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

Abstract 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.

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