On the Fast Construction of Spatial Hierarchies for Ray Tracing

Abstract

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 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 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 log log N) 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.

Parallel BVH construction using k-means clustering

“…Several techniques have been proposed to reduce the constants behind the asymptotic complexity. For example, Havran et al [16], Wald et al [33], and Ize et al [19] used approximate SAH cost function evaluation based on binning. Hunt et al [18] suggested using the structure of the scene graph to speed up the BVH construction process.…”

Reducing Render Time in Ray Tracing by Pixel Averaging

“…They did not used low level optimization methods or kinds of methods are used to accelerate. Havran [13] recently proposed a method based on hierarchical acceleration structures in kd-tree. Moreover he introduced a SAH based on accelerate combined methods; using specification total 3D space will be formed.…”

Spatial splits in bounding volume hierarchies

“…Therefore, a simple counter for each bin, like in conventional kD-tree binning methods, is not sufficient. Instead, we need to store one AABB per bin, similar to techniques for BVHs [Havran et al 2006;Wald 2007]. The actual binning process for a reference considers all bins that the reference AABB overlaps.…”