17873            142984  double              
  ans               1x35                   70  char                
  cmdout            1x33                   66  char                

interpE = scatteredInterpolant(Xout(:),Yout(:),Zout(:),Ex_Field_out(:),'natural');
subplot(4,1,1)
scatter3(Xout(:), Yout(:), Zout(:), [], real(Ex_Field_out(:)) ); title('real Ex_Field_out'); colorbar
subplot(4,1,2)
scatter3(Xout(:), Yout(:), Zout(:), [], imag(Ex_Field_out(:)) ); title('imag Ex_Field_out'); colorbar
subplot(4,1,3)
qX = (Xout(1:end-1) + Xout(2:end))/2;
qY = (Yout(1:end-1) + Yout(2:end))/2;
qZ = (Zout(1:end-1) + Zout(2:end))/2;
qiE = interpE(qX, qY, qZ);
scatter3(qX(:), qY(:), qZ(:), [], real(qiE(:)) ); title('real InterpE'); colorbar
subplot(4,1,4)
scatter3(qX(:), qY(:), qZ(:), [], imag(qiE(:)) ); title('imag InterpE'); colorbar

[Mhamad Hantro]

@Stephen23 @Walter Roberson Thank you for your replies. One point at which I can see a problem is: (0,0,1e-9).

[Walter Roberson]

Unfortunately I am not familiar with natural neighbour interpolation, and do not understand the wikipedia description at the moment.

[Mhamad Hantro]

Thanks for trying though :)

I don't know much about the algorithm either, I just looked it up in Matlab's documentation, and read in some blog that although it's more accurate but still it's not the default method due to the fact that it came much later. I did try a simple example where I created a random function, and the interpolation worked, though for some reason, it's not working here.

Thanks again :)