Matlab分散数据的4D插值图

Question

I have a set of data with a value at some x,y,z coordinates. However, the coordinates are not evenly spaced. I would like to interpolate the data and have a 3D interpolated plot where the color is the interpolated value at each x,y,z coordinates (not the value of z).

Also I should mention that my data are confined in space and I only want to interpolate between points that are close. I have multiple sheet-like structures and I do not want interpolation between the sheets. I would therefore need a distance between points criteria I guess.

My problem can be seen with this MATLAB test program

x = rand(100,1)*16 - 8;
y = rand(100,1)*16 - 8;
z = rand(100,1)*16 - 8;
d = rand(100,1)*16 - 8;

The scatter plot of that works very well

scatter3(x,y,z,5,d);
colormap(jet);
colorbar;

I would like to have an nice surface with color of that. Of course the interpolation of the above will be very bad since it is random points and color(value) but for my case it has more meaning.

Any ideas on how to accomplish this?

Edit

I shall emphasize the localized nature of my problem (see picture below using scatter3).

The very interesting solution proposed by Suever using scatteredInterpolant on the same data as the first figure gives me the following picture

Thank you,

Samuel

Answer 1

Since your input data is scattered, you're going to want to use scatteredInterpolant . This allows for interpolation of non-uniformly-spaced input data.

For your specific data, you would use something similar to the following where xq , yq , and zq are the points at which you want to interpolate the input.

S = scatteredInterpolant(x,y,z,d);
values = S(xq,yq,zq);

As far as your specific conditions on the definition of neighboring data, you'll want to look at the various interp methods provided for scatteredInterpolant to see if any of them meet your needs.

Edit

Upon closer reading, it seems like you may want to interpolate both z and d over a regular grid. If that's the case, you can still use scatteredInterpolant in the following way.

% First interpolate for z
S = scatteredInterpolant(x,y,z);

xrange = linspace(min(x), max(x), 1000);
yrange = linspace(min(y), max(y), 1000);

[xq, yq] = meshgrid(xrange, yrange);

% These are now the interpolated z values (height of surface)
znew = S(xq,yq);

% Now we want to use x,y,z to interpolate d at the new grid points
S = scatteredInterpolant(x,y,z,d);

% Interpolate d at the new points
dnew = S(xq, yq, znew);

So we apply this to the random data you've provided, we can plot a surface like you were talking about.

S = surf(xq, yq, znew, 'CData', dnew);

The original data points (x,y,z) are shown as a scatter plot with black outlines. You can see that the data interpolates these points and the color of the surface should also be interpolated from these points.