# How to form a sphere with 1's in a 3D matrix

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Vinit Nagda on 31 Aug 2021
Commented: Vinit Nagda on 31 Aug 2021
I have a matrix X=zeros(m,n,p);
If I know the radius value and matrix index for centroid position of sphere, how do I distribute 1's in the matrix such that it forms a sphere in the matrix? (Ignore part of sphere if it goes outside matrix dimensions)
Thank you.

Wan Ji on 31 Aug 2021
Edited: Wan Ji on 31 Aug 2021
If there is no scale factor effect with different directions:
m = 80; n = 100; p=90;
[px,py,pz] = meshgrid(1:n, 1:m, 1:p);
xc = 40; yc = 30; zc = 60; % the center of sphere
logicalSphere = (px-xc).^2 + (py-yc).^2 + (pz-zc).^2 <=radius*radius;
X = zeros(m,n,p);
X(logicalSphere) = 1; % set to zero
You can also show this sphere with isosurface and patch function
axis([0,n,0,m,0,p])
p=patch(isosurface(px,py,pz,X,0));
set(p, 'FaceColor', 'red', 'EdgeColor', 'none');
daspect([1 1 1])
view(3)
hold on
scatter3(px(:),py(:),pz(:),1,X(:),'filled')
camlight; lighting phong
The sphere is shown like

### More Answers (2)

Matt J on 31 Aug 2021
Edited: Matt J on 31 Aug 2021
Using ndgridVecs from the file exchange
[dX,dY,dZ]=ndgridVecs((1:m)-cm, (1:n)-cn, (1:p)-cp); %centroid=[cm,cn,cp]
sphere3D=(dX.^2 + dY.^2 + dZ.^2<=radius^2); %the result
##### 1 CommentShowHide None
Vinit Nagda on 31 Aug 2021
@Matt J Thanks a lot for your response. Using ndgridVecs fucntion is actually very efficient.

Chunru on 31 Aug 2021
Edited: Chunru on 31 Aug 2021
[m, n, p] = deal(10, 12, 14);
[xg, yg, zg] = ndgrid(1:m, 1:n, 1:p);
xc = round(m/2); yc=round(n/2); zc=round(p/2); % center
r = 3;
idx = (xg-xc).^2 + (yg-yc).^2 + (zg-zc).^2 <= r.^2;
s = false(size(xg)); % the sphere
s(idx) = true;
plot3(xg(s), yg(s), zg(s), 'o');
grid on; box on

R2020b

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