Is any one know how to draw voronoi diagram in 3d. And how to compute volume and surface area of each cell. If any function is available in MATLAB for computing then its is good otherwise any other tool are also fine.
N=100
k=1:N;
k=fliplr(k);
hk=-1+(2.*(k-1))./(N-1);
Thetak=acos(hk);
Thetak=fliplr(Thetak);
Phik(1)=0;
for n=2:N-1;
Phik(n)=mod((Phik(n-1)+(3.6./sqrt(N)).*1/sqrt(1-hk(n).^2)),2*pi);
end
Phik(1)=0;
Phik(N)=2*pi;
R=ones(size(Thetak));
x = cos(Phik).*sin(Thetak);
y = sin(Phik).*sin(Thetak);
z = cos(Thetak);
x = x';
y = y';
z = z';
matrix = [x y z];
[V,C] = voronoin(matrix);
figure('Color','w')
plot3(x,y,z,'Marker','.','MarkerEdgeColor','b','MarkerSize',10, 'LineStyle', 'none')
axis equal
view([90 90 90])
k=N;
for k=1:length(C)
if all(C{k}~=1)
VertCell = V(C{k},:);
KVert = convhulln(VertCell);
patch('Vertices',VertCell,'Faces',KVert,'FaceColor','b','FaceAlpha',0.9)
end
end
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