Corrections to the surface area metric with respect to mail boxing
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Corrections to the Surface Area Metric with Respect to Mail-Boxing. Warren Hunt. Introduction. The Surface Area Metric is the most common cost metric for acceleration structures The metric doesn’t account for the effects of mail-boxing (when present). What is Mail-boxing?.

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Corrections to the Surface Area Metric with Respect to Mail-Boxing

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Corrections to the surface area metric with respect to mail boxing

Corrections to the Surface Area Metric with Respect to Mail-Boxing

Warren Hunt


Introduction

Introduction

  • The Surface Area Metric is the most common cost metric for acceleration structures

  • The metric doesn’t account for the effects of mail-boxing (when present)


What is mail boxing

What is Mail-boxing?

  • Optimization for partitioning based acceleration structures

  • Attempts to avoid multiple intersection tests between the same ray/object pair


Contribution overview

Contribution Overview

  • Present a correction to the surface area metric for mail-boxing

    • Extremely simple to implement

    • Significant reduction in intersection tests

    • Modest improvement in performance

    • Improves the effectiveness of mail-boxing


The surface area metric

The Surface Area Metric

  • Cost(s) = P(sleft)Cost(sleft) + P(sright)Cost(sright)

  • P is the probability function (based on surface area)

  • During build, cost is estimated by the number of objects overlapping each side

    • Mail-boxing changes this cost!


Corrected surface area metric

Corrected Surface Area Metric

  • Cost(s) = P(sleft)*Cost(sleft)+ P(sright)*Cost(sright)- P(sright^left)*Cost(sright^left)

  • P(sleft^right) is the probability that a ray strikes both sides of the split

    • Partition is convex, use ratio of surface areas

  • Cost(sleft^right) is the number of objects that occur on both sides of the split


Effects of the modification

Effects of the Modification

  • Fundamentally changes the effectiveness of kd-trees when using mail-boxing

    • Allows splits that the SAH wouldn’t previously allow

    • Allows mail-boxing to fully address the integral duplication problem in kd-trees (explained shortly!)


Example abutted cells

KD-Tree

Split Plane

Left BV

Right BV

Example: Abutted Cells

1

1

1


Example overlapping cells

KD-Tree

Split Planes

Left BV

Right BV

KD-Tree

Split Plane

Example: Overlapping Cells

1-Δ

  • Original SAM wouldn’t allow either of these splits!

  • Detailed explanation in the paper

1


Results

Results

  • ~30% reduction in intersection tests when compared to the uncorrected SAM

  • ~5% reduction in overall render-time

  • ~5% increase in traversal steps

  • Results are fairly consistent between off-line and real-time ray-tracers


Specific results teaser

Specific Results Teaser

  • Using an interactive ray-tracer


Conclusions

Conclusions

  • Presented a correction to the surface area metric for mail-boxing

    • Extremely simple to implement

    • Significant reduction in intersection tests

    • Modest improvement in performance

    • Improves the effectiveness of mail-boxing


Questions

Questions?


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Perspective questions

Perspective Questions?


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