Ray Disk intersection

Question

So if I have a ray parameterized as $O + tD$ where $O$ is the origin, $D$ is the direction and $t$ is the parameter variable and a flat circular disk with a center point $P$ in 3D space and a radius $r$, how do I determine if they intersect?

Answer 1

First, find the equation for the plane that contains the circular disk. Second, find the intersection of the line and the plane. Third, determine if the intersection point is in the right direction from the origin (the ray points only one way). Lastly, determine if the intersection point is distance at most $r$ from the center of the disk.