用MATLAB随机曲面切割3D点云

Question

I have a 3D point cloud in a cube with a specified side length, filled with particles at totally random positions. Also, I have a surface that has the same side length as the cube, but with random values of Z for each X and Y, which makes it a random rough surface. All of these data are in my access in XYZ format.

What I want to do is to delete the particles in the cube that stands above that rough surface.

The following generates a simple configuration of the problem:

samples = 1000;

%data extrema
l = -2; h = 2;
zl = 0; zh = 5;

%The point cloud
xC = random('Uniform',l,h,[samples,1]);
yC = random('Uniform',l,h,[samples,1]);
zC = random('Uniform',zl,zh,[samples,1]);

scatter3(xC,yC,zC,1);

% # grid points
gp = 20;

% grid costruction
xS = linspace(l,h,gp);
yS = linspace(l,h,gp);
[xS,yS] = meshgrid(xS,yS);
xS = xS(:);
yS = yS(:);

% random rough surface
zS = random('Uniform',zl+2,zh-2,[length(xS),1]);

hold on
scatter3(xS,yS,zS);

Any help is appreciated.

Answer 1

Using the following code, I could solve the problem:

%% THE PROBLEM
samples = 1000;

% data extrema
l = -2; h = 2;
zl = 0; zh = 5;

% the point cloud
xC = random('Uniform',l,h,[samples,1]);
yC = random('Uniform',l,h,[samples,1]);
zC = random('Uniform',zl,zh,[samples,1]);

scatter3(xC,yC,zC,1);

% # grid points
gp = 20;

% sample grid costruction
xS = linspace(l,h,gp);
yS = linspace(l,h,gp);
[xSm,ySm] = meshgrid(xS,yS);
zSm = random('Uniform',zl+2,zh-2,[length(xS),length(yS)]);
xS = xSm(:);
yS = ySm(:);
zS = zSm(:);
hold on
scatter3(xS,yS,zS);

%% THE SOLUTION
% estimation of the zS for XY of each point
for i = samples:-1:1
    x_t = xC(i);
    y_t = yC(i);
    Zq = interp2(xSm,ySm,zSm,x_t,y_t,'linear');

    % delete the point if it is located above the surface
    if zC(i)>Zq
        xC(i) = [];
        yC(i) = [];
        zC(i) = [];
    end
end
scatter3(xC,yC,zC,30,'b');