A large particle with radius r hits the plane with perpendicular 'n' and passing through ,q'. I need to check whether it hits the plane or not. In order to do that I need to find the point of contact. My question is: we should shorten the 'p' by r to get the point of contact?
If you represent the particle position by the position of the center of the particle, you can move the plane by one radius along the normal. The particle contacting the plane is the same as the center being in the new plane.