“Analytic spherical harmonic gradients for real-time rendering with many polygonal area lights” by Wu, Cai, Zhao and Ramamoorthi
Conference:
Type:
Title:
- Analytic spherical harmonic gradients for real-time rendering with many polygonal area lights
Session/Category Title: Differentiable Rendering and Applications
Presenter(s)/Author(s):
Abstract:
Recent work has developed analytic formulae for spherical harmonic (SH) coefficients from uniform polygonal lights, enabling near-field area lights to be included in Precomputed Radiance Transfer (PRT) systems, and in offline rendering. However, the method is inefficient since coefficients need to be recomputed at each vertex or shading point, for each light, even though the SH coefficients vary smoothly in space. The complexity scales linearly with the number of lights, making many-light rendering difficult. In this paper, we develop a novel analytic formula for the spatial gradients of the spherical harmonic coefficients for uniform polygonal area lights. The result is a significant generalization, involving the Reynolds transport theorem to reduce the problem to a boundary integral for which we derive a new analytic formula, showing how to reduce a key term to an earlier recurrence for SH coefficients. The implementation requires only minor additions to existing code for SH coefficients. The results also hold implications for recent efforts on differentiable rendering. We show that SH gradients enable very sparse spatial sampling, followed by accurate Hermite interpolation. This enables scaling PRT to hundreds of area lights with minimal overhead and real-time frame rates. Moreover, the SH gradient formula is a new mathematical result that potentially enables many other graphics applications.
References:
1. T Annen, J Kautz, F Durand, and H Seidel. 2004. Spherical Harmonic Gradients for Mid-range Illumination. Proceedings of the 15th Eurographics Conference on Rendering Techniques (2004), 331–336.Google Scholar
2. J Arvo. 1994. The irradiance Jacobian for partially occluded polyhedral scenes. In SIGGRAPH 94. 343–350.Google Scholar
3. J Arvo. 1995. Applications of irradiance tensors to the simulation of non-Lambertian phenomena. In SIGGRAPH 95. 335–342.Google Scholar
4. L Belcour, G Xie, C Hery, M Meyer, W Jarosz, and D Nowrouzezahrai. 2018. Integrating clipped spherical harmonics expansions. ACM Transactions on Graphics 37, 2 (2018), 19:1–19:12.Google ScholarDigital Library
5. N Benty, K Yao, L Chen, T Foley, M Oakes, C Lavelle, and C Wyman. 2019. The Falcor Rendering Framework. https://github.com/NVIDIAGameWorks/FalcorGoogle Scholar
6. B Cabral, N Max, and R Springmeyer. 1987. Bidirectional Reflection functions from surface bump maps. In SIGGRAPH 87. 273–281.Google Scholar
7. M Chen and J Arvo. 2000. A Closed-Form Solution for the Irradiance Due to Linearly-Varying Luminaires. Proceedings of the 11th Eurographics Workshop on Rendering (2000), 137–148.Google ScholarCross Ref
8. M Chen and J Arvo. 2001. Simulating Non-Lambertian Phenomena Involving Linearly-Varying Luminaires. Proceedings of the 12th Eurographics Workshop on Rendering (2001), 25–38.Google ScholarDigital Library
9. G Greger, P Shirley, P Hubbard, and D Greenberg. 1998. The Irradiance Volume. IEEE Computer Graphics & Applications 18, 2 (1998), 32–43.Google ScholarDigital Library
10. E. Heitz, J. Dupuy, S. Hill, and D. Neubelt. 2016. Real-Time Polygonal-Light Shading with Linearly Transformed Cosines. ACM Transactions on Graphics 35, 4 (2016), 41:1–41:8.Google ScholarDigital Library
11. N Holzschuch and F Sillion. 1995. Accurate Computation of the Radiosity Gradient with Constant and Linear Emitters. Rendering Techniques 1995, Eurographics Symposium on Rendering (1995), 186–195.Google Scholar
12. N Holzschuch and F Sillion. 1998. An Exhaustive Error-Bounding Algorithm for Hierarchical Radiosity. Computer Graphics Forum 17 (1998), 197–218.Google ScholarCross Ref
13. W Jarosz, C Donner, MZwicker, and H Jensen. 2008a. Radiance Caching for Participating Media. ACM Transactions on Graphics 27, 1 (2008), 7:1–7:11.Google ScholarDigital Library
14. W Jarosz, V Schönefeld, L Kobbelt, and H Jensen. 2012. Theory, Analysis and Applications of 2D Global Illumination. ACM Transactions on Graphics 31, 5 (2012), 125:1–125:21.Google ScholarDigital Library
15. W Jarosz, M Zwicker, and H Jensen. 2008b. Irradiance Gradients in the Presence of Participating Media and Occlusions. Computer Graphics Forum (Proceedings of EGSR) 27, 4 (2008), 1087–1096.Google ScholarDigital Library
16. J Křivánek, K Bouatouch, S Pattanaik, and J Žára. 2006. Making Radiance and Irradiance Caching Practical: Adaptive Caching and Neighbor Clamping. Rendering Techniques 2006, Eurographics Symposium on Rendering (2006), 127–138.Google Scholar
17. J Křivánek, P Gautron, K Bouatouch, and S Pattanaik. 2005a. Improved Radiance Gradient Computation. SCCG ’05: Proceedings of the 21th spring conference on computer graphics (2005), 155–159.Google Scholar
18. J Křivánek, P Gautron, S Pattanaik, and K Bouatouch. 2005b. Radiance Caching for Efficient Global Illumination Computation. IEEE Transactions on Visualization and Computer Graphics 11, 5 (2005), 550–561.Google ScholarDigital Library
19. J Křivánek, P Gautron, G Ward, H Jensen, E Tabellion, and P Christensen. 2008. Practical Global Illumination with Irradiance Caching. In SIGGRAPH Courses.Google Scholar
20. L. Gary Leal. 2007. Advanced Transport Phenomena: fluid mechanics and convective transport processes. Vol. 7. Cambridge University Press.Google Scholar
21. P Lecocq, A Dufay, G Sourimant, and J Marvie. 2017. Analytic Approximations for Real-Time Area Light Shading. IEEE Transactions on Visualization and Computer Graphics 99 (2017).Google ScholarDigital Library
22. J Lehtinen. 2007. A Framework for Precomputed and Captured Light Transport. ACM Transactions on Graphics 26, 4 (2007), 13:1–13:22.Google ScholarDigital Library
23. T. Li, M. Aittala, F. Durand, and J. Lehtinen. 2018. Monte Carlo ray tracing through edge sampling. ACM Transactions on Graphics 37, 6 (2018), 222:1–222:11.Google Scholar
24. T. Li, J. Lehtinen, R. Ramamoorthi, W. Jakob, and F. Durand. 2015. Anisotropic Gaussian mutations for Metropolis Light Transport Through Hessian-Hamiltonian Dynamics. ACM Transactions on Graphics 34, 6 (2015), 209:1–209:13.Google ScholarDigital Library
25. H Liu, M Tao, C Li, D Nowrouzezahrai, and A Jacobson. 2019. Beyond Pixel Norm-Balls: Parametric Adversaries using an Analytically Differentiable Renderer. International Conference on Learning Representations (2019).Google Scholar
26. G Loubet, N Holzschuch, and W Jakob. 2019. Reparameterizing discontinuous integrands for differentiable rendering. ACM Transactions on Graphics 38, 6 (2019), 228:1–228:14.Google ScholarDigital Library
27. T MacRobert. 1948. Spherical harmonics: an elementary treatise on harmonic functions with applications. Dover Publications.Google Scholar
28. J Marco, A Jarabo, W Jarosz, and D Gutierrez. 2018. Second-Order Occlusion-Aware Volumetric Radiance Caching. ACM Transactions on Graphics 37, 2 (2018), 20:1–20:14.Google ScholarDigital Library
29. R Ng, R Ramamoorthi, and P Hanrahan. 2003. All-Frequency Shadows using NonLinear Wavelet Lighting Approximation. ACM Transactions on Graphics 22, 3 (2003), 376–381.Google ScholarDigital Library
30. R Ng, R Ramamoorthi, and P Hanrahan. 2004. Triple Product Wavelet Integrals for All-Frequency Relighting. ACM Transactions on Graphics (Proc. SIGGRAPH 04) 23, 3 (2004), 475–485.Google Scholar
31. D Nowrouzezahrai, P Simari, and E Fiume. 2012. Sparse Zonal Harmonic Factorization for Efficient SH Rotation. ACM Transactions on Graphics 31, 3 (2012), 23:1–23:9.Google ScholarDigital Library
32. J Pantaleoni, L Fascione, M Hill, and T Aila. 2010. PantaRay: fast ray-traced occlusion caching of massive scenes. ACM Transactions on Graphics 29, 4 (2010).Google ScholarDigital Library
33. R Ramamoorthi. 2009. Precomputation-Based Rendering. Foundations and Trends in Computer Graphics and Vision 3, 4 (2009), 281–369.Google ScholarDigital Library
34. R Ramamoorthi, D Mahajan, and P Belhumeur. 2007. A First Order Analysis of Lighting, Shading, and Shadows. ACM Transactions on Graphics 26, 1 (2007).Google ScholarDigital Library
35. Z Ren, R Wang, J Snyder, K Zhou, X Liu, B Sun, P Sloan, H Bao, Q Peng, and B Guo. 2006. Real-time Soft Shadows in Dynamic Scenes using Spherical Harmonic Exponentiation. ACM Transactions on Graphics 25, 3 (2006), 977–986.Google ScholarDigital Library
36. J Schwarzhaupt, H Jensen, and W Jarosz. 2012. Practical Hessian-Based Error Control for Irradiance Caching. ACM Transactions on Graphics 31, 6 (2012), 193:1–193:10.Google ScholarDigital Library
37. P Sloan, J Kautz, and J Snyder. 2002. Precomputed Radiance Transfer for Real-Time Rendering in Dynamic, Low-Frequency Lighting Environments. ACM Transactions on Graphics 21, 3 (2002), 527–536.Google ScholarDigital Library
38. J. Snyder. 1996. Area Light Sources for Real-Time Graphics. Technical Report MSR-TR-96-11. Microsoft Research.Google Scholar
39. B Sun and R Ramamoorthi. 2009. Affine double and triple product wavelet integrals for rendering. ACM Transactions on Graphics 28, 2 (2009).Google ScholarDigital Library
40. C. F. Van Loan. 1996. Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB. Prentice-Hall, Inc.Google Scholar
41. J Wang and R Ramamoorthi. 2018. Analytic Spherical Harmonic Coefficients for Polygonal Area Lights. ACM Transactions on Graphics 37, 4 (2018), 54:1–54:11.Google ScholarDigital Library
42. G Ward and P Heckbert. 1992. Irradiance Gradients. In Eurographics Rendering Workshop 92. 85–98.Google Scholar
43. G Ward, F Rubinstein, and R Clear. 1988. A Ray Tracing Solution for Diffuse Interreflection. SIGGRAPH 22, 4 (1988), 85–92.Google ScholarDigital Library
44. H Yuan, D Nowrouzezahrai, and P Sloan. 2012. Irradiance Rigs. Journal of Graphics, GPU, and Game Tools 16, 1 (2012).Google Scholar
45. C. Zhang, L. Wu, C. Zheng, I. Gkioulekas, R. Ramamoorthi, and S. Zhao. 2019. A Differential Theory of Radiative Transfer. ACM Transactions on Graphics 38, 6 (2019).Google ScholarDigital Library
46. K Zhou, Y Hu, S Lin, B Guo, and H Shum. 2005. Precomputed shadow fields for dynamic scenes. ACM Transactions on Graphics 24, 3 (2005), 1196–1201.Google ScholarDigital Library
