scatteredInterpolant function is providing too much noise in interpolation

Hello there.

I have a function V = f(X,Y). Where the mesh on X,Y is non uniform and its boundaries aren't rectangular. I am trying to use scatteredinterpolant function to evaluate Vq = f(Xq, Yq), but MATLAB always provide a lot of noise in the interpolated results, and I am not able to identify the reason.

Please refer to the attached data file for the numerical values of the variables (X,Y,V,Xq,Yq). I am using the following code,

clc
clear

load('Interpolation.mat')

surf(X,Y,V)
h=gca;
xlabel ('X');ylabel ('Y');
zlabel ('V');
set(h,'xscale','log')

F = scatteredInterpolant(X(:),Y(:),V(:));

Warning: Duplicate data points have been detected and removed - corresponding values have been averaged.

Vq = F(Xq,Yq);

surf(Xq,Yq,Vq)
h=gca;
xlabel ('Xq');ylabel ('Yq');
zlabel ('Vq');
set(h,'xscale','log')

Can anyone tell what is the reason and how can I fix the noise in the results?

Thanks and best,

Ahmad

Answer 1

[Bruno Luong]

The problem raises from the fact that scatteredInterpolant use Delaunay triangulation, meaning that X and Y are assumed to have the same unit.

In your case not only they do not have the proper normalization, but it seems X is log scale.

To fix it, you have to transform your variables:

load('Interpolation.mat');

ScaleLogX = 10;
ScaleY = 2000000;
F = scatteredInterpolant(log(X(:))/ScaleLogX,Y(:)/ScaleY,V(:));

Warning: Duplicate data points have been detected and removed - corresponding values have been averaged.

Vq = F(log(Xq)/ScaleLogX,Yq/ScaleY);
surf(Xq,Yq,Vq)
h=gca;
xlabel ('Xq');ylabel ('Yq');
zlabel ('Vq');
set(h,'xscale','log')

Answer 2

[KSSV]

Read about griddata. Also explores the methods in these interpolations. Go for the method nearest.

[Ahmad Gad]

The function griddata produced a very similar noise. I will try to explore different options in each function. Thanks for your comment.