Bounding Interval Hierarchy - Overview

Overview

Bounding interval hierarchies (BIH) exhibit many of the properties of both bounding volume hierarchies (BVH) and kd-trees. Whereas the construction and storage of BIH is comparable to that of BVH, the traversal of BIH resemble that of kd-trees. Furthermore, BIH are also binary trees just like kd-trees (and in fact their superset, BSP trees). Finally, BIH are axis-aligned as are its ancestors. Although a more general non-axis-aligned implementation of the BIH should be possible (similar to the BSP-tree, which uses unaligned planes), it would almost certainly be less desirable due to decreased numerical stability and an increase in the complexity of ray traversal.

The key feature of the BIH is the storage of 2 planes per node (as opposed to 1 for the kd tree and 6 for an axis aligned bounding box hierarchy), which allows for overlapping children (just like a BVH), but at the same time featuring an order on the children along one dimension/axis (as it is the case for kd trees).

It is also possible to just use the BIH data structure for the construction phase but traverse the tree in a way a traditional axis aligned bounding box hierarchy does. This enables some simple speed up optimizations for large ray bundles while keeping memory/cache usage low.

Some general attributes of bounding interval hierarchies (and techniques related to BIH) as described by are:

• Very fast construction times
• Low memory footprint
• Simple and fast traversal
• Very simple construction and traversal algorithms
• High numerical precision during construction and traversal
• Flatter tree structure (decreased tree depth) compared to kd-trees