how to define a 3D volume in a matrix

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?

Answer 1

[tlawren]

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.

Answer 2

[Walter Roberson]

If you are aligning the cylinder with a primary axes, then you can create a filled circle and copy that circle along the axes (e.g., repmat)

http://matlab.wikia.com/wiki/FAQ#How_do_I_create_a_circle.3F

You do have to be a bit careful about what you mean by "if it falls within the cylinder", when you examine the edge cubes. Even a cube whose center falls within the radius does not necessarily have half of its volume inside the cylinder.