1. Albert Mas Ignacio Martín Gustavo Patow Fast Inverse Reflector Design FIRD Graphics Group of Girona Institut d’Informàtica i Aplicacions Universitat de Girona Spain CEIG08, Barcelona

2. Introduction Lighting design GGG – IIiA - UdG

3. Introduction Light source – Uniform light distribution Reflector – Defines the lighting distribution – Specular material Holder GGG – IIiA - UdG Reflector Holder Light source

4. Introduction Lighting industry problem: Reflector Design The desired lighting is known, but not the reflector – Inverse design Iterative try and test process – High manufacturing costs ? GGG – IIiA - UdG

5. Introduction Inverse reflector design methods – Very restricted reflector shapes – Demand high computational costs – Hours or days to compute a solution – Not able to generate complex real world reflectors GGG – IIiA - UdG

6. Introduction Goals : – Computation of the best approximation, from a family of possible reflectors, to a given desired illumination distribution. – Fast GPU algorithm to calculate the reflected rays on the reflector. – Reflector parametrizable basis Parameters optimization – Use millions of light rays – Use highly complex reflector shapes GGG – IIiA - UdG

7. FIRD Introduction  State of the art Reflector lighting Optimization Results Conclusions and future work GGG – IIiA - UdG

8. Inverse reflector design (I) IGP problem (Survey Patow and Pueyo ’05) – Numerical solutions Local Illumination [Caffarelli et al. ‘99] – Paraboloid intersection – One bounce NURBS-based Inverse Reflector Design [Anson et al. ’08] Global Illumination [Patow et al. ‘07] State of the art GGG – IIiA - UdG

9. Global illumination [Patow et al. ‘07] – Polygonal meshes – More than one bounce inside reflector are considered – Global optimization method – Disadvantages High computational cost Reflector mesh resolution Number of traced rays Inverse reflector design (II) State of the art GGG – IIiA - UdG

10. GPU Ray Tracing (I) Global illumination method needs a large set of light source rays – High computational cost – Acceleration : GPU GPU has limitations GPU fits well in our problem State of the art GGG – IIiA - UdG

11. GPU Ray Tracing (III) Ray Engine [Carr et al. ‘02] Environment Mapping [Umenhoffer et al. ‘07] State of the art GGG – IIiA - UdG

12. GPU Ray Tracing (II) Reflector made by pressing procedure Height-map Relief Texture Mapping [Oliveira et al. ’00] Simplified Ray-Tracing model State of the art GGG – IIiA - UdG X Y Z

13. GPU Ray Tracing (IV) Space partitioning methods: Hierarchical subdivision structures – Octree Traversal (CPU) [Revelles et al. ‘00] – Displacement Mapping [Szirmay-Kalos and Umenhoffer ‘08] – Quadtree Relief Mapping [Schroders and Gulik ‘06] Quadtree represented into the GPU as a mip-map texture State of the art

14. FIRD Introduction State of the art  Reflector lighting Optimization Results Conclusions and future work GGG – IIiA - UdG

15. Overview Preprocessing of the input data Reflector geometry transformation Reflections computation Comparison to desired distribution Reflector Lighting GGG – IIiA - UdG

16. Input data Far-field – IES Reflector holder Light source – Light distribution – Position – Shape Reflector Lighting GGG – IIiA - UdG

17. Reflector geometry transformation Hierarchical height field representation of the reflector – Quadtree – Mip-map texture Store normal vectors into a texture Reflector Lighting GGG – IIiA - UdG

18. Reflections computation (I) Quadtree Relief Mapping [Schroders and Gulik ‘06] Intersection search going down the hierarchy Reflector Lighting GGG – IIiA - UdG

19. Reflections computation (I) Quadtree Relief Mapping Intersection search going down the hierarchy Reflector Lighting GGG – IIiA - UdG

20. Reflections computation (I) Quadtree Relief Mapping Intersection search going down the hierarchy Reflector Lighting GGG – IIiA - UdG

21. Reflections computation (I) Quadtree Relief Mapping Intersection search going down the hierarchy Reflector Lighting GGG – IIiA - UdG

22. Reflections computation (I) Quadtree Relief Mapping Intersection search going down the hierarchy Reflector Lighting GGG – IIiA - UdG

23. Reflections computation (I) Quadtree Relief Mapping Intersection search going down the hierarchy Reflector Lighting GGG – IIiA - UdG

24. Reflections computation (I) Quadtree Relief Mapping Intersection search going down the hierarchy Reflector Lighting GGG – IIiA - UdG

25. Reflections computation (I) Quadtree Relief Mapping Intersection search going down the hierarchy Reflector Lighting GGG – IIiA - UdG

26. Reflections computation (I) Quadtree Relief Mapping Intersection search going down the hierarchy Reflector Lighting GGG – IIiA - UdG

27. Reflections computation (I) Quadtree Relief Mapping Intersection search going down the hierarchy Reflector Lighting

28. Reflections computation (II) Quadtree Relief Mapping drawback: recursive reflections Intersection search going up the hierarchy Reflector Lighting GGG – IIiA - UdG

29. Reflections computation (II) Intersection search going up the hierarchy Reflector Lighting GGG – IIiA - UdG

30. Reflections computation (II) Intersection search going up the hierarchy Reflector Lighting GGG – IIiA - UdG

31. Reflections computation (II) Intersection search going up the hierarchy Reflector Lighting GGG – IIiA - UdG

32. Reflections computation (II) Intersection search going up the hierarchy Reflector Lighting GGG – IIiA - UdG

33. Reflections computation (II) Intersection search going up the hierarchy Reflector Lighting GGG – IIiA - UdG

34. Reflections computation (II) Intersection search going up the hierarchy Reflector Lighting GGG – IIiA - UdG

35. Reflections computation (II) Intersection search going up the hierarchy Reflector Lighting GGG – IIiA - UdG

36. Reflections computation (II) Intersection search going up the hierarchy Reflector Lighting GGG – IIiA - UdG

37. Reflections computation (II) Intersection search going up the hierarchy Reflector Lighting GGG – IIiA - UdG

38. Comparision to desired distribution (I) Comparison of far-fields Light distribution classification: Histogram on GPU Reflector Lighting GGG – IIiA - UdG

39. Comparision to desired distribution (II) Histogram comparision on GPU Distance metric: l 2 – GPU Reduction algorithm Reflector Lighting GGG – IIiA - UdG

40. FIRD Introduction State of the art Reflector lighting  Optimization Results Conclusions and future work GGG – IIiA - UdG

41. Optimization Based on [Patow et al. ‘05] Optimize the parameters used in the parametric reflector shape definition Standard optimization method – Brute Force – Linear steps Test all possible reflectors – Regenerate the height field texture for each reflector – Iterative process Stops when difference value is under a given threshold Test all possibilities and take the best one (less difference) Optimization GGG – IIiA - UdG

42. FIRD Introduction State of the art Reflector lighting Optimization  Results Conclusions and future work GGG – IIiA - UdG

43. Model A (I) Results 10 7 rays Effective raysMax bouncesReflector lighting time (sec.) Optimization time (hours) Tested reflectorsOptimized parameters 7.38x10 6 11.30.6317283 30 -30 0 -20 GGG – IIiA - UdG

44. Model A (II) Results GGG – IIiA - UdG

45. Model B (I) Results 5x10 6 rays Effective raysMax bouncesReflector lighting time (sec.) Optimization time (hours) Tested reflectorsOptimized parameters 5x10 6 53.22.224014 0 -10 0 -7 GGG – IIiA - UdG

46. Model B (II) Results GGG – IIiA - UdG

47. Model C (I) Results Effective raysMax bouncesReflector lighting time (sec.) Optimization time (hours) Tested reflectorsOptimized parameters 6.05x10 6 62.74.965614 10 7 rays 10 0 0 -6 GGG – IIiA - UdG

48. Model C (II) Results GGG – IIiA - UdG

49. Results (milliseconds) Mip-map texture size: 1200x800 -> 9 levels GGG – IIiA - UdG NVidia GeForce 8800 GTX

50. FIRD Introduction State of the art Reflector lighting Optimization Results  Conclusions and future work GGG – IIiA - UdG

51. Conclusions A fast inverse reflector lighting algorithm has been presented Calculates the reflected rays in the reflector in 2-3 seconds Multiple ray bounces inside the reflector Reflector geometry equivalent to 960000 triangles Independent of reflector geometry complexity Milions of traced rays Resulting light distributions close enough to desired ones Conclusions and Future Work GGG – IIiA - UdG

52. Future work Improve the optimization process – Reach the solution in a non-constant step size – Use other optimization procedures Tree on parameter space explored by probabilistic ways Conclusions and Future Work GGG – IIiA - UdG

53. Fast Inverse Reflector Design FIRD THANKS! GGG – IIiA - UdG