Assume you have the 3d coordinates of the player and another unit
N as well as the azimuth and elevation of a camera always looking at the player. In the following illustration the sun would be the camera of course:
Let's say one wants to draw something on a different transparent window (not using the game window or any hooks) that is always displayed on top of the unit. An example would be TurboHUD for Diablo. In the linked video you can see that it displays affixes using textboxes right on top of the blue elite mobs.
In Diablo doing this is much simpler since the camera cannot be rotated and moved thus only simple projections depending on the distance are necessary, but what about situations with more degrees of freedom? How can one estimate 2d coordinates to draw at that match the position of the 3d units on the screen without access to more than described in the first paragraph? What is the mathematical background and what are the necessary computations?