Corrections to the surface area metric with respect to mail-boxing

The surface area heuristic is the standard method for producing high quality acceleration structures for ray-tracing. High quality acceleration structures minimize per-ray costs for ray-tracing and thus rendering times. However, the metric used by the surface area heuristic makes several assumptions that do not hold in practice. Much work has been done to analyze these assumptions and provide a more accurate cost model but no-one has analyzed the surface area metricpsilas interaction with a common ray-tracing optimization, mail-boxing. We present a correction to the surface area metric for ray-tracing systems using mail-boxing. Additionally, we provide a concrete example of how our new metric improves the quality of kd-trees as compared to the original surface area metric. Finally, we show that our correction provides a noticeable (about 30%) reduction in the number of intersection tests performed during ray-tracing as well as improving run-time performance. We conclude that this algorithmic adjustment is so simple that anyone implementing mail-boxing should consider using it.