# How to detect if a point is below a bounding box (thread-safe)?

I am trying to cast a shadow on a set of points in Unity that are below a BoxCollider object (have an x and z that would be in the box but y is below it). I previously used InverseTransform point to check if the points were in the bounding box, however it doesn't seem to work here because it would only check if the point y in the box frame is below the box.

In addition, I am doing this calculation on a thread so I can't use raycasting or any of the other Unity APIs available. How might I check if a point is below the box using strictly vector/quaternion math?