On optimality of OBBs for visibility tests for frustum culling, ray shooting and collision detection

Bounding volume hierarchies are widely employed in many areas of computer graphics. Usually they are used as crude approximations of the scene geometry to speed up some time-consuming computations, such as visibility tests for frustum culling, ray shooting, collision detection, etc. A number of bounding volume types have been discussed by various researchers. They include bounding spheres, axis-aligned and oriented bounding boxes, and others. Although it is practically possible to use any of these bounding volumes, some types prove to be particularly useful in certain applications, e.g. Gortschalk et al. (1996) used oriented bounding boxes to implement a very effective exact collision detection scheme. The authors address the problem of efficient bounding volume selection, the solution of which allows one to significantly accelerate such operations as visibility tests for frustum culling, collision detection and ray shooting. They prove that minimal surface area (perimeter in 2D) oriented bounding box is optimal among all the oriented bounding boxes with respect to the three operations stated above. Then, they develop a number of algorithms to create optimal oriented bounding boxes and their approximations and finally discuss the results of the practical implementation.