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Last Time
More LTE
Path Tracing
02/14/05
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Today
Re-using paths
Irradiance Caching
Photon Mapping
02/14/05
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3. Pure Path Tracing: the Good
Path tracing concentrates on important paths only
Those that hit the eye
Those from bright emitters/reflectors
No need for meshing
General surfaces – only requires ray intersections
Unbiased estimates – at any point, the expected value is correct (although variance might be high)
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4. Pure Path Tracing: the Bad
It treats every pixel independently, and every point on every surface independently
Good for specularities, which vary quickly over surfaces
Bad for diffuse illumination, which varies very slowly over surfaces (except at sharp shadow boundaries)
Effort is wasted getting good estimates for
Direct illumination, which is responsible for the most obvious illumination discontinuities (edges)
Diffuse illumination, which varies slowly over a surface
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Path Re-Use
Consider a diffuse surface for which we want an outgoing radiance estimate
Typically, we would cast more rays to get it, but what if we already know what happened at a nearby spot?
02/14/05
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Diffuse Dependency
Diffuse reflectance depends only on the irradiance at the surface point
The total amount of light arriving – incoming direction is irrelevant
This tends to vary slowly over a surface
Directional light gives constant irradiance over a planar surface
Point light varies only with the cosine of the angle – slowly
What leads to sharp changes?
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Basic Idea
Store information about previous paths
When the irradiance at a point is required, construct irradiance estimates from the stored data
Variants on what you store and how the estimate is computed, as we’ll see
The sub-problems are:
How do you get the samples in the first place?
How to you store them?
How do you construct the estimate?
02/14/05
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8. Irradiance Caching (PBR 16.4)
Start with a basic path tracing algorithm, but …
Maintain a spatial data structure storing examples of irradiance arriving at points
If you hit a diffuse surface, try to build an estimate of irradiance at that point – but always compute direct lighting explicitly
If the estimate is good, use it
If not, use path tracing to estimate the irradiance and store it
Some questions:
How do we store the samples?
How do we decide whether to use an old value, or compute a new one?
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Storing Samples
It doesn’t much matter how you store the samples
Data structure must support insertion of new samples, and search for nearby samples, indexed on position
The RADIANCE system is an implementation of Irradiance Caching, and it uses Octrees
Question of precisely what to store:
Irradiance (how we compute this comes next …)
The location
The normal at that location (more later …)
The distance that we went to find nearby surfaces (more later …)
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Computing Irradiance
Use standard Monte Carlo estimator for Irradiance
Use path tracing to get samples of the incoming radiance – just like estimating incoming radiance to a pixel
Stratify outgoing directions according to cosine weighted distribution
02/14/05
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11. Quality of Existing Data
The quality of an estimate is based on geometric considerations
Examine:
Surface curvature between the required point and the existing data
diffuse illumination changes with curvature
Brightness and the distance to other surfaces
Influences how fast incoming illumination can change
Assume extreme variation in incoming radiance
If existing values are used, weigh contribution by quality
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Geometric Factors
Small distance, but maybe big change in irradiance
Points and normals should be close
Distance to nearby surfaces should be large – corners lead to fast changes in irradiance
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13. Locations of Estimates
PBR Fig 16.10
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14. Trading Variance for Bias
Irradiance Caching is a biased algorithm – there is no guarantee it computes the right result
Where does the error come from?
PBR Fig 16.9
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Implementation Notes
In a full system, choices must be made as to what constitutes a diffuse surface
PBRT assumes anything that isn’t specular
Error goes up as reflectance varies further from diffuse
Specular bounces are traced through to a diffuse surface
Have to be careful not to double count, but not too much of a problem
Also have to make sure that direct lighting is not double counted
Must account for transmission and reflection
Separate irradiance estimates for both sides of a surface
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16. Irradiance Caching Failure Modes?
Under what circumstances will irradiance caching fail?
What direction does it trace rays from?
What does it assume about BSDFs?
The commercial-quality implementation of this algorithm allows users to mark “secondary light sources”
The outgoing radiance field of these surfaces is estimated in a pre-process, then they are treated as light sources
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Particle Tracing
Some sub-paths are best sampled from the light
Anything where light is focused – caustics
Situations where most of the light’s energy goes to a small region of the world
We can fill our cache of radiance values by sampling from the light – particle tracing
Several variants …
02/14/05
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18. Basic Particle Tracing
Send out packets from light sources, distributed according to a particular model (eg spotlight, area light, …)
Store some portion of the energy at each surface, on a predefined mesh – typically use textures for storage
Trace eye rays to render final image, or render textures directly
02/14/05
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19. Adaptive Radiosity Textures
Heckbert 90
Store intensity in textures attached to the surfaces
Works for anything with reasonable texture coordinates
Texture is stored as a quadtree, and adapted
Shoot from lights to add intensity to textures
Also shoot from bright surfaces to get diffuse-diffuse transport
Eye ray trace to render, with direct lighting operation at each visible pixel
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Photon Mapping
A very well thought out version of particle tracing
Break LTE into several components
LDS*E and LS*E paths
LS*DS*E paths
L(S|D)*DDS*E paths
Use a different technique for each component
Note that S*E part is common – always start by tracing rays from the eye through specular bounces to a diffuse surface (or a light)
This is the “gather” operation for a pixel
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Gathering Phase
For each pixel cast ray and get hit point
Compute three contributions
Direct illumination (and shadows)
Caustic illumination from a caustic map
Indirect illumination: sample reflection directions and estimate incoming power from a global map
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Why Gather?
PBR Fig 16.17
Photon map lookup at first hit
Lookup for indirect only
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What’s in the Map?
Photon maps store
Position
Incoming direction
Incoming proportion of light’s power (radiant flux, )
Optional: store a normal
Estimation from map:
Find nearest neighbors (ignore those with very dissimilar normal)
Compute estimate of outgoing radiance
02/14/05
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24. Building the Photon Maps
Randomly sample paths from the light
Randomly choose a light/position/direction, cast a ray
Store a sample where it hits
A sample is: position, direction, weight
Sample a direction from the hit pt’s BRDF, cast a ray
Degrade weight according to BRDF
Repeat using Russian Roulette
If the path only experiences specular bounces form the light, store in the caustic map, otherwise in the global map
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Photon Locations
Doesn’t tell you power – not all photons are equal
PBR Fig 16.14
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Effects of Gather
PBR Fig 16.20
Direct lighting
Photon map directly
Photon map indirect
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Caustic Example
PBR Fig 16.18
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Sample Image
© Henrik wan Jensen
02/14/05
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More Impressive
© Henrik wan Jensen
02/14/05
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Photon Map Summary
Combines various techniques depending on the situation
Produces very good results reasonably efficiently
Geometric problems can still cause bleeding
Sampling from the light can cause problems if most of the light’s power fails to reach the image
02/14/05
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Photon Map Failure
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With Better Sampling
02/14/05
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Next Time
Radiosity
02/14/05
© 2005 University of Wisconsin