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Global Illumination:Radiosity, Photon Mapping & Path Tracing
Rama Hoetzlein, 2009Lecture NotesCornell University
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Rendering Equation
Outgoing light
Emitted light
Bidirectional ReflectanceDistribution Function(BRDF)
Incoming light
Incidentattenuation
X Surface pointw Outgoing directionλ Wavelengtht Current time
Integral over all incoming light directions
James Kajiya, 1982. The rendering equation. SIGGRAPH.
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incoming
outgoing
x
w
w’
N
Perfect Reflection: Light entering at one angle, leaves at same angle only.
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incoming
outgoing
x
w
w’
N
Phong Reflectance: Light entering at some angle, leaves in a uniform diffuse direction, and in a cone of around reflected angle.
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incoming
outgoing
x
w
w’
N
Diffuse Reflectance: Light entering at any angle, canleave at any angle, as a different color, or a different time.
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incoming
outgoing
x
w
w’
N
Diffuse Reflectance: Light entering at any angle, canleave at any angle, as a different color, or a different time.
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Mapping from incoming angle and color to outgoing angle and color,is called the:
Bidirectional Reflectance Distribution Function (BRDF)
Phong is a simple example of a BRDF:
incoming
outgoing
wavelength
time
position
= cos ( θ )n
Bidirectional Reflectance Distribution Function
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BRDF can be measured directly from materials.
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BRDF
How does a material respond at
every incoming light angle?
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Rendering Equation
Outgoing light
Emitted light
Bidirectional ReflectanceDistribution Function(BRDF)
Incoming light
Incidentattenuation
X Surface pointw Outgoing directionλ Wavelengtht Current time
Integral over all incoming light directions
James Kajiya, 1982. The rendering equation. SIGGRAPH.
![Page 13: Global Illumination: Radiosity, Photon Mapping & Path Tracing Rama Hoetzlein, 2009 Lecture Notes Cornell University.](https://reader036.fdocument.pub/reader036/viewer/2022081419/56649f565503460f94c7b2d7/html5/thumbnails/13.jpg)
Global Illumination
Consider all energy moving in a space,
not just the light that reaches the eye.
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First used in the study of Heat Transfer (1950s),
how does energy move around a room or object.
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First radiosity experiment. 1984
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Real box (color-sensitive photography)
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Spherical Harmonic Radiosity. 1991
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First used in Computer Graphics, 1984
Radiosity
Modeling the interaction of light between diffuse surfaces,C. Goral, K. E. Torrance, D. P. Greenberg and B. Battaile. 1984Computer Graphics, Vol. 18, No. 3.
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Fij
ij
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Radiosity Solution
One eqn. for each patch
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Radiosity - Overview
- Each patch contributes energy to other patches
- Each patch i has a Radiosity equation:
- Solve all equations simultaneously to get the energy at each patch
- What is the hardest part of this eqn?
Ei = Energy emitted Ri = Energy reflectedFij = Energy on patch I from j
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Radiosity - Form Factors
What things might contribute to the Form Factor?
Remember: Form Factor is amount of energy hitting patch i from patch j
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Radiosity - Form Factors
What things might contribute to the Form Factor?
Remember: Form Factor is amount of energy hitting patch i from patch j
1. Size of the patch Bigger = more energy
2. Angle between patches Direct = more energy
3. Dist. between patches Father = less energy
4. Objects between patches Occlusion = less energy
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How much does patch j block patch i ?
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Raytracing
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Raytracing /w Caustics
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Radiosity
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Radiosity
• Benefits 1. Very realistic (actually computes energy) 2. View independent.. Compute once, then view 3. Effects: Caustics, Color bleeding
• Drawbacks 1. Even more expensive than raytracing 2. Cannot simulate mirror reflections !
(energy travels diffusely, not coherently)
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Combine Raytracing and Radiosity:
- Radiosity to give energy transfer: Color bleeding Light diffusion Caustics Soft shadows
-Raytracing to give view-dependent terms: Reflections Refractions Specular highlights
Hybrid Rendering
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Lady and Gentleman at the Virginals Johannes Vermeer (Dutch), 1662-65
Two Pass RenderingWallace, Cohen, Greenberg, 1987
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Photon Mapping
Instead of computing all patches simultaneously,
cast “photon rays” from light source.Uses points instead of patches.
Photon Mapping - photons propogate Radiosity – patches don’t move
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Photon Mapping
- Much faster.. No form factors
- Need lots of photons but easier to compute.
- Realistic. Photons move the way light does.
Two pass approach:
1. Shoot photons around scene
2. Collect photons to create image (nearby photons are smoothed)
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Photon Mapping Made Easy, Yu, Lowther, Shene, SIGCSE 2005
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Photon Mapping Made Easy, Yu, Lowther, Shene, SIGCSE 2005
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Future Trends
Recent Developments (past 5 yrs):
- Ambient Occlusion – Approximation to Photon Mapping
- Real-Time Raytracing using GPUs
- Hybrid Rasterization and Raytracing
- Volumetric Raytracing & Radiosity