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On the use of local ray termination for efficiently constructing qualitative BSPs, BIHs and (S)BVHs

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Abstract

Acceleration data structures (ADSs) exploit spatial coherence by distributing a scene’s geometric primitives into spatial groups, effectively reducing the cost of ray tracing queries. The most effective ADSs are hierarchical, adaptive tree structures such as BSPs, BIHs and (S)BVHs. The de facto standard cost metric for building these structures is the Surface Area Heuristic (SAH), which assumes a scene-exterior isotropic ray distribution of non-terminating rays. Despite its restrictive assumptions, the SAH remains competitive against many fundamentally different cost metrics targeting more common ray distributions. Our goal is not to radically change and replace the SAH, but to adapt it by introducing the concept of local ray termination in the context of voxel partitioning during the ADS construction and voxel traversal order during ADS traversal. We develop heuristics to approximate local ray termination efficiently without additional preprocessing or ray (sub)sampling. Our heuristics are used for approximating the visibility probabilities in the Ray Termination Surface Area Heuristic (RTSAH) for constructing BSPs, BIHs and (S)BVHs for accelerating closest-hit ray queries and for approximating the hit probabilities in the Shadow Ray Distribution Heuristic for constructing dedicated BVHs for accelerating any-hit ray queries. The main aim of our paper is to analyze the potential of including local ray termination into the SAH. The results indicate rendering performance close to the references (SAH and NodeSATO) on average due to small and/or compensating gains in the number of ray-triangle intersection tests and ADS node traversal steps. Furthermore, prerendering build times are higher for the RTSAH due to triangle clipping.

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Acknowledgements

We would like to thank Naiwen Xie and especially Roald Frederickx for many fruitful discussions, and the anonymous reviewers for their feedback and suggestions. The Bedroom [4] scene is modeled by David Vacek and designed by David Tousek. The Kitchen [4] scene is modeled by Jeremy Birn. The Carnival [4] scene is modeled by Dan Konieczka. The Museum Hall [4] scene is modeled by Alvaro Luna Bautista and Joel Andersdon. The Conference Room [38] scene is created by Anat Grynberg and Greg Ward. The Crytek Sponza [38] scene is created by Frank Meinl. pbrt-v2 [46] is courtesy of Matt Pharr and Greg Humphreys.

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  1. Department of Computer Science, KU Leuven, Leuven, Belgium

    Matthias Moulin & Philip Dutré

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  1. Matthias Moulin
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Correspondence to Matthias Moulin.

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Matthias Moulin is a predoctoral fellow of the Research Foundation—Flanders (FWO).

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Appendix: Form Factors

Appendix: Form Factors

The (patch-to-patch) form factor, , between two surface area domains, and , describes the fraction of energy (i.e., irradiance in the context of radiosity algorithms or rays in the context of ray termination) leaving reaching :

(A.1)

where and belong to the surface area domain, and , respectively, is the binary visibility function (i.e., evaluates to 1 if and are mutually visible, 0 otherwise), and are the surface normals in and , respectively, and is the distance between and . Due to the visibility component, no tractable closed form expression can be found handling all geometrical configurations between both surface area domains, and . For the remainder we assume the absence of such geometrical configurations (i.e., ).

The form factor between two finite, orthogonal rectangles sharing one complete edge with length l, , and the form factor between two finite, parallel and identical rectangles separated by a distance l, , can be evaluated via the following tractable closed form expressions [25]:

(A.2)
(A.3)

Here, w, h and l are defined as shown in Fig. 4, and the dimensionless variables are defined as: and .

Fig. 4
figure 4

The two types of form factors between the rectangular planes of a bounding box: a the form factor between two finite, orthogonal rectangular planes sharing one complete edge with length l, , b the form factor between two finite, parallel and identical rectangular planes separated by a distance l,

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Moulin, M., Dutré, P. On the use of local ray termination for efficiently constructing qualitative BSPs, BIHs and (S)BVHs. Vis Comput 35, 1809–1826 (2019). https://doi.org/10.1007/s00371-018-1575-x

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