Interpolate 4D Scatter?

Hello, I was wondering if anyone could possibly help me with something for class. The goal was to make a 4D scatter plot, with the 4th dimension an output (in this case "D"). The x,y,z points are inputs. I can produce the scatter plot with colorbar and it looks good, but I was wondering if there is a way I could interpolate between the points as well to get a 4D surface?

x = [13.48, 13.7, 12.25, 12.84, 12.6, 13.89, 14.81, 12.27, 12.16, 12.82, 13.04, 12.92]';
y = [13.31, 13.04, 20.65, 30.67, 31, 31.31, 30.83, 31.41, 31.87, 32.39, 30.37, 30.41]';
z = [16.5, 16.54, 12.43, 8.48, 8.25, 8.17, 8.56, 8.27, 7.86, 7.97, 8.24, 8.69]';
D = [11134, 11064, 10122, 10999, 10812, 10642, 10324, 10625, 10501, 10244, 10464, 10439]';
scatter3(x, y, z, 20, D,'filled')
colorbar
title('Graph Title')
xlabel('x')
ylabel('y')
zlabel('z')

Answer 1

[Walter Roberson]

Not really.

You can do a gridded interpolant https://www.mathworks.com/help/matlab/ref/griddedinterpolant.html over a grid defined by min and max x y z values. That would get you a cuboid of values that you would have to slice() or isosurface() for presentation. It is unlikely to be the surface you are looking for.

Perhaps you should instead use boundary() to find an enclosing set of points, after which you could patch() the surface with CData set to something extracted from D, and probably with face color interpolation.