t] denotes the bounding box volume of a large object.
We will estimate the number of bounding box pair intersections among these sets.
Let [Laplace] be a set of n objects where each object has aspect ratio at most [Alpha], and the bounding box of each object has size either [Alpha] (small) or [Alpha][[Sigma].
Clearly, there are only three kinds of intersections: large-large, small-small, and large-small, and we use [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] to denote the corresponding bounding box intersection numbers.
i], we enlarge the bounding boxes in it to size [Alpha] [2.
Finally, every small-large pair of objects contributes an intersecting bounding box pair, and so [K.
We have analyzed the performance of a popular bounding box heuristic for collision detection in terms of two shape parameters: aspect ratio and scale factor.
Our theorems can be used to explain the empirical evidence that bounding boxes tend to improve performance.