Plot a circle around xyz plotted points and then get its volume?

If I have three vectors of points that I'm plotting with:

scatter3(xVector, yVector, zVector);

How can I draw a circle that encompasses all of these points and then calculate the volume?

[arich82]

You don't specify whether you need the minimum bounding sphere, or just an approximation to the minimum.

For either case, there are tools on the FEX, e.g. John D'Errico's or this one.

Alternatively, if you just need the volume of the point cloud, you can use the second output from convhull. Note that this could be substantially different from the volume of the minimum bounding sphere if the data are e.g. distributed in a disc...

How critical are accuracy (relative to the min bounding sphere) and speed, and how many points are you working with? Is this a one-time calculation?

Answer 1

[Star Strider]

I combined [xVector(:) yVector(:) zVector(:)] as ‘xyz’ here. The (:) reference creates column vectors from them, and that is absolutely necessary for this code.

This will do what you want:

xyz = randi(25, 30, 3);                                 % Consolidated: [xVector(:) yVector(:) zVector(:)]
C = mean(xyz);                                          % Calculate Centre
R = sum(bsxfun(@minus, xyz, C).^2, 2);                  % Calculate Radii
[Rmax, idx] = max(R);                                   % Calculate Maximum Radius
Volume = 4*pi*Rmax^3/3;                                 % Volume Of Sphere

[Xs,Ys,Zs] = sphere;                                    % Use ‘sphere’ Function
Rsph = sqrt(Rmax);                                      % Calculate Radius Of Sphere

figure(1)
plot3(xyz(:,1), xyz(:,2), xyz(:,3), '.')                % Plot Data
hold on
plot3(C(1), C(2), C(3), 'r*')                           % Plot Centre
plot3(xyz(idx,1), xyz(idx,2), xyz(idx,3), 'bp')         % Plot Maximum Radius
Sph = mesh(Rsph*Xs+C(1), Rsph*Ys+C(2), Rsph*Zs+C(3));   % Calculate Enveloping Sphere
hold off
grid on
axis equal
set(Sph, 'FaceAlpha',0.1)                               % Set Sphere Transparency
legend('Data', 'Centre', 'R_{max}', 'Location','EastOutside')

This code produces this plot that you can rotate when you plot it to see that it works:

[Felipe Guerrero Medina]

hi, And the same can be done for a cylinder?, in order to obtain the location of the generated points (similar to a mesh).

thanks !!