[2D, C#] Finding two coordinates in a line via two other coordinates

Unity Engine
1

Alright, so!
I’m experimenting with a camera control system that’s set up somewhat like Metroid Prime on the Wii, where the closer the cursor is to the edge of the screen (without going past a bounding box), the camera rotates.
So, here’s what I’m trying to do:
I have a Rect representing the bounding box, which is computed from a single float telling how much of the screen it covers.
After the mouse leaves the Rect, I want to find out the coordinates where a ray going from the center of the screen to the mouse would intersect on both the bounding box and the edge of the screen.
Those three coordinates would then be Math’d to figure out the distance from the bounding box and center of the screen (all at once), and then the result would be applied to the camera to rotate. I don’t really need help on this, just putting it here for completions sake.
For the life of me, I cannot figure out how to do this, and would really appreciate the help.

ed: I should also point out, this is an FPS, not a 2D game.
I mistyped and didn’t notice, earlier.

2

Why are you going so 3d on this?

Why not just have it where you get the cursor/mouse position.

Check it’s x position (2d), if it’s within some margin of the left or right of the screen (near 0 or screen width respectively), you apply a rotation. The closer, the faster the rotation.

3

Crap, typo.

I am in 3D, the camera’s an FPS.
Sorry for the confusion, I was a little out of it when I typed that.

4

you still don’t need to to any 3D , the screen, which is the surface you are checking mouse movement on, is 2D .
I would do something like :

Vector2 mouse = new Vector2(Input.mousePosition.x / Screen.width , Input.mousePosition.y / Screen.height );

mouse.x and mouse.y now is in the space 0 til 1 , so to check if your mouse position is at the left

float mouseSideTreshold = 0.2f;
if ( mouse.x < mouseSideTreshold){ //left side}
if (mouse.x > (1.0f - mouseSideTreshold)) { //right side}