1. CSCE 441: Computer Graphics Ray Tracing
Jinxiang Chai

2. Ray Tracing Is a global illumination technique
Provides rendering method with
Refraction/Transparent surfaces
Reflective surfaces
Shadows
Image taken from

3. Any difference for rendering three pixels?
Ray Tracing
Is a global illumination technique
Provides rendering method with
Refraction/Transparent surfaces
Reflective surfaces
Shadows
Any difference for rendering three pixels?
Image taken from

4. Local Illumination vs. Ray Tracing
- Reflective surface
- Realistic shadows

5. Ray Tracing Results
Click here

6. Overview Ray Tracing Algorithm Shadows, Reflection, Refraction
Surface Intersection
Infinite planes, spheres, polygons
Optimizations
Readings: HB 21-1

7. Essential Information for Ray Tracing
Eye point
Screen position/orientation
Objects
Material properties
Reflection/Refraction coefficients
Index of refraction
Light sources

8. Direct and Indirect Light
Every surface in an environment is illuminated by a combination of direct light and reflected light. The direct light is light energy which comes directly from a light source or light sources, attenuated only by some participating media (smoke, fog, dust). The reflected light is light energy which, after being emitted from a light source or light sources, is reflected off of one or more surfaces of the environment.
When light energy is reflected from a surface it is attenuated by the reflectivity of the surface, as some of the light energy may be absorbed by the surface, and some may pass through the surface. The reflectivity of a surface is often defined as its color.

9. Ray Tracing Assumption
The illumination of a point is determined by
- illumination/shadow ray (direct lighting from light sources)

10. Ray Tracing Assumption
The illumination of a point is determined by
- illumination/shadow ray (direct lighting from light sources)

11. Ray Tracing Assumption
The illumination of a point is determined by
- illumination/shadow ray (direct lighting from light sources)
- reflection ray (light reflected by an object)

12. Ray Tracing Assumption
The illumination of a point is determined by
- illumination/shadow ray (direct lighting from light sources)
- reflection ray (where the angle of reflection equals the angle of incidence)
- transparent ray (light passing through an object)

13. Ray Tracing Assumption
The illumination of a point is determined by
- illumination/shadow ray (direct lighting from light sources)
- reflection ray (where the angle of reflection equals the angle of incidence)
- transparent ray (light passing through an object)

14. Ray Tracing Assumption
The illumination of a point is determined by
- illumination/shadow ray (direct lighting from light sources)
- reflection ray (where the angle of reflection equals the angle of incidence)
- transparent ray (light passing through an object)

15. Illumination / Shadow Rays
A ray is cast from an object’s surface towards a light.
If the light is not occluded, then the light contributes to the object’s surface color.
If the light is occluded, then the light does not contribute to the object’s surface color.
If ray hits a semi-transparent object, scale the contribution of that light and continue to look for intersections
Occluder
Pixels

16. Reflected Rays
A ray is cast from the surface of an object based on its material properties.
The contribution results in the specular reflection.

17. Transparency/transmission/refracted Rays
Some objects are transparent or translucent.
The transmitted light also contributes to the surface color, called specular transmission.
The ray can be refracted based on the object’s composition.

18. Recursive Ray Tracing 3 L1 L2 4 1 2

19. Recursive Ray Tracing 3 L1 L2 4 1 2

20. Recursive Ray Tracing 3 L1 L2 4 1 2

21. Recursive Ray Tracing 3 L1 L2 4 1 2

22. Recursive Ray Tracing 3 L1 L2 4 1 2

23. Recursive Ray Tracing 3 L1 L2 4 1 2

24. Recursive Ray Tracing 3 L1 L2 4 1 2

25. Recursive Ray Tracing 3 L1 L2 4 1 2

26. Recursive Ray Tracing 3 L1 L2 4 1 2

27. What are real light paths?
Recursive Ray Tracing 3 L1 L2 4 1 2
What are real light paths?

28. Recursive Ray Tracing and Light path3 L1 L2 4 1 2
Ray tracing paths just reverses real light paths!

29. Recursive Ray Tracing and Light path3 L1 L2 4 1 2
Ray tracing paths just reverses real light paths!

30. Recursive Ray Tracing and Light path3 L1 L2 4 1 2
Ray tracing paths just reverses real light paths!

31. Recursive Ray Tracing and Light path3 L1 L2 4 1 2
Ray tracing paths just reverses real light paths!

32. Recursive Ray Tracing and Light path3 L1 L2 4 1 2
Ray tracing paths just reverses real light paths!

33. Recursive Ray Tracing and Light path3 L1 L2 4 1 2
Ray tracing paths just reverses real light paths!

34. Ray Tree Eye Shadow of Obj 4 Object 1 L2 Reflection Transmission L1 L1

35. Recursive Ray Tracing For each pixel
Intersect ray from eye through pixel with all objects in scene
Find closest (positive) intersection to eye
Compute lighting at intersection point
Recur for reflected and refracted rays (if necessary)

36. Recursive Ray Tracing

37. Termination Criterion
1. The ray intersects no surfaces
2. The ray intersects a light source that is not a reflecting surface
3. The tree has been generated to its maximum allowable depth.

38. Three Issues Ray-object intersection - hidden surface removal
Reflection direction
- mirror direction
Refraction direction
- Snell’s law

39. Ray-object Intersection
screen
eye
Similar to ray casting!

40. Ray-object Intersection
screen
eye
Similar to ray casting!
But how to determine the intersection point between a ray and an object such as sphere or triangle?

41. Ray Casting Implementation - Parameterize each ray as
- Each object Ok returns tk>0 such that first intersection with ok occurs at r(tk)
- Q: given the set {tk}, what is the first intersection point?

42. Ray-Sphere Intersection

43. Ray-Triangle Intersection
First, intersecting the ray with plane
Then, check if point is in triangle

44. Ray-Plane Intersection

45. Ray-Triangle Intersection
Check if point is inside triangle algebraically For each side of triangle evaluate if the intersection point P is above or below the plane
P on the equation:
(P-P0)∙N1=0
P above the plane:
(P-P0)∙N1>0
P below the plane:
(P-P0)∙N1<0

46. Ray-Triangle Intersection
Check if point is inside triangle algebraically For each side of triangle
// P is outside triangle

47. Reflection
Mirror-like/Shiny objects
Surface

48. Refraction
Bending of light caused by different speeds of light in different medium
Each (semi-)transparent
object has an index of
refraction ni
Use Snell’s law to find
refracted vector
Image taken from

49. Snell’s Law
Surface

50. How to compute Transmission Ray?
Surface n2
Given V and N, as well as n1 and n2, how to compute R?

51. Snell’s Law
Surface

52. Snell’s Law
Surface

53. Snell’s Law
Surface

54. Snell’s Law
Surface

55. Snell’s Law
Surface

56. Snell’s Law
Surface

57. Snell’s Law
Surface

58. Snell’s Law
Surface

59. Snell’s Law
Surface

60. Snell’s Law
Surface

61. Snell’s Law
Surface

62. Recursive Ray Tracing
Recur for reflective/transparent objects

63. Recursive Ray Tracing
Recur for reflective/transparent objects

64. Optimizations Lots of rays to cast!
Ray-Surface intersections are expensive
Associate with each object
Bounding box in 3-space
If ray doesn’t intersect box, then ray doesn’t intersect object

65. Parallel Processing Ray tracing is a trivially parallel algorithm!
Cast rays in parallel
Cast reflection, refraction, shadow rays in parallel
Calculate ray/surface intersections independently in parallel

66. Ray Tracing Results: Special Effects
Copyright Newline Cinema

67. Ray Tracing Results: Video Games
These images are from a prototype computer game running in realtime on the ray tracer. It consists of more than 40 million polygons and all optical effects are fully simulated at rendering time. All trees are fully models and no LOD is being used.

68. Ray Tracing Results: Massive Models
Ray tracing has been the first and (to our knowledge) only technology to interactively render the entire Boeing 777 data set. It consists of 350 million polygons and takes up to 30 GB of data on disk. Every detail is models including tiny screws, cables, pipes, values, and many more. With ray tracing this model can be rendered interactively even on a dual-processor PC with 2-3 fps at video resolution.
The right image contains plants with a total of roughly 1.5 billion polygons. All leafs use alpha-mapped textures leading to an extremely high depth complexity. Still the scene can be rendered with interactive performance on a decent PC cluster. Even smooth lighting from the sky dome can be integrated. An good approximation is then shown during interaction but the image converges to a high quality solution with a few seconds.

69. Pros and Cons of Ray Tracing
Advantages of ray tracing
All the advantages of the local illumination model
Also handles shadows, reflection, and refraction
Disadvantages of ray tracing
Computational expense
No diffuse inter-reflection between surfaces (i.e., color bleeding)
Not physically accurate
Other techniques exist to handle these shortcomings, at even greater expense!

70. Ray Tracing References
Peter Shirley, “Realistic Ray Tracing”, ISBN
Andrew Glassner, “An Introduction to Ray Tracing”, ISBN
Steve Pettifer (
Anselmo Lastra (
Paul Rademacher (
Mark Harris (
Kenny Hoff (
POV-Ray (

71. Environment Mapping An alternative way for modeling global reflections
How to create this effect?

72. Environment Mapping
An efficient technique for approximating the appearance of a reflective surface by means of a precomputed texture image.

73. Environment Mapping Cheap attempt at modeling reflections
Makes surfaces look metallic
The poor person’s ray tracing method (only consider reflection ray)
Use six textures to model faces of a cube
Assume cube faces infinitely far away
The normal (or reflected eye vector) is used to find which of the textures to use and what texture coordinate

74. Environment Mapping

75. Environment Mapping

76. Environment Mapping

77. Environment Mapping

78. environment texture image
Environment Mapping
Reflected ray: r=2(n·v)n-v
viewer n
Incident ray
reflected ray v r
reflective surface
environment texture image
Texture is transferred in the direction of the reflected ray r from the environment map onto the object
What is in the map?

79. How to represent the map
viewer

80. How to represent the map
viewer

81. How to represent the map
viewer

82. How to represent the map
viewer
Store colors of every possible direction in texture maps

83. How to represent the mapc
viewer c c c c v
Store colors of every possible direction in texture maps

84. How to represent the mapc
viewer c c c c v
Store colors of every possible direction in texture maps
Look up texture maps based on reflected vector

85. Cubic Mapping
The map resides on the surfaces of a cube around the object
Typically, align the faces of the cube with the coordinate axes
To generate the map:
For each face of the cube, render the world from the center of the object with the cube face as the image plane
Rendering can be arbitrarily complex (it’s off-line)
To use the map:
Index the R ray into the correct cube face
Compute texture coordinates

86. Cubic Map Example

87. How to represent the map
viewer
Store colors of every possible direction in texture maps

88. Sphere Mapping Map lives on a sphere To generate the map:
Render a spherical panorama from the designed center point
To use the map:
Use the orientation of the R ray to index directly into the sphere

89. Example

90. Environmental Mapping: Limitations
Assume distant environment
Only work for convex objects (i.e., no self-interreflections)