On the CPU-side of an 3D first-person / ego perspective game I need to check whether what the players currently sees on screen is the inside of a box object defined by world space coordinates (the player might be outside of that box but on screen sees only/mostly the inside of the box, or vice-versa, looks from within the box to the outside).

The "casual" way of performing such a check would incorporate frustum culling but such an approach would be hard to achieve with my given set of engine parameters which I'd like to avoid if there is a simpler way.

What I actually have at the point where I would like to do the check (high-level script on CPU, not GPU side):

• Camera world position
• Camera direction
• Camera FOV
• Two Box corner world coordinates (left-bottom-front, right-top-back)

What I do not have right away:

• View frustrum definition (near/far plane or say 6 planes defining frustum)
• Any specific pixel information (uv, view space position, depth or the like)

What I would like to calculate:

• Percentage of screen "covered" by box.

Any hints on how to perform such calculation?