[Math] Projecting 3D Point to Plane

Question

I have a plane defined by the equation $Ax + By + Cz + D = 0$. It does not pass through the origin.

I have projected the origin of my global coordinate system onto the plane, so it is at $(a, b, c)$.

I have a known point $P$ on the plane at $(d, e, f)$.

If I view the plane square-on as a 2D space then I can consider the projected origin point to be at $(0, 0)$. So the 3D point $(a, b, c)$ becomes the 2D $(0, 0)$.

How do I find the 2D coordinates $(x, y)$ of my known 3D point $P$ $(d, e, f)$?

Sorry if my terminology is incorrect.

Thanks, Andy

Answer 1

The coordinates of the point P(d,e,f) will become (d-a,e-b) in 2D