# Project point onto surface using yaw, pitch, roll rotation and standard trig formulas

Given the known coordinates of location A (0,0,50), at which we have a laser pointer aimed downward, I need a series of equations that calculate the projected point onto the flat surface below (x,y,0) using and in the order yaw, pitch, roll. Rotations follow right hand rule. There are four quadrants, so the equations should be able to work around the entire circle. I’d like a series of standard trig equations, not matrix. Thanks!

• Convert from spherical coordinates to get the direction vector of the beam, after which you have a straightforward ray-plane intersection with $z=0$. – amd Jan 9 at 2:08
• Could you share code that does so as appropriate for Excel or R? – user3324138 Jan 9 at 2:36