1. Ray Tracing Fall, 2009

2. Introduction Simple idea  Forward Mapping  Natural phenomenon infinite number of rays from light source to object to viewer  Backward Mapping  Ray Tracing finite number of rays from viewer through each sample to object to light source (or other object)

3. Rendering with Ray Tracing Ray Tracing Algorithm  Generate primary ( ‘ eye ’ ) ray ray goes out from eye through a pixel center (or any other sam ple point on image plane)  Find closest object along ray path find first intersection between ray and an object in scene  Compute light sample use illumination model to determine direct contribution from light sources for greater accuracy recursively generate secondary rays at equal

4. Raytracing versus scan conversion  scan conversion After meshing and projection 3D  2D  Image Based on transforming geometry for each triangle in scene  Raytracing 3D  Image Geometric reasoning about light rays for each sample in pixel image…

5. Ray Tracing : Global Illumination Effects

6. Raytracing Overview  Eye, view plane section, and scene  Launch ray from eye through pixel (Generating Rays)  see what it hits (Ray-Scene Intersection)  Compute color and fill-in the pixel (Computing light sample)

7. Generating Rays (1/2) Ray equation  Through eye at t = 0  At pixel center at t = 1 R(t) = E + td E E + td

8. Ray-Scene Intersection  Intersections with geometric primitives Sphere Triangle Groups of primitives (scene)  Acceleration techniques Bounding volume hierarchies Spatial partitions –Uniform grids –Octrees –BSP trees

9. Ray-Sphere Intersection

11.  Need normal vector at intersection for lighting calculations

12. Ray-Triangle Intersection  First, intersect ray with plane  Then, check if point is inside triangle

13. Ray-Triangle Intersection intersect ray with plane

14. Ray-Triangle Intersection Check if point is inside triangle algebraically

15. Other Ray-Primitive Intersections Cone, cylinder, ellipsoid:  Similar to sphere Box  Intersect 3 front-facing planes, return closest Convex polygon  Same as triangle (check point-in-polygon algebraically) Concave polygon  Same plane intersection  More complex point-in-polygon test

16. Ray-Scene Intersection Find intersection with front-most primitive in group

17. Bounding Volumes Check for intersection with simple shape first  If ray doesn’t intersect bounding volume, then it doesn’t intersect its contents  If found another hit closer than hit with bounding box, then can skip checking contents of bounding box

18. Bounding Volume Hierarchies Use hierarchy to accelerate ray intersections  Intersect node contents only if hit bounding volume

19. Computing light sample Local Illumination  Ray Casting

20. Computing light sample Recursive Ray Tracing  Shadows and direct lighting  Reflection and refraction  Antialiasing, motion blur, soft shadows, and depth of field

21. Shadow Rays Detect shadow by rays to light source

22. Shadow Rays Test for occluder  No occluder, shade normally ( e.g. Phong model )  Yes occluder, skip light ( don’t skip ambient )

23. Reflection Ray Recursive shading  Ray bounces off object  Treat bounce rays (mostly) like eye rays  Shade bounce ray and return color Shadow rays Recursive reflections  Add color to shading at original point Specular or separate reflection coefficient V B S

24. Refracted Ray Transparent materials bend light  Snell’s Law

25. “Distributed” Raytracing Send multiple rays through each pixel Average results together Jittering trades aliasing for noise Use multiple rays for reflection and refraction How many rays???

26. “Distributed” Raytracing : Soft Shadows Soft shadows result from non-point lights  Some part of light visible, some other part occluded Area Light Occluder

27. “Distributed” Raytracing : Soft Shadows Distribute shadow rays over light surface

28. Soft Shadows

29. “Distributed” Raytracing : Glossy Reflection multiple reflection rays polished surface θ θ Justin Legakis

30. “Distributed” Raytracing : Glossy Translucency Jittering the rays about the actual transmission angle produces a blurred effect N I T Bound of jittered reflection rays

31. “Distributed” Raytracing : Motion Blur Distribute rays over time  More when we talk about animation...

32. Pinhole camera – everything in focus. Camera with lens – utilized depth of field “Distributed” Raytracing : Depth of Field Image Plane Focal Plane Pinhole Camera Camera with lens

33. “Distributed” Raytracing : Depth of Field (DoF) Distribute rays over a lens assembly  multiple rays per pixel

34. Depth of Field multiple rays per pixel Justin Legakis focal length film

35. Depth of Field

36. Bidirectional Ray tracing Created by H. Wann Jensen caustic

37. Bidirectional Ray tracing Caustic - (Concentrated) specular reflection/refraction onto a diffuse surface Standard ray tracing cannot handle caustics caustic Created by H. Wann Jensen

38. Examples : POV-ray created using POV-ray, http://www.povray.org/

39. POV-ray created using POV-ray, http://www.povray.org/

40. POV-ray created using POV-ray, http://www.povray.org/

41. POV-ray created using POV-ray, http://www.povray.org/

42. Summary Writing a simple ray casting renderer is easy  Generate rays  Intersection tests  Lighting calculations Recursive Ray Tracing  Shadows and direct lighting  Reflection and refraction  Antialiasing, motion blur, soft shadows, and depth of field Bidirectional Ray tracing  Caustic : specular reflection/refraction onto a diffuse surface  Standard ray tracing cannot handle caustics