1. (c) 2002 University of Wisconsin
Last Time
An introduction to global illumination
We can’t solve the general case, so we look to special cases
Light paths as a way of classifying rendering algorithms: L(S|D)*E
Raytracing
Captures LDS*E paths: Start at the eye, any number of specular bounces before ending at a diffuse surface and going to the light
Can also do LSE and LE if light source is not a point
12/10/02
(c) 2002 University of Wisconsin

2. (c) 2002 University of Wisconsin
Today
A bit more on ray-tracing
Bi-directional ray-tracing
Radiosity
Take home point: What algorithms do what sort of light paths, and what assumptions do they make
12/10/02
(c) 2002 University of Wisconsin

3. (c) 2002 University of Wisconsin
Mapping Techniques
Raytracing provides a wealth of information about the visible surface point:
Position, normal, texture coordinates, illuminants, color…
Raytracing also has great flexibility
Every point is computed independently, so effects can easily be applied on a per-pixel basis
Reflection and transmission and shadow rays can be manipulated for various effects
Even the intersection point can be modified
12/10/02
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4. (c) 2002 University of Wisconsin
Bump Mapping Examples
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5. (c) 2002 University of Wisconsin
Displacement Mapping
Bump mapping changes only the normal, not the intersection point
Silhouettes will not show bumps, even though shading does
Displacement mapping actually shifts the intersection point according to a map
Gives bump map effects and also correct silhouettes and self shadowing, if implemented fully
12/10/02
(c) 2002 University of Wisconsin

6. (c) 2002 University of Wisconsin
From RmanNotes
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7. (c) 2002 University of Wisconsin
Soft Shadows
Light sources that extend over an area (area light sources) should cast soft-edged shadows
Some points see all the light - fully illuminated
Some points see none of the light source - the umbra
Some points see part of the light source - the penumbra
To ray-trace area light sources, cast multiple shadow rays
Each one to a different point on the light source
Weigh illumination by the number that get through
12/10/02
(c) 2002 University of Wisconsin

8. (c) 2002 University of Wisconsin
Soft Shadows
Penumbra
Umbra
Penumbra
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9. (c) 2002 University of Wisconsin
Soft Shadows
All shadow rays go through
No shadow rays go through
Some shadow rays go through
12/10/02
(c) 2002 University of Wisconsin

10. Ray-Tracing and Sampling
Basic ray-tracing casts one ray through each pixel, sends one ray for each reflection, one ray for each point light, etc
This represents a single sample for each point, and for an animation, a single sample for each frame
Many important effects require more samples:
Motion blur: A photograph of a moving object smears the object across the film (longer exposure, more motion blur)
Depth of Field: Objects not located at the focal distance appear blurred when viewed through a real lens system
Rough reflections: Reflections in a rough surface appear blurred
12/10/02
(c) 2002 University of Wisconsin

11. Distribution Raytracing
Distribution raytracing casts more than one ray for each sample
Originally called distributed raytracing, but the name’s confusing
How would you sample to get motion blur?
How would you sample to get rough reflections?
How would you sample to get depth of field?
12/10/02
(c) 2002 University of Wisconsin

12. Distribution Raytracing
Multiple rays for each pixel, distributed in time, gives you motion blur
Object positions have to vary continuously over time
Casting multiple reflection rays at a reflective surface and averaging the results gives you rough, blurry reflections
Simulating multiple paths through the camera lens system gives you depth of field
12/10/02
(c) 2002 University of Wisconsin

13. (c) 2002 University of Wisconsin
Motion Blur
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(c) 2002 University of Wisconsin

14. Distribution Raytracing
Depth of Field
From Alan Watt, “3D Computer Graphics”
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(c) 2002 University of Wisconsin

15. (c) 2002 University of Wisconsin
Missing Paths
Basic recursive raytracing cannot do:
LS*D+E: Light bouncing off a shiny surface like a mirror and illuminating a diffuse surface
LD+E: Light bouncing off one diffuse surface to illuminate others
Basic problem: The raytracer doesn’t know where to send rays out of the diffuse surface to capture the incoming light
Also a problem for rough specular reflection
Fuzzy reflections in rough shiny objects
12/10/02
(c) 2002 University of Wisconsin

16. Bi-directional Raytracing
Cast rays from the light sources out into the scene
When a ray hits a diffuse surface, accumulate some light there
Surfaces record the amount of light that hits them
Store the light in texture maps
Store the light in quadtrees
Store the light in photon maps
Cast rays from the eye out into the scene
When a ray hits a diffuse surface, look up the amount of light that hit it in the light-ray phase
What paths does it capture?
What sort of visual effects do you see?
12/10/02
(c) 2002 University of Wisconsin

17. Caustics Standard raytracer: Bi-directional raytracer
Diffuse table and blue ball, mirrors left, right and back, transparent red ball
Bi-directional raytracer
More rays in the light pass
Note the LS*DS*E paths
From Alan Watt, “3D Computer Graphics”
12/10/02
(c) 2002 University of Wisconsin

18. (c) 2002 University of Wisconsin
Refraction caustic
Henrik wann Jensen,
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19. (c) 2002 University of Wisconsin
Refraction caustics
Henrik wann Jensen,
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20. (c) 2002 University of Wisconsin
Still Missing…
LD*E paths – Diffuse-diffuse transport
Formulated and solved with radiosity methods
L(S|D)*E paths
Solved with Monte-Carlo renderers – very very inefficient
Also solvable with multi-pass methods, but also very very inefficient, and subject to aliasing
An unsolved problem
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21. (c) 2002 University of Wisconsin
Real World LD*E Paths
From Alan Watt, “3D Computer Graphics”
12/10/02
(c) 2002 University of Wisconsin

22. Radiosity Assumptions
All surfaces are perfectly diffuse
Means that is doesn’t matter which way light hits or leaves a surface
Illumination is constant over a patch
Can break the world up into a discrete number of pieces
Problems at sharp illumination boundaries - shadows
Ways around these problems, but less efficient and less able to manage scene complexity
Assumptions allow us to solve for LD*E paths
12/10/02
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23. (c) 2002 University of Wisconsin
Radiosity Example
Color bleeding is extreme in this example
Textures are applied after solving for illumination
Some meshing artifacts are visible - note the banding around the pictures on the wall
From Alan Watt, “3D Computer Graphics”
12/10/02
(c) 2002 University of Wisconsin

24. (c) 2002 University of Wisconsin
Radiosity Meshing
Each patch is colored with its illumination
Note the discrete nature of the solution
The previous image was obtained by pushing color to vertices and then Gourand shading
From Alan Watt, “3D Computer Graphics”
12/10/02
(c) 2002 University of Wisconsin