About the relation between spatial subdivisions and object hierarchies used in ray tracing

Abstract

In this paper we study the relation between object hierarchies (such as bounding volume hierarchies) and spatial subdivisions (such as kd-trees and octrees) in the context of ray tracing for static scenes. First, we recall the principles used in efficient ray tracing algorithms and discuss the changes to the performance model more appropriate to current computer architectures. Second, we show how kd-trees can be emulated via bounding volume hierarchies. More importantly we show how bounding volume hierarchies can be emulated via kd-trees in six-dimensional space. Through emulation of one data structure via the second one we show that both data structures are computationally equivalent, assuming that their construction is carried out in top-down fashion.