1. (c) 2002 University of Wisconsin
Last Time
Ray-tracing implementation
Recall the light paths that ray-tracing captures
Technically, we are talking about “eye ray tracing,” which traces rays originating at the eye
Some people use the terms forward or backward ray-tracing, but there is no agreement in which direction is forward!
05/07/02
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2. (c) 2002 University of Wisconsin
Which paths are present?
Which paths are missing?
Ray-traced Cornell box, due to Henrik Jensen,
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4. (c) 2002 University of Wisconsin
Today
Rendering algorithms that capture other light paths
Distribution ray-tracing
Radiosity
Bi-directional ray tracing
05/07/02
(c) 2002 University of Wisconsin

5. 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
05/07/02
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6. 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?
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7. Distribution Raytracing
Depth of Field
From Alan Watt, “3D Computer Graphics”
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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
05/07/02
(c) 2002 University of Wisconsin

9. 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?
05/07/02
(c) 2002 University of Wisconsin

10. 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”
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(c) 2002 University of Wisconsin

11. (c) 2002 University of Wisconsin
Refraction caustic
Henrik wann Jensen,
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12. (c) 2002 University of Wisconsin
Refraction caustics
Henrik wann Jensen,
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13. (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 (unsolvable?) problem
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Real World LD*E Paths
From Alan Watt, “3D Computer Graphics”
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15. 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
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16. (c) 2002 University of Wisconsin
Radiosity Equation
Derived from the global illumination equation using radiosity assumptions
Bi is the radiosity (brightness) of patch i
i is the diffuse reflection coefficient
Fij is the form factor, which quantifies how much light patch j contributes to patch i
The brightness of each patch depends on how much light it gets from all the others, and its diffuse reflection
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(c) 2002 University of Wisconsin

17. Solving the Radiosity Eqn
Radiosity algorithms use one of several methods to solve the radiosity equation
Basically a very large linear system, so techniques can all be mapped onto linear system solvers
A large part of the computation is in finding form factors
Describe how much light gets from each patch to every other patch
Geometric in nature - do not depend on the illumination, just the layout of the scene
Another key factor is finding good meshing strategies - ways of laying out the patches
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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”
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19. (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”
05/07/02
(c) 2002 University of Wisconsin