Representing objects as rays, or how to pile up an octree?

Quadtrees, octrees, and in general k-trees have established themselves as useful hierarchical data structures in computer graphics, image processing, and solid modeling. A fundamental operation in a system based on k-trees is the construction of a k-tree. Here, we review a new way of doing this operation. Basically, we have invented a method to store an object as a set of rays and an algorithm for converting such a set into a k-tree. (For example, in 3D a ray is a thin parallelepiped.) The algorithm is conceptually simple, works for any k, and piles up, using an approach we call stacking, a k-tree from the rays very fast. It produces a minimal k-tree and does not lead to intermediate storage swell. For large-scale realistic objects, which consist of many thousands of rays, the algorithm debunks the "expensive octree creation" myth. © 1989