On fast construction of spatial hierarchies for ray tracing

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