### How to get real world projection coordinate

I have a TV screen (dimension of TV is known say width, w and height, h) and I have a Camera somewhere nearby and the physical distance between camera and TV screen's center is known say (Δx,Δy,Δz). The camera and TV screen might be facing in different angles, the vertical angle and horizontal angle, that both make with each other say, θv and θh is also known.

Now the camera has recorded the gaze of a person in terms of yaw, pitch (and roll too, but roll is not needed in this case). Also, the person's real world distance from camera is known z-dist, x-dist and y-dist.

How to project this person's gaze on the TV's plane and get whether the gaze intersect the TV's screen, given ~~the ~~TV's physical dimension, if yes, then know ~~the pixel ~~relative position of the plane's intersection with the gaze.