1. Find a more efficient way to transform axis-aligned bounding boxes by taking advantage of the symmetries of the problem: because the eight corner points are linear combinations of three axis-aligned basis vectors and a single corner point, their transformed bounding box can be found more efficiently than by the method we have presented (Arvo 1990).
  2. Instead of boxes, tighter bounds around objects could be computed by using the intersections of many nonorthogonal slabs. Extend the bounding box representation in pbrt to allow the user to specify a bound comprised of arbitrary slabs.
  3. The DirectionCone::BoundSubtendedDirections() method bounds the directions that a Bounds3f subtends from a given reference point by first finding a sphere that bounds the Bounds3f and then bounding the directions it subtends. While this gives a valid bound, it is not necessarily the smallest one possible. Derive an improved algorithm that acts directly on the bounding box, update the implementation of BoundSubtendedDirections(), and render scenes where that method is used (e.g., those that use a BVHLightSampler to sample light sources). How are running time and image quality affected? Can you find a scene where this change gives a significant benefit?
  4. Change pbrt so that it transforms Normal3fs just like Vector3fs, and create a scene that gives a clearly incorrect image due to this bug. (Do not forget to revert this change from your copy of the source code when you are done!)