CS-184: Computer Graphics. Today. Lecture #16: Global Illumination. Sunday, November 8, 2009

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1 C-184: Computer Graphics Lecture #16: Global Illumination Prof. James O Brien University of California, Berkeley V2009-F Today The Rendering Equation Radiosity Method Photon Mapping Ambient Occlusion 2

2 local only soft shadows caustics indirect illumination 3 The Rendering Equation n!! n The light shining on from is equal to: - the emitted light from toward, plus - for each bit of surface in the scene, how much light shines from that bit onto and is reflected toward, scaled appropriately 4

3 The Rendering Equation The light shining on from is equal to: - the emitted light from toward, plus - for each bit of surface in the scene, how much light shines from that bit onto and is reflected toward, scaled appropriately L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d 4 The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d

4 The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d Light energy hitting from The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d

5 The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d Can see? The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d

6 The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d Light emitted from toward The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d

7 The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d sum over every bit of surface in the scene The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d

8 The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d Light emitted from toward The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d

9 The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d scaled down by the BRDF of The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d

10 The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d scaled down by distance and relative orientation ( form factor The Rendering Equation L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d

11 Radiosity Assume all materials are perfectly Lambertian (diffuse only, no specularities Removes all dependance on directions Reduces dimensionality of lightfield Allows a FEM solution (break up into chunks Can also rela assumption slightly... 6 Early radiosity from Hanrahan

12 Assume Lambertian L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d L s (, =δ(, E + ρ L s (, cos(θ cos(θ 2 d 8 Assume Lambertian L s (, =δ(, E(, + ρ (, L s (, cos(θ cos(θ 2 d L s (, =δ(, E + ρ L s (, cos(θ cos(θ 2 d Only term dependent on 8

13 Rewrite in Terms of Radiosity L s (, =δ(, E + ρ L s (, cos(θ cos(θ 2 d H = E + ρ δ(, H 2π cos(θ cos(θ 2 d Note: we changed defn of E here. 9 Discretize into Patches Piece-wise constant patches Eample mesh for Cornell Bo by Mark chmelzenbach 10

14 Discretize into Patches The Candlestick Theater, Mark Mack Architects. 11 Discretize into Patches The Candlestick Theater, Mark Mack Architects. 12

15 Rewrite in Terms of Patches H = E + ρ H i = E i + ρ i H j j δ(, H 2π cos(θ cos(θ 2 d cos(θ i cos(θ j δ ij j 2π c i 2 d c j P j ci P i 13 Rewrite in Terms of Patches H = E + ρ H i = E i + ρ i H j j δ(, H 2π cos(θ cos(θ 2 d cos(θ i cos(θ j δ ij j 2π c i 2 d c j Form factor from j to i, F ij P j ci P i 13

16 Rewrite in Terms of Patches H = E + ρ H i = E i + ρ i H j j δ(, H 2π cos(θ cos(θ 2 d cos(θ i cos(θ j δ ij j 2π c i 2 d c j Form factor from j to i, F ij ci P i P j Eample of a rough approimation: F ij δ ij cos(θ i cos(θ j 2π c i c j 2 A j 13 Radiosity Method Given the First compute Then solve E i Comments: and F ij ρ i The matri A is typically very large It is also sparse (why? H i = E i + ρ i H j F ij j hould be solved with an iterative method e.g.: Jacobi or Gauss-eidel olution is view independent h = e + Ah (I Ah = e 14

17 Radiosity Method Given the light emitted and surface properties First compute, form factors between patches Then solve a linear system to balance energy between all patches Comments: F ij The system is very large It is also sparse (why? hould be solved with an iterative method e.g.: Jacobi or Gauss-eidel olution is view independent 1 Progressive Radiosity If magnitude of eigenvalues of A<1 (I A 1 = I + A + A 2 + A 3 + True for form-factor matrices Use Gauss-eidel-like iteration but reorder by priority h k+1 = h k + u k+1 u k+1 = Au k h 0 = 0 u 0 = e Idea: let important sources of light energy emit first, maybe don t even bother with dark things outhwell Relaation 16

18 Progressive Radiosity From dissertation "Efficient and predictive realistic image synthesis" by Karol Myszkowski 17 Touchup Each patch will have a constant color mooth solution (e.g. average to vertices Eample mesh for Cornell Bo by Mark chmelzenbach Does not match but you get the idea... 18

19 Other Things Each patch will have a constant color mooth solution (e.g. average to vertices No specular reflection Add Phong specular term or raytraced specular reflection Grid artifacts Be clever with grid Hierarchical Radiosity Light smoothes with distance Compare 1/h 2 with 1/(h 2 + d 2 as h gets large 20

20 Hierarchical Radiosity Light smoothes with distance Compare 1/h 2 with 1/(h 2 + d 2 as h gets large Group patches into hierarchy Far interactions use lower-res form factors 21 Computing Form Factors Form factors have a geometric meaning Images from IGGRAPH 93 Education lide et by tephen pencer 22

21 Computing Form Factors Form factors have a geometric meaning Hemicube algorithm uses regular scan conversion Images from IGGRAPH 93 Education lide et by tephen pencer 23 Computing Form Factors Form factors have a geometric meaning Hemicube algorithm uses regular scan conversion Also computed by ray-based sampling In practice, computing form factors is the bottleneck 24

22 Photon Mapping Lights cast photons into environment Cast in random directions Trace into environment tore records at intersections 2 Photon Mapping Lights cast photons into environment Cast in random directions Trace into environment tore records at intersections With KD-Trees... 26

23 Comparison Ray Tracing Ray Tracing w/ Photon Map Catherine Bendebury and Jonathan Michaels C 184 pring Photon Mapping A ray traced image Note: Dark shadows Unlit corners Nice reflections Image by Per Christensen 28

24 Photon Mapping Raw photons Note: Noisy parse Image by Per Christensen 29 Photon Mapping Interpolated Photons Note: till noisy Biased Image by Per Christensen 30

25 Photon Mapping Interpolated Photons (multiplied by diffuse Note: till noisy Biased Image by Per Christensen 31 Photon Mapping Final Gather Ray trace scene Direct and specular rays as normal Diffuse rays traced into photon map Diffuse reflection smoothes noise 32

26 Photon Mapping Final Image Note: Not noisy Nice lighting Reflections May still be biased Image by Per Christensen Final gather often bottleneck Ambient Occlusion A hack to create more realistic ambient illumination cheaply Assume light from everywhere is partially blocked by local objects At a point on the surface cast rays at random Ambient term is proportional to percent of rays that hit nothing Weight average by cosine of angle with normal Take into account how far before occluded 34

27 Ambient Occlusion 3 Ambient Occlusion Diffuse Only Ambient Occlusion Combined 36

28 Ambient Occlusion nvidia Gelato Demo Image 37

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