# Object Partitioning Considered Harmful: Space Subdivision for BVHs

Stefan Popov, Iliyan Georgiev, Rossen Dimov, and Philipp Slusallek *HPG '09: Proceedings of the 1st ACM conference on High Performance Graphics , page 15--22.*

Publisher: ACM, New York, NY, USA 2009.

ISBN: 978-1-60558-603-8

# Abstract

A major factor for the efficiency of ray tracing is the use of good acceleration structures. Recently, bounding volume hierarchies (BVHs) have become the preferred acceleration structures, due to their competitive performance and greater flexibility compared to KD trees. In this paper, we present a study on algorithms for the construction of optimal BVHs.

Due to the exponential nature of the problem, constructing optimal BVHs for ray tracing remains an open topic. By exploiting the linearity of the surface area heuristic (SAH), we develop an algorithm that can find optimal partitions in polynomial time. We further generalize this algorithm and show that every SAH-based KD tree or BVH construction algorithm is a special case of the generic algorithm.

Based on a number of experiments with the generic algorithm, we conclude that the assumption of non-terminating rays in the surface area cost model becomes a major obstacle for using the full potential of BVHs. We also observe that enforcing space subdivision helps to improve BVH performance. Finally, we develop a simple space partitioning algorithm for building efficient BVHs.