How to get a smooth scalar field on regular grids from irregularly distributed sample data?

I have irregularly distributed sample data (Rs, Zs, phi00), its contourf plot looks smooth like:

I use:

phi=griddata(Rs,Zs,phi00,Rgrid,Zgrid,'cubic');

to get the data on regular grids. There are some zigzags on the contourf plot from regular grids like:

Since we can get a smooth contourf plot from the irregular sample data, I believe that there must a simple way to get the smooth data on regular grids. How can I get it?

The sample data points and the contourf plot and the scatteredinterpolant figures are:

[Torsten]

Did you try a different interpolation method instead of "cubic" ?

[Zhichen]

The "linear" method gives similar zigzags at the lower part. The other methods "natural" and "nearest" cannot give ideal results.

[Torsten]

The usual way ist to use "scatteredInterpolant" to return the interpolant for the given data and then to evaluate this interpolant at query points (usually on a structured grid):

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

I don't know whether this gives better results than your method - especially because it seems that you have to extrapolate your data to a region where no data points are given.

[Zhichen]

"griddata" calls "scatteredInterpolant" to generate data on structured grid.

I used "scatteredInterpolant" to calculate the value on structured grid. There are similar zig-zags at the same positions.

The region without data points does not matter.

It seems "scatteredInterpolant" is not as good as "contourf" in MATLAB. I do not know is there any ohter method can get data on structured grid from unstructured data as smooth as "contourf"?

[Mathieu NOE]

@Zhichen

can you share the data ?

[Zhichen]

@Mathieu NOE

Attached please find the data. the scalar field is modified a little, but the zig-zags still there.

[Mathieu NOE]

well, maybe scatteredInterpolant is not very happy with your complex shape

there are "cuts" that probably causes some trouble here

we may have to find another (custom) solution

must those cuts remain or can we consider it could be a continuous surface ?

[Zhichen]

These cuts are considered to be continuous surfaces. There is no problem due to these cuts from scatteredInterpolant.

Answer 1

[Zhichen]

After interpolation to get additional (fake) sample data according to the original data points in their coordinates, the ScatteredInterpolation or the griddata function can get similar contourf plot as the it is ploted using the original data.

It seems contourf plot may interpolate data in thier original format (coordinates) to get a smooth figure in 2D space. It is more advanced than ScatteredInterpolation in MATLAB. I think MATLAB should have a Interpolation function behaves as contour plot, who can automatically smooth the data depending on how it is arranged.

If any one have any other simpler method in MATLAB to generate smooth data on structured grid, please post it. I will appreciate and accept your answer.

Original data and contourf plot:

The more (fake) sample data:

Smooth data on structed gird by "griddata", similar as the plot from original data:

[Mathieu NOE]

FYI, I could get a fairly smooth plot with the original data (coarse) , thanks to : surfir - Surface plot from irregular data points - File Exchange - MATLAB Central

code is traightforward :

x = readmatrix('Rs.dat');
y = readmatrix('Zs.dat');
z = readmatrix('000.dat');

figure
subplot(1,2,1)
scatter3(x(:),y(:),z(:))
title('data points')

subplot(1,2,2)
surfir(x(:),y(:),z(:));
title('surface plot')

[Zhichen]

A very smooth figure can be plotted using contourf plot in MATLAB with original data (as shown in the 1st figure in my question).

In MATLAB, it seem that the only way to get a smooth scalar field on structured grid using the original data I have here is to increase the sample data points in some regions according to the original sample data distribution, as how I did in my answer.

Answer 2

[Image Analyst]

See my attached scattered interpolant demo. It will make a smooth function everywhere. If you don't want it for certain pixels, then you can mask the final interpolated image with a mask of where you want it.

finalOutputImage(mask) = 0;

[Zhichen]

Read and get the data from a smooth image file is the last solution to this problem. We may need to dealing with the gaps in the image file carefully.

We may also interpolant the data in their original coordinates to get more samlpe points (as how the contour data is stored in matlab contour figure) and then scatteredInterpolant to the R-Z structured grid. This can reduce the non-smooth effect a lot.

The question here is that how can the contourf plot can give a smooth figure everyhwere using the limited sample points, but we can not get similar reslults using scatteredInterpolant in MATLAB? Is there or should there be any direct method in MATLAB to get similar data as contourf plot?

The sample data points and the contourf plot and the scatteredinterpolant figures are:

[Image Analyst]

It looks like the non-smooth dotted lines in your figures are probably actually in the data and are not an artifact of the interpolation. Correct me if I'm wrong. If so then why do you want it to be smoother than the actual data, which looks like a smooth analytical function because I don't see any random noise in it. Anyway, you can do any number of smoothing filters on the interpolation image to smooth out sharp edges and glitches.

[Zhichen]

Yes, the the dots are original data. They are listed in 2D array. In one direction, the field changes slowly, so the dots are further away from each other, while in the other direction, they need to be close to each other to record the rapidly varied field. Contour plot knows this, it might interpolate data on the directions along the 2D array, and can give a smooth 2D figure based on the 2D data, but the interpolation functions in MATLAB will not.

I think an interpolation function based on multidimensional array will be usefaull in MATLAB.

Answer 3

[TED MOSBY]

Hi @Zhichen,

You can try using the function "gridfit" which can be downloaded from here:

https://www.mathworks.com/matlabcentral/fileexchange/8998-surface-fitting-using-gridfit?s_tid=srchtitle_support_results_1_gridfit

You can unzip the zipped file and add it to path to start using the function.

"gridfit" works as it does not insist on hitting every data point; instead it balances data fidelity against smoothness. By letting a few points move a little, the fitted surface can stay globally smooth rather than sacrificing smoothness to hit every sample exactly.

Below is a practical workflow of this:

% data already in Rs, Zs, phi0
rvec  = linspace(min(Rs), max(Rs), 300);
zvec  = linspace(min(Zs), max(Zs), 300);
[Rg,Zg] = meshgrid(rvec, zvec);

phiGF = gridfit(Rs, Zs, phi0, rvec, zvec, ...
                    'smooth', 0.02, ...     
                    'interp', 'bilinear');  


figure('Color','w');
contourf(Rg, Zg, phiGF, 20, 'LineColor','none');
axis equal tight, colorbar
title('\phi  gridfit,  smooth = 0.02');

Hope this helps!

[Mathieu NOE]

hmm, I tried this one too but I think it does not provide a 100% satisfying result, as this leads to unrealistic values where gridfit extrapolates in (yellow) areas where there is no original data

this is your code :

Rs = readmatrix('Rs.dat');
Zs = readmatrix('Zs.dat');
phi0 = readmatrix('000.dat');

figure('Color','w');
contourf(Rs, Zs, phi0, 20, 'LineColor','none');
caxis([min(phi0(:)) max(phi0(:))]);
axis equal tight, colorbar

% data already in Rs, Zs, phi0
rvec  = linspace(min(Rs(:)), max(Rs(:)), 300);
zvec  = linspace(min(Zs(:)), max(Zs(:)), 300);
[Rg,Zg] = meshgrid(rvec, zvec);
phiGF = gridfit(Rs, Zs, phi0, rvec, zvec, ...
                    'smooth', 0.02, ...     
                    'interp', 'bilinear');  
figure('Color','w');
contourf(Rg, Zg, phiGF, 20, 'LineColor','none');
caxis([min(phi0(:)) max(phi0(:))]);
axis equal tight, colorbar
title('\phi  gridfit,  smooth = 0.02');