This question is in the context of computer graphics. We have a scene with $n$ triangles and a ray. We want to find if the ray intersects any triangle and get the closest one.
There is a datastructure called Bounding Volume Hierachy (BVH) which groups triangles and fits a bounding volume (e.g. AABBs - axis-aligned bounding boxes) around it. The idea is that if the ray does not intersect the bounding volume, it does not intersect any of the contained triangles / other bounding volumes.
Now assume a BVH with AABB bounding volumes and a scene of $n$ triangles is given. You can spend arbitrary much time for constructing the BVH, but you don't know which rays will come.
What is the worst case time complexity for intersecting a ray with such a BVH? What would a worst case scene look like?
edit: What is the worst case time complexity if triangles may not cross each other?
I thought of something like the following, where the bounding volumes intersect with themselves a lot (think of a recursive definition where the scene is continued to the center).