Fill cylinder inside a matrix

Given a 3d matrix:

vx = 1; % mm
vy = 1; % mm
vz = 1; % mm
nx = 500; %Number of elements in x direction
ny = 500; %Number of elements in y direction
nz = 100; %Number of elements in z direction
x = linspace(-vx/2,vx/2,nx); 
y = linspace(-vy/2,vy/2,ny); 
z = linspace(-vz/2,vz/2,nz); 
[X,Y,Z] = ndgrid(x,y,z); 
mat= zeros(size(X)); %Matrix to fill with cyliinders

and 2 random points on the edge of the cube,

How can I make a cylinder of radius R between those 2 points?

I want to fill up the binary matrix with 1 where the cylinder is placed and 0 everywhere else.

Thank you for your help.

Answer 1

[Matt J]

Suppose the two end points are r1=[x1,y1,z1], r2=[x2,y2,z2]

[X,Y,Z] = ndgrid(x,y,z); 

dXYZ=[X(:),Y(:),Z(:)].'-r1(:);

u=r1-r2;
u=repmat(u(:)./norm(u),1,nx*ny*nz);

mat=vecnorm( cross(dXYZ,u) ,2,1 )<=R;

mat=reshape(mat,nx,ny,nz);

[DG]

I think this is perfect and exactly I what I wanted.

Thank you!!!

Can you explain the formulas that you applied. I think variable u is a direction matrix between the points. But what is the role of:

vecnorm( cross(dXYZ,u) ,2,1 )<=R;

I dont understand that part.

Thanks a lot for your help.

[Matt J]

Yes, u is the direction vector of the central line of the cylinder. The left hand side of the inequality is the formula for the distance of points in your ndgrid to that line.

[Matt J]

It should be giving you filled cylinders.

Answer 2

[Matt J]

Choose a coordinate (xcenter,ycenter) where the cylinder will be centered and do,

mat = (   (x-xcenter).^2 + (y-ycenter).^2 <= R^2   );

[DG]

But I want cylinder between two locations. This won't work for a tilted cylinder, I think. Something like the attached picture. In this case, if I take a slice in z axis, it will form some kind of ellipse and not a circle.

Hope this makes it clear.

Thank you!