MATLAB: How to make sphere using smaller spheres

MATLAB and Simulink Student Suitesphere packing

How can I make sphere of say unit length using smaller spheres of 1/4 length?

Best Answer

r = 0.1;
R = 1;
[x, y, z] = sphere(12);
w = linspace(-R + r, R - r, 1 + R / r);
figure;
axes('NextPlot', 'add', 'XLim', [-R, R], 'YLim', [-R, R], 'ZLim', [-R, R]);
for ix = w
   for iy = w
      for iz = w
          if (ix)^2 + (iy)^2 + (iz)^2 <= R^2
              surf(x * r + ix, y * r + iy, z * r + iz, ...
                  'FaceColor', [0.9, 0.9, 0.9], ...
                  'FaceLighting', 'gouraud', ...
                  'AmbientStrength',  0.5, ...
                  'DiffuseStrength',  0.6, ...
                  'EdgeColor', 'none');
          end
      end
   end
end
view(3)
light

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MATLAB: Randomly generated spheres in a volume in Matlab

function P = GetRandomSpheres(nWant, Width, Radius)
% INPUT:
%   nWant:  Number of spheres
%   Width:  Dimension of 3d box as [1 x 3] double vector
%   Radius: Radius of spheres
% OUTPUT:
%   P:      [nWant x 3] matrix, centers
P = zeros(nWant, 3);
R2     = (2 * Radius) ^ 2;   % Squared once instead of SQRT each time
W      = Width - 2 * Radius; % Avoid interesction with borders
iLoop  = 1;                  % Security break to avoid infinite loop
nValid = 0;
while nValid < nWant && iLoop < 1e6
  newP = rand(1, 3) .* W + Radius;
  % Auto-expanding, need Matlab >= R2016b. For earlier versions:
  % Dist2 = sum(bsxfun(@minus, P(1:nValid, :), newP) .^ 2, 2);
  Dist2 = sum((P(1:nValid, :) - newP) .^ 2, 2);
  if all(Dist2 > R2)
    % Success: The new point does not touch existing sheres:
    nValid       = nValid + 1;  % Append this point
    P(nValid, :) = newP;
  end
  iLoop = iLoop + 1;
end
% Stop if too few values have been found:
if nValid < nWant
  error('Cannot find wanted number of points in %d iterations.', iLoop)
end
end

And a demo code:

n = 10;
R = 10;
P = GetRandomSpheres(n, [100, 100, 100], R);
figure
axes('NextPlot', 'add', ...
    'XLim', [0, 100], 'YLim', [0, 100], 'ZLim', [0, 100]);
view(3);
[X, Y, Z] = sphere();
for k = 1:n
    surf(X * R + P(k, 1), Y * R + P(k, 2), Z * R + P(k, 3));
end

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