For a point cloud do there exist algorithms to tell the bounding volume that bounds the points in the most compact way, or in a way that minimizes the empty spaces inside the bounding volume? Examples of the bounding volumes in question are bounding boxes, spheres, cylinders and capsules.
Algorithm to find optimal bounding volume for point cloud
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The problem is trivial for the axis-aligned boxes.
For arbitrary boxes, I guess that a generalization of rotating calipers is possible (compute the convex hull and try all orientations defined by a plane that contains a face and another plane containing an edge).
For spheres, use the Welzl algorithm.
For a cylindre or a capsule, mh, good luck...