I have a 3D point $P$ from Microsoft Kinect (relative to the Kinect camera plane - call it plane $A$), and I want to find point $P'$ that's mapped to $P$ on another plane (call it $B$) that I have an equation for ($ax + by + cz + d = 0$).
For example:
$P$ (on original plane $A$): $(1,2,3)$
Plane $B$: $2x + 3y + 4z + 5 = 0$
And I need to find $P'$, the mapping of $P$, but relative to plane $B$.
I understand that it can be done using a transformation matrix, but I'm not sure how to do it.