On the 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 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 $O(N \log N)$ is a lower bound required for construction of any spatial hierarchy, which corresponds to sorting based on comparisons, using an approximate method based on space discretization, we propose a new hierarchical data structures with expected $O(N \log\log N)$ time complexity. We also discuss the constants behind the construction algorithms of spatial hierarchies that are important in practice. We document the performance of our algorithms by results obtained from nine different scenes