Counitng the number of scatter points above a surface

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Hi All,
I am having some troubles and hoping someone out there much smarter with MATLAB than me can help.
The problem I have i
  • I have plotted some data as a 3D scatter plot.
  • I have then plotted a surface which is a ‘limiting condition’ for the data I have.
  • I need to count the number of data points that fall above and below the surface.
Is this something that can be done?
I have been reading up on slices and searching these forums for help but cant find anything close.
Any help is appreciated.
The code is;

Accepted Answer

Mike Garrity
Mike Garrity on 11 Aug 2015
You can use interp2 to evaluate the surface at the X & Y coordinates of your scatter data.
Consider the following example:
% Make up some sample data
[sx,sy,sz] = peaks(12);
px = randn(1,100);
py = randn(1,100);
pz = 5*randn(1,100);
% draw the surface and points
h1 = surf(sx,sy,sz);
hold on
h2 = scatter3(px,py,pz,'filled');
% Evaluate surface's function @ point's X & Y
spz = interp2(sx,sy,sz, px,py);
% Build mask of points which are above surface
mask = pz > spz;
% Delete old scatter
% Replace with two scatters with different colors
h3 = scatter3(px(mask),py(mask),pz(mask),'filled');
h4 = scatter3(px(~mask),py(~mask),pz(~mask),'filled');
h3.MarkerFaceColor = 'red';
h4.MarkerFaceColor = 'blue';
But you should read this blog post to understand some of the subtleties of how surface does it's interpolation before you go too far down this path.
Octavian Macari
Octavian Macari on 20 Mar 2018
Mike Garrity, is it possible to make a surface pace above for all points?

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More Answers (1)

Lukas Bystricky
Lukas Bystricky on 11 Aug 2015
Edited: Lukas Bystricky on 11 Aug 2015
Can your surface be expressed as z = f(x,y)? If so for every scatter point (at position (x0,y0, z0)), you can do:
h = z0 - f(x0,y0)
If h > 0 your point is above the surface.
If you can't express your surface as z = f(x,y), you can use interp2 or something to get an approximation to z at any (x,y) and do the same as above.

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