On the Fast Construction of Spatial Hierarchies for Ray Tracing

In this paper we will address the problem of fast construction of spatial hierarchies for ray tracing with applications in animated environments including non-rigid animations. We will discuss the properties of currently used techniques with O(N logN) construction time for kd-trees and bounding volume hierarchies. Further, we will propose a hybrid data structure blending a spatial kd-tree with bounding volume primitives. We will keep our novel hierarchical data structures algorithmically efficient and comparable with kd-trees by using a cost model based on surface area heuristics. Although the time complexity O(N logN) is a lower bound required for construction of any spatial hierarchy that corresponds to sorting based on comparisons, using approximate method based on space discretization, we propose novel hierarchical data structures with an expected O(N loglogN) time complexity. We will also discuss constants behind the construction algorithms of spatial hierarchies important in practice. We have documented the performance of our algorithms by results obtained from implementation on nine scenes.