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Abstract:
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.
