In a 3D-space there is a random number of objects ($X$s) of which their exact position is known.
These objects can be observed through a "screen" which has a certain dimension, position and orientation.
Its position and orientation is related to point $P$. The "screen" can be moved around this point with a fixed distance.
(I'm imagining the "screen" moving on the hull of a sphere around $P$ and the line of touching point and $P$ is always orthogonal to the plane).
Then, there is the observer point ($O$) which is on the opposite side of $P$ related to the plane, maybe with the same distance or less.
The observer now looks "through" the "screen" into the 3D world and sees some of the $X$s.
My questions is, what approach should I follow to calculate where the line between $O$ and one of the $X$ touches the "screen"? What variables do I have to calculate?
My math-lessons date and I'm a little bit rusty when it comes to terms and ideas. Please bear with me and do not hesitate to ask for more details.
Also, I'm aware that this is a quite complete problem-question, but I prefer to ask one big question and maybe get a new idea of how to get along rather than thinking about it on my own and asking only detail-questions and missing out the genius idea.