Collision detection and solving of a spherical ball in a cylindrical boundary

I'm trying to write a code in which a spherical ball moving at a given velocity in a solid cylindrical boundary in which when it makes contat with the boundary there should be an elastic collision that reflects the ball. However im unsure on how to detect the collision and solve it for the new reflected velocity.

This is my code so far:

Obj = [0 0 0];
velocity = [2e-8 2e-8 2e-8];
for i = 1 : 20
    clf
    r = 5e-7;
    [X,Y,Z] = cylinder(r);
    h = 20e-7;
    Z = Z*h-2*r;
    cyl = surf(X+0.5e-6,Y,Z,'FaceColor','none');
    rotate(cyl, [0 1 0], 90)
    hold on
    [x,y,z] = sphere;
    radius = 5e-8;
    plot3(radius*x+Obj(1,1),radius*y+Obj(1,2),radius*z+Obj(1,3),'k');
    xlabel('x')
    ylabel('y')
    zlabel('z')
    Obj  = Obj + velocity;
    view([-30,6])
    set(gca,'xlim',[-5e-7 15e-7])
    set(gca,'ylim',[-10e-7 5e-7])
    set(gca,'zlim',[-1e-6 1e-6])

    drawnow
end

any help would be appreciated thanks.

Answer 1

[Andrew Ouellette]

Hi Victor,

You can detect a collision between the ball and the cylinder if the distance between the center of the ball and the outside of the cylinder is less than or equal to the radius of the ball.

To do that, you will need to increase the number of points along the circumference of the cylinder such that the gap between the points is less than the radius of the ball.

I have modified your code below to show an example of how to detect collisions:

Obj = [0 0 0];
velocity = [2e-8 2e-8 2e-8];
r = 5e-7;
radius = 5e-8;
for i = 1:20
    clf
    N = ceil(2*pi*r/radius);
    [X,Y,Z] = cylinder(r,N);
    h = 20e-7;
    Z = Z*h-2*r;
    cyl = surf(X+0.5e-6,Y,Z,'FaceColor','none');
    rotate(cyl, [0 1 0], 90)
    hold on
    [x,y,z] = sphere;
    plot3(radius*x+Obj(1,1),radius*y+Obj(1,2),radius*z+Obj(1,3),'k');
    xlabel('x')
    ylabel('y')
    zlabel('z')
    Obj  = Obj + velocity;
    view([-30,6])
    set(gca,'xlim',[-5e-7 15e-7])
    set(gca,'ylim',[-10e-7 5e-7])
    set(gca,'zlim',[-1e-6 1e-6])
    drawnow
    displacements = Obj(2:3)-[cyl.YData(1,:) cyl.YData(2,:);cyl.ZData(1,:) cyl.ZData(2,:)]';
    distances = vecnorm(displacements,2,2);
    collision = any(distances <= radius);
    if collision
        fprintf('Collision occurred on iteration %g',i);
        break;
    end
end

Collision occurred on iteration 17

As far as updating the velocity after that point, it is up to you which method you wish to use for the update.