1. CSCE 641: Photon Mapping Jinxiang Chai

2. Outline Rendering equation Photon mapping

3. Ray Tracing and Photon Mapping What are differences between the two rendered pictures?

4. Ray Tracing and Photon Mapping caustics color bleeding What are differences between the two rendered pictures?

5. The Rendering Equation

6. OutgoingEmittedReflected

7. The Rendering Equation Emitted light [known]

8. The Rendering Equation BRDF [known]

9. BRDF (bi-directional reflectance distribution function) How to model surface reflectance property? for a given incoming direction, the amount of light that is reflected in a certain outgoing direction

10. Dimensionality of the BRDF This is 6-D function - x: 2D position - (θ i,φ i ): incoming direction - (θ r,φ r ): outgoing direction Usually represented as 4-D - ignoring x - homogenous material property

11. Gonioreflectometer

12. Scattering Models

13. The BSSRDF Bidirectional Surface Scattering Reflectance- Distribution Function Translucency

14. The Rendering Equation BRDF [known] Emitted light [known] Directional irradiance [unknown]

15. Global Illumination Various Rendering techniques solve some portion of the rendering equation If a technique approximates the integral, it is part of the family of “Global Illumination”

16. Global Illumination Techniques Radiosity Ray Tracing Photon Mapping

17. Radiosity Solves geometry term in form factor Approximates integral completely for diffuse-diffuse –No reflection or transmission

18. Ray Tracing Works well for reflection and refraction Solves geometry eq. through ray intersection tests Solves emission properly Only solves integral for reflection and refraction to maxDepth –Diffuse reflectance ignored

19. Global Illumination Techniques Radiosity Ray Tracing Photon Mapping

21. Two challenges: - Q1: how to compute the incoming radiance L i ? - Q2: how to efficiently evaluate the integral?

22. Photon Mapping Two challenges: - Q1: how to compute the incoming radiance L i ? A1: compute L i based on precomputed photon map - Q2: how to efficiently evaluate the integral? A2: compute the integral based on Monte Carlo ray tracing

23. Photon Mapping Is often used to simulate the interaction of light with a variety transparent substances (caustics ) - glass, water - diffuse inter-reflections between illuminated objects - effects of particulate matter, e.g. smoke - etc.

24. Photon Mapping Phase I: shoot and store photons - photons are shot from the light into the scene - photons are allowed to interact with objects in the environment - where photons fall are stored in special data structure called a “photon map” - 10000s of photons not billions (Statistical approximation based on density)

25. Photon Mapping Phase I: shoot and store photons [Forward] - photons are shot from the light into the scene - photons are allowed to interact with objects in the environment - where photons fall are stored in special data structure called a “photon map” - 10000s of photons not billions (Statistical approximation based on density)

26. Shooting Photons Point light source directional lightsquare lightgeneral light

27. Shooting Photons Point light source directional lightsquare lightgeneral light The power of light The number of photons The power of an emitted photon

28. Pseudocode for Emission of Photons from Point Light Source

29. Basic idea: - Radiant intensity as a probability function. - Generate photons by sampling the probability function.

30. Photon Mapping Phase I: shoot and store photons - photons are shot from the light into the scene - photons are allowed to interact with objects in the environment - where photons fall are stored in special data structure called a “photon map” - 10000s of photons not billions (Statistical approximation based on density)

31. Photon Tracing Photons are only stored when it hits diffuse surface Specular surface does not store any photons.

32. Photon Map

33. What information does each photon store?

34. Photon Map The photon: Placed in K-D tree for efficient access

35. Three Photon Maps Caustic photon map - interact with at least one specular surface Global photon map - interact with diffuse surfaces only Volume photon map - indirect illumination of participating medium

36. Global Photon Map Basic idea: - Launch photons from the light sources in all directions - Store a photon (position, power, and direction) in each intersection of the photon with the scene. - Compute the kind of interaction with the surface by using the Russian roulette.

37. Global Photon Map The types of interactions are: - Diffusion: the photon is reflected in a random direction (projected hemisphere) or taking into account a BRDF. - Reflection: Perfect reflection of the photon. - Refraction: The photon is refracted using Snell's law. - Absorption: We don't launch that photon again. The Russian roulette method decides which interaction to consider in function of the material.

38. Caustics Photon Map The global photon map has very weak caustics effects. We need to construct an additional map only for caustics. - Launch the rays only over the objects that can generate caustics. - Store the photons when they hit a diffuse surface only if previously it hit a reflective or refractive surface.

39. Caustics & Global Photon Map The caustics photon map The global photon map

40. Photon Mapping Phase 2: Gather illumination - use ray tracing - direct illumination determined by ray tracing - indirect illumination determined by stochastically sampling photon map (gather photon within volume in the required direction)

41. Rendering Using Photon Map

42. Two main issues: - How to compute incoming radiance L i ? - How to evaluate the integral efficiently?

43. Basic idea: Radiance Estimate

44. Basic Idea: Radiance Estimate How to evaluate reflected radiance based on the photon map?

45. Basic Idea: Radiance Estimate Evaluate the radiance based on nearby photons

46. Basic idea: Radiance Estimate Evaluate the radiance based on nearby photons: Find N photons with the shortest distance to the intersection point

47. Radiance Estimate Using Photon Map

51. locally flat surface

52. Radiance Estimate Using Photon Map locally flat surface

53. Radiance Estimated Using Photon Map 200000 photons 500 photons 100 photons

54. Photon Mapping: Rendering

56. L i,l : direct illumination by light from the light sources L i,c : caustics—indirect illumination from the light sources via specular surface L i,d : indirect illumination from the light sources (diffuse inter- reflection)

57. Light Sources

58. L i,l L i,d L i,c

59. Photon Mapping: Rendering

60. Diffuse surfacesSpecular surfaces

61. Photon mapping: the rendering equation

63. Accurate evaluation of the direct illumination Similar to the evaluation of shadow rays in ray tracing

64. Photon mapping: the rendering equation

65. Evaluation of the Specular and Glossy term Similar to the evaluation of reflection rays in ray tracing

66. Photon mapping: the rendering equation

67. Evaluation of the caustics Evaluate this term using the caustics photon map directly

68. Photon mapping: the rendering equation

69. Evaluation of the indirect diffuse illumination Accurate evaluation of the integral using monte carlo ray tracing method

70. Results Ray tracing global photon map - 200000 photons - 100 photons for estimate

71. Cornell box with water