1. Improved Radiance Gradient Computation Jaroslav Křivánek Pascal Gautron Kadi Bouatouch Sumanta Pattanaik ComputerGraphicsGroup

2. Improved Radiance Gradient Computation 2/35 Indirect lighting on glossy surfaces With indirectWithout indirect

3. Improved Radiance Gradient Computation 3/35 Indirect lighting on glossy surfaces With indirectWithout indirect

4. Improved Radiance Gradient Computation 4/35 Problem to solve Illumination integral evaluation at each visible point

5. Improved Radiance Gradient Computation 5/35 Brute Force Approach Monte Carlo gathering For each visible point Slow convergence rate Cast hundreds of rays

6. Improved Radiance Gradient Computation 6/35 Slow Monte Carlo Convergence - Example 40 samples per pixel Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/

7. Improved Radiance Gradient Computation 7/35 Slow Monte Carlo Convergence - Example 100 samples per pixel Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/

8. Improved Radiance Gradient Computation 8/35 Slow Monte Carlo Convergence - Example 300 samples per pixel Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/

9. Improved Radiance Gradient Computation 9/35 Slow Monte Carlo Convergence - Example 600 samples per pixel Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/

10. Improved Radiance Gradient Computation 10/35 Slow Monte Carlo Convergence – Example 1200 samples per pixel Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/

11. Improved Radiance Gradient Computation 11/35 Observation Indirect lighting on rough glossy surfaces is rather smooth: abrupt changes are rare

12. Improved Radiance Gradient Computation 12/35 Radiance Caching Approach Sparse sampling of indirect illumination Interpolation Based on gradients

13. Improved Radiance Gradient Computation 13/35 Radiance Caching Scene Radiance Cache P1P1 Radiance cache lookup Cache Miss! Sample hemisphere Project to hemispherical harmonics P1P1 Store in cache L o = ∫ x BRDF(P 1 ) x cos θ dω Lo(P1)Lo(P1) P2P2 Radiance cache lookup L o (P 2 )= ∫ x BRDF(P 2 ) x cos θ dω Lo(P2)Lo(P2)

14. Improved Radiance Gradient Computation 14/35 Problem Reality P1P1 P2P2 With radiance caching P1P1 P2P2 L i (P 1 ) = L i (P 2 )L i (P 1 ) != L i (P 2 ) Wrong extrapolation

15. Improved Radiance Gradient Computation 15/35 Wrong Extrapolation How does L i (P) change with P? ( L i (P) = incoming radiance at P ) First approximation = RADIANCE GRADIENT Our contribution New radiance gradient computation

16. Improved Radiance Gradient Computation 16/35 Wrong Extrapolation

17. Improved Radiance Gradient Computation 17/35 Corrected with the New Gradients

18. Improved Radiance Gradient Computation 18/35 Radiance Gradients: Problem Definition – Prerequisites Incoming radiance L i (P) representation L i (P) is defined over a hemisphere Represented using hemispherical harmonics L i (P) represented by a set of coefficients Coefficients Basis functions

19. Improved Radiance Gradient Computation 19/35 Radiance Gradients: Problem Definition – Prerequisites Coefficients computed with Monte Carlo quadrature Uniform hemisphere sampling Stratification Sum over all strata Incoming radiance from the sampled direction Multiplied by the basis function

20. Improved Radiance Gradient Computation 20/35 Radiance Gradients: Problem Definition Coefficients – hemisphere sampling Gradients from the same hemisphere sampling Something like

21. Improved Radiance Gradient Computation 21/35 Previous Work - Polygonal emitters Arvo 1994 Irradiance Jacobian due to partially occluded polygonal emitters of constant radiosity Holzschuch and Sillion 1995 Polygonal emitters of arbitrary radiosity

22. Improved Radiance Gradient Computation 22/35 Previous Work - Hemisphere sampling Ward and Heckbert 1992 “Irradiance gradients” Specifically for irradiance Cosine-proportional, uniformly weighted samples over the hemisphere We extend this to uniformly distributed, arbitrarily weighted samples Křivánek et al. 2005, Annen 2004 Radiance gradient Works mostly fine, except when there is occlusion in the sampled environment We improve quality of this

23. Improved Radiance Gradient Computation 23/35 Gradient Computation 1. Compute contribution from each hemisphere cell 2. Sum it all together

24. Improved Radiance Gradient Computation 24/35 Gradient Computation for One Cell

25. Improved Radiance Gradient Computation 25/35 Gradient Computation for One Cell

26. Improved Radiance Gradient Computation 26/35 Gradient Computation for One Cell Wall movement => cell area changes Cell area change => solid angle changes Solid angle change => incoming radiance changes

27. Improved Radiance Gradient Computation 27/35 Putting it all together Sum incoming radiance changes from all cells Use the basis functions H as a weighting factor Basis functions do not change with displacement Cell area change Incoming radiance change Weighting by the basis function

28. Improved Radiance Gradient Computation 28/35 Results Old gradientsNew gradients - smooth

29. Improved Radiance Gradient Computation 29/35 Results New gradientsOld gradients

30. Improved Radiance Gradient Computation 30/35 Results Old gradients

31. Improved Radiance Gradient Computation 31/35 Results New gradients

32. Improved Radiance Gradient Computation 32/35 Gradients for GPU-based irradiance and radiance caching Hemisphere sampling = GPU rasterization Camera position = hemisphere center Very non-uniform density of samples over the hemisphere The same gradient derivation still holds (and WORKS!). P

33. Improved Radiance Gradient Computation 33/35 Gradients for GPU-based irradiance and radiance caching Irradiance caching video Offline irradiance caching video Radiance caching video – castle, walt disney hall

34. Improved Radiance Gradient Computation 34/35 Conclusion New translational gradient computation Use information from hemisphere sampling Based on the Irradiance Gradients by Ward and Heckbert Generalized to support Arbitrary distribution of radiance samples over the hemisphere Arbitrary weighting of radiance samples

35. Improved Radiance Gradient Computation 35/35 Thank you ? ?