Ray Tracing (graphics) - Bounding Volumes

Bounding Volumes

We enclose groups of objects in sets of hierarchical bounding volumes and first test for intersection with the bounding volume, and then only if there is an intersection, against the objects enclosed by the volume.

Bounding volumes should be easy to test for intersection, for example a sphere or box (slab). The best bounding volume will be determined by the shape of the underlying object or objects. For example, if the objects are long and thin then a sphere will enclose mainly empty space and a box is much better. Boxes are also easier for hierarchical bounding volumes.

Note that using a hierarchical system like this (assuming it is done carefully) changes the intersection computational time from a linear dependence on the number of objects to something between linear and a logarithmic dependence. This is because, for a perfect case, each intersection test would divide the possibilities by two, and we would have a binary tree type structure. Spatial subdivision methods, discussed below, try to achieve this.

Kay & Kajiya give a list of desired properties for hierarchical bounding volumes:

• Subtrees should contain objects that are near each other and the further down the tree the closer should be the objects.
• The volume of each node should be minimal.
• The sum of the volumes of all bounding volumes should be minimal.
• Greater attention should be placed on the nodes near the root since pruning a branch near the root will remove more potential objects than one farther down the tree.
• The time spent constructing the hierarchy should be much less than the time saved by using it.