MATLAB: How to generate n cubes to define a sphere

cubed sphere

I would like to generate cubes in a sphere. For example I would like to start simple where I can generate a central cube with 26 surrounding cubes that fit in a sphere defined by the size of the cubes. I am not concerned about filling the sphere completely. This would be my first attempt where I have to find the center of the surrounding cubes with respect to the center cube. Once I get my program working where I perform a calculation on the surrounding 26 cubes I would like to extend it to many cubes where I can record the center of each cube. So my program will subtend n cubes surrounding a central cube.

I would like to plot the 27 cubes and record the central (x,y,z) of each cube. I have tried using some examples but they are far move involved than I need. I appreciate the help.

Chad

http://www.mathworks.com/matlabcentral/fileexchange/25027-cubed-sphere

Best Answer

To create the cubes and visualize them I would start with something like the following:

http://www.mathworks.com/matlabcentral/fileexchange/?term=platonic+solid

It has proven useful in the past but requires the use of patches, if you are not familiar with them I suggest looking in the help

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MATLAB: Plane fitting using 3D points

Try this:

P = bsxfun(@times, rand(49, 3), [1 10 100]);                            % Create Matrix [x, y, z]
B = [P(:,1), P(:,2), ones(size(P,1),1)] \ P(:,3);                       % Linear Regression
xv = [min(P(:,1)) max(P(:,1))];
yv = [min(P(:,2)) max(P(:,2))];
zv = [xv(:), yv(:), ones(2,1)] * B;                                     % Calculate Regression Plane
figure
stem3(P(:,1), P(:,2), P(:,3), '.')
hold on
patch([min(xv) min(xv) max(xv) max(xv)], [min(yv) max(yv) max(yv) min(yv)], [min(zv) min(zv) max(zv) max(zv)], 'r', 'FaceAlpha',0.5)
hold off
grid on
xlabel('X')
ylabel('Y')

producing (with this set of random data):

Plane fitting using 3D points - 2019 03 26.png

MATLAB: Solve system of large linear symbolic equations

On my system, Maple ran out of memory trying to solve() that equation. There is a possibility that a system with more memory might be able to arrive at an answer, given enough time.

Solving the entire system of 12 equations when they are each this large, would take a lot of time and memory.

I would recommend following John's advice to simplify the system.

Best Answer

Related Solutions

MATLAB: Plane fitting using 3D points

MATLAB: Solve system of large linear symbolic equations

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