bound

Additional Key Words and Phrases: Aspect ratio, bounding box, collision detection, scale factor

Many computer graphics algorithms use bounding boxes to improve their performance.

Bounding boxes are useful in algorithms that should process only the intersecting objects.

The bounding box heuristic is used in rendering algorithms, including the traditional visible-surface determination [Foley et al.

Although there is ample empirical evidence that the bounding box heuristic improves performance in practice, the goal of formally proving that bounding boxes maintain high performance in the worst case has remained elusive.

Then, the performance of the bounding box heuristic can be judged by

There are two ways to measure the scale--either as a ratio of the largest to smallest bounding box, or as the ratio of largest to smallest core.

In practical terms, however, all the theorems validate the empirical evidence on the bounding box heuristic-since [n.sup.1/3] is a relatively slow-growing function, it seems justifiable that the bound on [Rho] is small for bounded aspect ratio and scale factor.