skip to main content
research-article
Best Paper

Bringing Linearly Transformed Cosines to Anisotropic GGX

Published:04 May 2022Publication History
Skip Abstract Section

Abstract

Linearly Transformed Cosines (LTCs) are a family of distributions that are used for real-time area-light shading thanks to their analytic integration properties. Modern game engines use an LTC approximation of the ubiquitous GGX model, but currently this approximation only exists for isotropic GGX and thus anisotropic GGX is not supported. While the higher dimensionality presents a challenge in itself, we show that several additional problems arise when fitting, post-processing, storing, and interpolating LTCs in the anisotropic case. Each of these operations must be done carefully to avoid rendering artifacts. We find robust solutions for each operation by introducing and exploiting invariance properties of LTCs. As a result, we obtain a small 84 look-up table that provides a plausible and artifact-free LTC approximation to anisotropic GGX and brings it to real-time area-light shading.

Skip Supplemental Material Section

Supplemental Material

References

  1. James Arvo. 1995. Applications of Irradiance Tensors to the Simulation of Non-Lambertian Phenomena. In Proc. ACM SIGGRAPH. 335--342.Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. D. R. Baum, H. E. Rushmeier, and J. M. Winget. 1989. Improving Radiosity Solutions Through the Use of Analytically Determined Form-factors. Computer Graphics (Proc. SIGGRAPH) 23, 3 (1989), 325--334.Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Anis Benyoub. 2019. Leveraging Ray Tracing Hardware Acceleration In Unity. In ACM SIGGRAPH Courses 2019.Google ScholarGoogle Scholar
  4. Benedikt Bitterli, Chris Wyman, Matt Pharr, Peter Shirley, Aaron Lefohn, and Wojciech Jarosz. 2020. Spatiotemporal reservoir resampling for real-time ray tracing with dynamic direct lighting. ACM Trans. Graph. 39, 4 (2020).Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Nicolas Bonneel, Julien Rabin, Gabriel Peyré, and Hanspeter Pfister. 2015. Sliced and Radon Wasserstein Barycenters of Measures. J. Math. Imaging Vis. 51, 1 (2015), 22--45.Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Stavros Diolatzis, Adrien Gruson, Wenzel Jakob, Derek Nowrouzezahrai, and George Drettakis. 2020. Practical Product Path Guiding Using Linearly Transformed Cosines. Computer Graphics Forum (2020).Google ScholarGoogle Scholar
  7. MichałDrobot. 2014. Physically based area lights. In GPU Pro 5. 67--100.Google ScholarGoogle Scholar
  8. Jonathan Dupuy and Wenzel Jakob. 2018. An Adaptive Parameterization for Efficient Material Acquisition and Rendering. Transactions on Graphics (Proceedings of SIGGRAPH Asia) 37, 6 (2018), 274:1-274:18.Google ScholarGoogle Scholar
  9. Eric Heitz. 2014. Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs. Journal of Computer Graphics Techniques (JCGT) 3, 2 (2014), 48--107.Google ScholarGoogle Scholar
  10. Eric Heitz. 2018. Sampling the GGX Distribution of Visible Normals. Journal of Computer Graphics Techniques (JCGT) 7, 4 (2018), 1--13.Google ScholarGoogle Scholar
  11. Eric Heitz, Jonathan Dupuy, Stephen Hill, and David Neubelt. 2016. Real-Time Polygonal-Light Shading with Linearly Transformed Cosines. ACM Trans. Graph. 35, 4, Article 41 (2016).Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Eric Heitz and Stephen Hill. 2017a. Linear-Light Shading with Linearly Transformed Cosines. In GPU Zen.Google ScholarGoogle Scholar
  13. Eric Heitz and Stephen Hill. 2017b. Real-Time Line- and Disk-Light Shading with Linearly Transformed Cosines. In ACM SIGGRAPH Courses 2017.Google ScholarGoogle Scholar
  14. Eric Heitz, Stephen Hill, and Morgan McGuire. 2018. Combining Analytic Direct Illumination and Stochastic Shadows. In Proceedings of the ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games. Article 2.Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Stephen Hill and Eric Heitz. 2016. Real-Time Area Lighting: a Journey from Research to Production. In ACM SIGGRAPH Courses 2016.Google ScholarGoogle Scholar
  16. Stephen Hill, Stephen McAuley, Laurent Belcour, Will Earl, Niklas Harrysson, Sébastien Hillaire, Naty Hoffman, Lee Kerley, Jasmin Patry, Rob Pieké, Igor Skliar, Jonathan Stone, Pascal Barla, Mégane Bati, and Iliyan Georgiev. 2020. Physically Based Shading in Theory and Practice. In ACM SIGGRAPH 2020 Courses. Article 11, 12 pages.Google ScholarGoogle Scholar
  17. Soheil Kolouri, Gustavo K. Rohde, and Heiko Hoffmann. 2018. Sliced Wasserstein Distance for Learning Gaussian Mixture Models. In Conference on Computer Vision and Pattern Recognition, CVPR 2018.Google ScholarGoogle Scholar
  18. Aakash Kt, Parikshit Sakurikar, and P. J. Narayanan. 2021. Fast Analytic Soft Shadows from Area Lights. In Eurographics Symposium on Rendering - DL-only Track, Adrien Bousseau and Morgan McGuire (Eds.).Google ScholarGoogle Scholar
  19. Sébastien Lagarde and Charles de Rousiers. 2014. Physically Based Shading in Theory and Practice: Moving Frostbite to PBR. In ACM SIGGRAPH Courses 2014.Google ScholarGoogle Scholar
  20. Johann Heinrich Lambert. 1760. Photometria, sive De mensura et gradibus luminus, colorum et umbrae. (1760).Google ScholarGoogle Scholar
  21. Pascal Lecocq, Arthur Dufay, Gaël Sourimant, and Jean-Eudes Marvie. 2016. Accurate analytic approximations for real-time specular area lighting. In Proceedings of the 20th ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games. 113--120.Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Pascal Lecocq, Gaël Sourimant, and Jean-Eudes Marvie. 2015. Accurate Analytic Approximations for Real-time Specular Area Lighting. In ACM SIGGRAPH 2015 Talks. Article 68, 1 pages.Google ScholarGoogle Scholar
  23. Tzu-Mao Li, Miika Aittala, Frédo Durand, and Jaakko Lehtinen. 2018. Differentiable Monte Carlo Ray Tracing through Edge Sampling. ACM Trans. Graph. (Proc. SIGGRAPH Asia) 37, 6 (2018).Google ScholarGoogle Scholar
  24. Addy Ngan, Frédo Durand, and Wojciech Matusik. 2005. Experimental Analysis of BRDF Models. In Proceedings of the Eurographics Symposium on Rendering. 117--226.Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban Desmaison, Andreas Kopf, Edward Yang, Zachary DeVito, Martin Raison, Alykhan Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu Fang, Junjie Bai, and Soumith Chintala. 2019. PyTorch: An Imperative Style, High-Performance Deep Learning Library. In Advances in Neural Information Processing Systems 32. 8024--8035.Google ScholarGoogle Scholar
  26. Christoph Peters. 2021. BRDF Importance Sampling for Polygonal Lights. ACM Trans. Graph. 40, 4 (2021), 14 pages.Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Julien Rabin, Gabriel Peyré, Julie Delon, and Marc Bernot. 2012. Wasserstein Barycenter and Its Application to Texture Mixing. In Scale Space and Variational Methods in Computer Vision. 435--446.Google ScholarGoogle Scholar
  28. Sebastian Ruder. 2016. An overview of gradient descent optimization algorithms. arXiv preprint arXiv:1609.04747 (2016).Google ScholarGoogle Scholar
  29. John M. Snyder. 1996. Area Light Sources for Real-Time Graphics. Technical Report MSR-TR-96-11. Microsoft Research.Google ScholarGoogle Scholar
  30. Bruce Walter, Stephen R. Marschner, Hongsong Li, and Kenneth E. Torrance. 2007. Microfacet Models for Refraction through Rough Surfaces. In Proceedings of the Eurographics Symposium on Rendering Techniques 2007. 195--206.Google ScholarGoogle Scholar
  31. Lifeng Wang, Zhouchen Lin, Wenle Wang, and Kai Fu. 2008. One-Shot Approximate Local Shading. Technical Report.Google ScholarGoogle Scholar
  32. Marcus Wassmer, Jerome Platteaux, Arne Schober, and Ignacio Llamas. 2018. Cinematic Lighting in Unreal Engine. In Game Developers Conference 2018.Google ScholarGoogle Scholar
  33. Yang Zhou, Lifan Wu, Ravi Ramamoorthi, and Ling-Qi Yan. 2021. Vectorization for Fast, Analytic, and Differentiable Visibility. ACM Trans. Graph. 40, 3 (2021).Google ScholarGoogle ScholarDigital LibraryDigital Library

Index Terms

  1. Bringing Linearly Transformed Cosines to Anisotropic GGX

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in

    Full Access

    • Published in

      cover image Proceedings of the ACM on Computer Graphics and Interactive Techniques
      Proceedings of the ACM on Computer Graphics and Interactive Techniques  Volume 5, Issue 1
      May 2022
      252 pages
      EISSN:2577-6193
      DOI:10.1145/3535313
      Issue’s Table of Contents

      Copyright © 2022 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 4 May 2022
      Published in pacmcgit Volume 5, Issue 1

      Permissions

      Request permissions about this article.

      Request Permissions

      Check for updates

      Qualifiers

      • research-article
      • Research
      • Refereed
    • Article Metrics

      • Downloads (Last 12 months)67
      • Downloads (Last 6 weeks)5

      Other Metrics

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader
    About Cookies On This Site

    We use cookies to ensure that we give you the best experience on our website.

    Learn more

    Got it!