Counitng the number of scatter points above a surface

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

s;

• 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;

Answer 1

[Mike Garrity]

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
delete(h2)

% 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.

[Adam Bartle]

Thats great - Thanks Mike!

Very much appreciated.

[Octavian Macari]

Mike Garrity, is it possible to make a surface pace above for all points?

Answer 2

[Lukas Bystricky]

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.

[Adam Bartle]

Hi Lukas, Thanks for the quick response!

I am still confused however as I cant express z=f(x,y).

Some more background;

• z is is a series of test results as a [8 x 16] matrix.
• I have used interp2 to create zq as a [526 x 301].
• My scatter data is (X,Y,Z) with 46752 points!

I understand the principle of your suggestion and it seems to make sense, but I dont get how to execute it. If I want to check h > 0, I need to lookup Z value from my scatter data, and then use zq approximation for corresponding X and Y value right??

How can I do this if zq which I created using interpt2 is a [526 x 301] matrix with no real order to it.

Thanks for the help. I really appreciate it.

[Lukas Bystricky]

You could try to use scatteredInterpolant to evaluate all your points. The process might look something like this:

   F = scatteredInterpolant(x, y, z) % x, y and z can be unordered

Then for each point you could call:

   z_surface = F(point_x, point_y);

Although this may take a while to run for 46752 points. If you're planning on doing this several times that might be an issue.

[Adam Bartle]

Thanks Lukas,