1. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A 1 Real-time Rendering of Heterogeneous Translucent Objects with Arbitrary Shapes Yajun Wang, Jiaping Wang, Nicolas Holzschuch, Kartic Subr, Jun-Hai Yong, Baining Guo

2. Simulating translucency 2 Subsurface scattering

3. Simulating translucency 3 Subsurface scattering

4. Previous work 4

5. Monte-Carlo methods [DEJ99, PH00, LPT05 ] physically accurate  slow (several hours) 5 [DEJ99] [PH00]

6. Previous work Dipole diffusion approximation [JMLH01] faster (minutes)  homogenous, no complex shape 6 [JMLH01]

7. Previous work Extension of Dipole model real-time [DS03],multi-layer [DJ05], scalable [AWB08]  homogenous 7 [DS03] [AWB08] [DJ05]

8. Previous work Precomputed Radiance Transfer [XGL07] [WCPW08] real-time  precomputation 8 [ XGL07 ][ WCPW08 ]

9. Previous work Diffusion Equation [Ish78, Sta95] Regular grid and multi-grid scheme [Sta95] first step  off-line The polygrid method [WZT08] real-time, heterogeneous  simple shape 9

10. Challenges 1. real-time rendering and editing 2. heterogeneous materials 3. complex shapes 10

11. Our Method 1. in real-time 2. with heterogeneous materials 3. in arbitrary domain 11

12. Our Method Overview Solving the Diffusion Equation ▫Quadgraph ▫Discretized Diffusion Equation ▫Implementation on GPU Results Limitations and Conclusions 12

13. Regular Grid 13 Our Method Incoming radiance L i InitializationIteration Outgoing radiance L o Optical PropertiesRadiant Fluence Regular grid introduces shape constraintsOur domain for diffusion: tetrahedralized geometryInput: radiance incident on surface Diffusion: Flux within objectOutput: Exiting radiance on surface Extract exiting radiance from flux at boundary Diffusion Equation +FEM (2D example)

14. Our Method Overview Solving the Diffusion Equation ▫Quadgraph ▫Discretized Diffusion Equation ▫Implementation on GPU Results Limitations and Conclusions 14

15. QuadGraph 1.Representation of the object volume 2.GPU-friendly 15

16. QuadGraph Construction : Tetrahedralization Goal: Regular connection 16 Output : 4 classes of tetrahedra [ACSYD05]

17. QuadGraph Construction: Splitting Goal: Regular connection 17 Only tetrahedra in C0 and C1 left

18. QuadGraph Construction: Transformation Goal: Regular connection 18 C0 C1 inner node inner node + boundary node

19. QuadGraph Result: Regular connection grid For inner nodes -> 4 neighbors For surface nodes -> 1 neighbor 19

20. Our Method Overview Solving the Diffusion Equation ▫Quadgraph ▫Discretized Diffusion Equation ▫Implementation on GPU Results Limitations and Conclusions 20

21. Discretized DE Using the same method in [Sta95] [WZT08] Based on Quadgraph 21 For inner nodes For surface nodes

22. Our Method Overview Solving the Diffusion Equation ▫Quadgraph ▫Discretized Diffusion Equation ▫Implementation on GPU Results Limitations and Conclusions 22

23. Preprocess and Storage Per-node values stored using textures one part for interior nodes one part for surface nodes 23

24. Iteration on GPU 1.Initialization according to the illumination 2.Iteration on GPU until convergence 24 InitalizationDuring iterationConvergence

25. Speeding up scheme GPU cache coherence (Speed + 30%) 25 Packing the data of nodes by its spatial location

26. Speeding up scheme Multi-resolution (Speed + >100% ) Several Quadgraphs with different resolution 26

27. Our Method Overview Solving the Diffusion Equation ▫Quadgraph ▫Discretized Diffusion Equation ▫Implementation on GPU Results Limitations and Conclusions 27

28. High genus 28 Surface nodes: 121k Inner nodes: 260k Speed: 29.4 FPS

29. 29

30. High curvature 30 Surface nodes: 82k Inner nodes: 226k Speed: 22.1FPS

31. 31 Real-time rendering

32. 32

33. Real-time editing of materials 33

34. 34

35. Real-time editing of geometry shape 35

36. 36

37. Speed 37

38. 38 Quality

39. Our Method Overview Solving the Diffusion Equation ▫Quadgraph ▫Discretized Diffusion Equation ▫Implementation on GPU Results Limitations and Conclusions 39

40. Limitations 40 1.Materials with high frequency 2.Deformation changing the topology

41. Conclusions A new volumetric representation(Quadgraph) for solving the diffusion equation. Real-time rendering and editing Heterogeneous materials Complex shapes 41

42. 42 Questions ?

43. Thank you! 43