# how to define a 3D volume in a matrix

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A on 29 Jun 2012
I need to define a cylinder(diameter=20cm and height=25cm) in a 3D matrix A(40x40x50) such that each element represents a 5mm x 5mm x 5mm cube. Cube A(i,j,k)=1 if it falls within the cylinder and A(i,j,k)=0 if it falls outside the cylinder. What's the best way to populate this matrix?

tlawren on 29 Jun 2012
Edited: tlawren on 29 Jun 2012
A somewhat sloppy, yet direct way could be ...
% Set dimensions
ds = 5; % mm
xlim = ds*40/2;
ylim = xlim;
zlim = ds*50/2;
% Forms a 41x41x51 matrix
[X,Y,Z] = meshgrid(-xlim:ds:xlim,-ylim:ds:ylim,-zlim:ds:zlim);
% Convert to cm
X = X./10;
Y = Y./10;
Z = Z./10;
% A matrix (matrix of radii)
A = sqrt(X.^2 + Y.^2);
% Set center axis to 1
A(A == 0) = 1;
% Anything outside of cylinder radius (10 cm) set to 0
A(abs(A) > 10) = 0;
% Convert all non-zeros to 1 (all pts on and inside cylinder)
A(abs(A) > 0) = 1;
Here, A is not 40x40x50, but instead 41x41x51. The odd size allows for a center center-axis.