1 Temporal Radiance Caching P. Gautron K. Bouatouch S. Pattanaik

2 Global Illumination P L o (P, ω o ) ∫ L i (P, ω i ) = * BRDF(ω o, ω i ) *cos(θ)dω i

3 GI: Computation L o (P, ω o ) ∫ L i (P, ω i ) = * BRDF(ω o, ω i ) *cos(θ)dω i No analytical solution Numerical methods - Radiosity - Photon mapping - Path tracing - Bidirectional path tracing - Irradiance & Radiance caching - …

4 GI: Computation L o (P, ω o ) ∫ L i (P, ω i ) = * BRDF(ω o, ω i ) *cos(θ)dω i No analytical solution Numerical methods - Radiosity - Photon mapping - Path tracing - Bidirectional path tracing - Irradiance & Radiance caching - …

5 (Ir)Radiance Caching R Spatial weighting function Ward et al. 88: A Ray Tracing Solution for Diffuse Interreflections

6 (Ir)Radiance Caching Spatial gradients Ward et al. 88: A Ray Tracing Solution for Diffuse Interreflections

7 (Ir)Radiance Caching Ward et al. 88: A Ray Tracing Solution for Diffuse Interreflections

8 (Ir)Radiance Caching Record LocationGI Solution Ward et al. 88: A Ray Tracing Solution for Diffuse Interreflections

9 (I)RC in Dynamic Scenes

10 (I)RC in Dynamic Scenes

11 (I)RC in Dynamic Scenes

12 (I)RC in Dynamic Scenes

13 Contributions Temporal (ir)radiance interpolation scheme Temporal weighting function Temporal gradients Fast estimate of future indirect lighting

14 Outline - Introduction - Irradiance and Radiance Caching - Temporal Radiance Caching - Results - Conclusion

15 Outline - Introduction - Irradiance and Radiance Caching - Temporal Radiance Caching - Results - Conclusion

16 Irradiance Caching: Observations - Indirect lighting is costly -Indirect lighting changes slowly over a surface Ward et al. 88: A Ray Tracing Solution for Diffuse Interreflections

17 Irradiance Caching: Principle Record LocationGI Solution Ward et al. 88: A Ray Tracing Solution for Diffuse Interreflections

18 IC Records: Zone of Influence Close objects = Small zoneDistant objects = Large zone

19 IC: Spatial Weighting Function Spatial change of indirect lighting depends on - Local geometry - Surrounding geometry nknk n P PkPk

20 IC: Spatial Weighting Function nknk n P PkPk Upper bound of the change change = ||P-P k || RkRk + 1-n.n k Distance Normals divergence Mean dist. to the surrounding geometry

21 IC: Spatial Weighting Function nknk n P PkPk w k (P) = 1 ||P-P k || RkRk + 1-n.n k Distance Normals divergence > 1/a Mean dist. to the surrounding geometry

22 IC: Spatial Gradients No GradientsWith Gradients Estimate of the spatial change wrt. - Distance - Normals divergence

23 Radiance Caching Extension of irradiance caching to glossy interreflections Cache directional distribution of light Hemispherical Harmonics Krivanek et al. 05: Radiance Caching for Efficient Global Illumination Computation

24 Radiance Caching Same weighting function as IC Transl. gradient for each coef. Rot. gradient replaced by rotation Krivanek et al. 05: Radiance Caching for Efficient Global Illumination Computation

25 (I)RC in Dynamic Scenes New cache for each frame High cost Flickering Reuse records across frames

26 Outline - Introduction - Irradiance and Radiance Caching - Temporal Radiance Caching - Results - Conclusion - Temporal Weighting Function - Estimate of the Future Incoming Lighting - Temporal Gradients

27 Outline - Introduction - Irradiance and Radiance Caching - Temporal Radiance Caching - Results - Conclusion - Temporal Weighting Function - Estimate of the Future Incoming Lighting - Temporal Gradients

28 Temporal Weighting Function Estimate the temporal change rate of indirect lighting

29 Temporal Weighting Function Estimate the temporal change rate of indirect lighting

30 Temporal Weighting Function Estimate the temporal change rate of indirect lighting ≈ E t -E t+1 δtδt ∂E ∂t (t 0 ) = E 0 (-1) = E t+1 /E t

31 Temporal Weighting Function Inverse of the temporal change rate of indirect lighting = E t+1 /E t ( -1)(t-t 0 ) 1 w k t (t) => 1/a t Problem : Lifespan is determined when the record is created

32 Lifespan Thresholding P At point P and time t: Static environment = E t+1 /E t = 1 w k t (t) = ∞ for all t Infinite Lifespan

33 Lifespan Thresholding P At point P and time t: Static environment = E t+1 /E t = 1 w k t (t) = ∞ for all t Infinite Lifespan

34 Lifespan Thresholding P At point P and time t: Static environment = E t+1 /E t = 1 w k t (t) = ∞ for all t Infinite Lifespan Incorrect w k t (t) = 0 if t-t k >δ tmax

35 Record Replacement

36 Temporal Weighting Function Determines the lifespan of the records Lifespan depends on the local change of incoming radiance If the environment is static, threshold the lifespan to a maximum value = E t+1 /E t Requires the knowledge of future irradiance However

37 Outline - Introduction - Irradiance and Radiance Caching - Temporal Radiance Caching - Results - Conclusion - Temporal Weighting Function - Estimate of the Future Incoming Lighting - Temporal Gradients

38 Future Incoming Lighting PP ≈ Time tTime t+1 E(P, t) = E(P, t+1) =

39 Future Incoming Lighting Assumption: Animation is predefined Future transformation matrices are known Use reprojection to estimate the future incoming lighting

40 Reprojection k EtEt E t+1

41 Reprojection t+1 t k EtEt OK E t+1 Hemisphere sampling

42 Reprojection t+1 ? ? EtEt OK E t+1 Reprojection

43 Reprojection EtEt OK E t+1 t+1 ? ? Depth culling

44 Reprojection EtEt OK E t+1 Hole filling t+1 ? ?

45 Reprojection EtEt OK E t+1 t+1 OK

46 Future Incoming Lighting Simple reprojection No additional hemisphere sampling Easy GPU Implementation

47 Temporal Interpolation k E t =

48 Temporal Interpolation k E t = Recompute Irradiance

49 Temporal Interpolation: Goal k E t =

50 Outline - Introduction - Irradiance and Radiance Caching - Temporal Radiance Caching - Results - Conclusion - Temporal Weighting Function - Estimate of the Future Incoming Lighting - Temporal Gradients

51 Extrapolated Gradients E t computed by hemisphere sampling E t+1 estimated by reprojection Δ t extra ≈ E t+1 -E t Δ t = ∂E / ∂t

52 Extrapolated Gradients k E t extra = E 0 = Computed E 1 = Estimated E t actual = E t actual -E t extra =

53 Extrapolated Gradients

54 Interpolated Gradients: Pass 1 k E 0 = Computed E t actual =

55 Interpolated Gradients: Pass 2 k E t inter = E 0 = Computed E t = Computed E t actual = E t actual -E t inter =

56 Interpolated Gradients E t computed by hemisphere sampling E t+n computed by hemisphere sampling Δ t = ∂E / ∂t Δ E t+n -E t n t inter ≈

57 Temporal Gradients Extrapolated 1 pass Possible flickering Interpolated 2 passes No flickering

58 Outline - Introduction - Irradiance and Radiance Caching - Temporal Radiance Caching - Results - Conclusion

59 Flying Kite

60 Japanese Interior

61 Japanese Interior

62 Spheres

63 Conclusion Temporal radiance interpolation scheme Reuse records across frames Quality improvementSpeedup Easily integrates within (ir)radiance caching-based renderers GPU Implementation Work submitted for publication Dynamic objects, light sources, viewpoint

64 Future Work Avoid the need of maximum lifespan Propose an interpolation method adapted to fast changes (temporal details are smoothed out by the gradients)

65 On the web: OR Google ‘pascal gautron’ P. Gautron, K. Bouatouch, S. Pattanaik Temporal Radiance Caching Technical Report no. 1796, IRISA, Rennes, France

66 Flying Kite: Records Lifespan