How to generate a random point in the volume of a cylinder

I have a cylinder in three-dimensions with a long-axis defined by the endpoints ?1 and ?2, and radius ?. p1=[0.5, 0.3, 1]; p2=[0.4, 0.5, 0.7]; R=0.5;

[James Tursa]

What have you done so far? What specific problems are you having with your code? Do you know how to generate a random point inside a circle? Do you know how to rotate vectors in 3D space?

[John D'Errico]

I showed you how to rotate vectors in 3-d space.

Answer 1

[John D'Errico]

Since you already have an answer posted... Pretty easy, actually. So two points that define the ends of the cylinder, and a known radius.

p1=[0.5, 0.3, 1];
p2=[0.4, 0.5, 0.7];
R=0.5;
N = 100000; % # of points to generate

First, generate a random point along the cylinder axis. The vector that defines the axis is given by:

axialvec = p2 - p1;
axialvec = axialvec/norm(axialvec);
axialpoints = p1 + (p2 - p1).*rand(N,1);

Next, we work in a cylindrical coordinate system around the centerline. Generate points at random inside a circle of radius R, in TWO dimensions.

circr = sqrt(rand(N,1))*R;
circtheta = rand(N,1)*2*pi;
circpoints = [cos(circtheta).*circr,sin(circtheta).*circr];

Rotate the points into the plane perpendicular to the axis.

axnull = null(axialvec);
points = axialpoints + circpoints*axnull.';

And plot.

plot3(points(:,1),points(:,2),points(:,3),'.')
grid on
box on
axis equal

Rotate it around to convince yourself the points form a cylinder.