A bounding volume is used to approximate the space an object occupies. If a more precise understanding beyond an approximation is required, the object itself is then inspected to determine what space it occupies. Often, a simple volume (such as an axis-aligned box) is used as bounding volume to approximate the space occupied by an object. But objects can be arbitrary, complicated shapes. So a simple volume often does not fit the object very well. That causes a lot of space that is not occupied by the object to be included in the approximation of the space being occupied by the object. Hardware-based techniques are disclosed herein, for example, for efficiently using multiple bounding volumes (such as axis-aligned bounding boxes) to represent, in effect, an arbitrarily shaped bounding volume to better fit the object, and for using such arbitrary bounding volumes to improve performance in applications such as ray tracing.