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Compact tetrahedralization-based acceleration structures for ray tracing

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Abstract

We propose compact and efficient tetrahedral mesh representations to improve the ray-tracing performance. We reorder tetrahedral mesh data using a space-filling curve to improve cache locality. Most importantly, we propose efficient ray-traversal algorithms. We provide details of the regular ray-tracing operations on tetrahedral meshes and the GPU implementation of our traversal method. We demonstrate our findings through a set of comprehensive experiments. Our method outperforms existing tetrahedral mesh-based traversal methods and yields comparable results to the traversal methods based on the state-of-the-art acceleration structures such as k-dimensional (k-d) tree and Bounding Volume Hierarchy (BVH) in terms of speed. Storage-wise, our method uses less memory than its tetrahedral mesh-based counterparts, thus allowing larger scenes to be rendered on the GPU.

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References

  • Aman A, Demirci S, Güdükbay U, Wald I (2021) Multi-level tetrahedralization-based accelerator for ray-tracing animated scenes. Comput Anim Virtual World 32(3–4):e2024

    Google Scholar 

  • Berk H, Aykanat C, Gudukbay U (2003) Direct volume rendering of unstructured grids. Comp & Graph 27:387–406

    Article  Google Scholar 

  • Bowyer A (1981) Computing dirichlet tessellations. Comput J 24(2):162–166

    Article  MathSciNet  Google Scholar 

  • Duff T, Burgess J, Christensen P, Hery C, Kensler A, Liani M, Villemin R (2017) Building an orthonormal basis, revisited. J Comp Graph Tech 6(1):1–8

    Google Scholar 

  • Edelsbrunner H, Shah NR (1992) Incremental topological flipping works for regular triangulations. In: Proc. Eighth Ann. Symp. Comp. Geom., ACM, New York, NY, USA, SCG ’92, pp 43–52

  • Fellegara R, Floriani LD, Magillo P, Weiss K (2020) Tetrahedral trees: A family of hierarchical spatial indexes for tetrahedral meshes. ACM Trans Spat Algo Syst 6(4):23, 34 p

    Google Scholar 

  • Fujimoto A, Tanaka T, Iwata K (1988) ARTS: accelerated ray-tracing system. In: Joy KI, Grant CW, Max NL, Hatfield L (eds) Tutorial: Computer Graphics. Image Synthesis, Computer Science Press Inc, New York, NY, USA, pp 148–159

    Google Scholar 

  • Garrity MP (1990) Raytracing irregular volume data. In Proc. Eighth Joint Eurographics/IEEE VGTC Conf. Vis., ACM, New York, NY, USA, VVS ’90, pp 35–40

  • Garth C, Joy KI (2010) Fast, memory-efficient cell location in unstructured grids for visualization. IEEE Trans Vis Comput Graph 16(6):1541–1550

    Article  Google Scholar 

  • Glassner AS (1984) Space subdivision for fast ray tracing. IEEE Comp Graph App 4(10):15–24

    Article  Google Scholar 

  • Goldsmith J, Salmon J (1987) Automatic creation of object hierarchies for ray tracing. IEEE Comp Graph App 7(5):14–20

    Article  Google Scholar 

  • Gunther J, Popov S, Seidel HP, Slusallek P (2007) Realtime ray tracing on GPU with BVH-based packet traversal. In Proc. IEEE Symp. Interactive Ray Tracing, IEEE Computer Society, Washington, DC, USA, RT ’07, pp 113–118

  • Haines E, Greenberg D (1986) The light buffer: a shadow-testing accelerator. IEEE Comp Graph App 6(9):6–16

    Article  Google Scholar 

  • Havran V, Bittner J (2002) On improving kd tree for ray shooting. J WSCG 10:209–216

    Google Scholar 

  • Hu Y, Zhou Q, Gao X, Jacobson A, Zorin D, Panozzo D (2018) Tetrahedral meshing in the wild. ACM Trans Graph 37(4):60

    Google Scholar 

  • Hu Y, Schneider T, Gao X, Zhou Q, Jacobson A, Zorin D, Panozzo D (2019) TriWild: Robust triangulation with curve constraints. ACM Trans Graph 38(4):52

    Article  Google Scholar 

  • Hunt W, Mark W (2008) Adaptive acceleration structures in perspective space. In: Proc. IEEE Symp. Interactive Ray Tracing, RT ’08, pp 11–17

  • Koyamada K (1992) Fast traverse of irregular volumes. In: Kunii TL (ed) Vis Comput. Springer Japan, Tokyo, pp 295–311

    Chapter  Google Scholar 

  • Lagae A, Dutré P (2008) Accelerating ray tracing using constrained tetrahedralizations. Comp Graph Forum 27(4):1303–1312

    Article  Google Scholar 

  • Lagae A, Dutré P (2008) Compact, fast and robust grids for ray tracing. Comput Graph Forum 27(4):1235–1244

    Article  Google Scholar 

  • MacDonald DJ, Booth KS (1990) Heuristics for ray tracing using space subdivision. Vis Comput 6(3):153–166

    Article  Google Scholar 

  • Maria M, Horna S, Aveneau L (2014) Topological space partition for fast ray tracing in architectural models. In: Proc. Int. Conf. Comp. Graph. Theory App., GRAPP ’14, pp 1–11

  • Maria M, Horna S, Aveneau L (2017) Constrained convex space partition for ray tracing in architectural environments. Comput Graph Forum 36(1):288–300

    Article  Google Scholar 

  • Maria M, Horna S, Aveneau L (2017b) Efficient ray traversal of constrained Delaunay tetrahedralization. In: Proc. Int. Joint Conf. Comp. Vis., Imag. Comp. Graph. Theory Appl., VISIGRAPP ’17, vol 1, pp 236–243

  • Marmitt G, Slusallek P (2006) Fast ray traversal of tetrahedral and hexahedral meshes for direct volume rendering. In: Proc. Eighth Joint Eurographics/IEEE VGTC Conf. Vis., Eurographics Assoc., Aire-la-Ville, Switzerland, EUROVIS ’06, pp 235–242

  • Maximo A, Ribeiro S, Bentes C, Oliveira A, Farias R (2008) Memory efficient GPU-based ray casting for unstructured volume rendering. In: Proc. Fifth Eurographics / IEEE VGTC Symp. Point-Based Graphics, Eurographics Assoc., Goslar, DEU, SPBG’08, pp 155–162

  • Mebarki A (2018) XOR-based compact triangulations. Comp & Inform 37:367–384

    Article  Google Scholar 

  • Miller GL, Talmor D, Teng SH, Walkington N, Wang H (1996) Control volume meshes using sphere packing: Generation, refinement and coarsening. In: Proc. 5th Int. Meshing Roundtable, pp 47–61

  • Pharr M, Jakob W, Humphreys G (2016) Physically based rendering: from theory to implementation, 3rd edn. Morgan Kaufmann Publishers Inc, San Francisco, CA, USA

    Google Scholar 

  • Platis N, Theoharis T (2003) Fast ray-tetrahedron intersection using Plücker coordinates. J Graph Tool 8(4):37–48

    Article  Google Scholar 

  • Ribeiro S, Maximo A, Bentes C, Oliveira A, Farias R (2007) Memory-aware and efficient ray-casting algorithm. In: Proc. XX Brazilian Symp. Comp. Graph. Img. Process., SIBGRAPI ’07, pp 147–154

  • Sahistan A, Demirci S, Morrical N, Zellmann S, Aman A, Wald I, Güdükbay U (2021) Ray-traced shell traversal of tetrahedral meshes for direct volume visualization. In: Proc. IEEE Vis. Conf.-Short Papers, VIS ’21, pp 91–95

  • Shewchuk JR (1996) Adaptive precision floating-point arithmetic and fast robust geometric predicates. Disc & Comp Geom 18:305–363

    Article  MathSciNet  Google Scholar 

  • Si H (2015) TetGen, a Delaunay-based quality tetrahedral mesh generator. ACM Trans Math Soft 41(2):11, 36 p

    Article  MathSciNet  Google Scholar 

  • Silva CT, Mitchell JSB (1997) The lazy sweep ray casting algorithm for rendering irregular grids. IEEE Trans Vis Comp Graph 3(2):142–157

    Article  Google Scholar 

  • Silva CT, Mitchell JSB, Kaufman AE (1996) Fast rendering of irregular grids, Proc. Symp. Vol. Vis., VIS '96, 1996, pp. 15–22

  • Sinha P (2004) A memory-efficient doubly linked list. Linux J, Available at https://www.linuxjournal.com/article/6828. Accessed 5 May 2022

  • Stich M, Friedrich H, Dietrich A (2009) Spatial Splits in Bounding Volume Hierarchies. In: Proc. Conf. High Perf. Graph., ACM, New York, NY, USA, HPG ’09, pp 7–13

  • Wald I (2007) On fast construction of SAH-based bounding volume hierarchies. In: Proc. IEEE Symp. Interactive Ray Tracing, IEEE Computer Society, Washington, DC, USA, RT ’07, pp 33–40

  • Wald I, Havran V (2006) On building fast kd-trees for ray tracing, and on doing that in O(N log N). In: Proc. IEEE Symp. Interactive Ray Tracing, IEEE Computer Society, Washington, DC, USA, RT '06, pp 61–69

  • Watson DF (1981) Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes. Comput J 24(2):167–172

    Article  MathSciNet  Google Scholar 

  • Wodniok D, Goesele M (2017) Construction of bounding volume hierarchies with SAH cost approximation on temporary subtrees. Comp & Graph 62:41–52

    Article  Google Scholar 

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Acknowledgements

This research is supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) under Grant No. 117E881. We are grateful to Dr. Maxime Maria and his colleagues for providing us their implementation of the tetrahedral mesh traversal method.

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Authors and Affiliations

  1. Department of Computer Engineering, Bilkent University, 06800, Ankara, Turkey

    Aytek Aman, Serkan Demirci & Uğur Güdükbay

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  1. Aytek Aman
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  2. Serkan Demirci
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  3. Uğur Güdükbay
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Correspondence to Uğur Güdükbay.

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Aman, A., Demirci, S. & Güdükbay, U. Compact tetrahedralization-based acceleration structures for ray tracing. J Vis 25, 1103–1115 (2022). https://doi.org/10.1007/s12650-022-00842-x

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  • DOI: https://doi.org/10.1007/s12650-022-00842-x

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