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Improved Radiance Gradient Computation
Jaroslav Křivánek
Pascal Gautron
Kadi Bouatouch
Sumanta Pattanaik
ComputerGraphicsGroup
Improved Radiance Gradient Computation2/35
Indirect lighting on glossy surfaces
With indirect Without indirect
Improved Radiance Gradient Computation3/35
Indirect lighting on glossy surfaces
With indirect Without indirect
Improved Radiance Gradient Computation4/35
Problem to solve Illumination integral evaluation at each visible
point
P
i),( ii PL
iiioiioo dBRDFPLPL cos),(),(),(
i
Improved Radiance Gradient Computation5/35
Brute Force Approach Monte Carlo gathering For each visible point
Slow convergence rate
Cast hundreds of rays
Improved Radiance Gradient Computation6/35
Slow Monte Carlo Convergence - Example 40 samples per pixel
Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/
Improved Radiance Gradient Computation7/35
Slow Monte Carlo Convergence - Example 100 samples per pixel
Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/
Improved Radiance Gradient Computation8/35
Slow Monte Carlo Convergence - Example 300 samples per pixel
Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/
Improved Radiance Gradient Computation9/35
Slow Monte Carlo Convergence - Example 600 samples per pixel
Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/
Improved Radiance Gradient Computation10/35
Slow Monte Carlo Convergence – Example 1200 samples per pixel
Acknowledgement: Jason Lawrence, http://www.cs.princeton.edu/gfx/proj/brdf/
Improved Radiance Gradient Computation11/35
Observation Indirect lighting on rough glossy surfaces is
rather smooth: abrupt changes are rare
Improved Radiance Gradient Computation12/35
Radiance Caching Approach Sparse sampling of indirect illumination Interpolation
Based on gradients
Improved Radiance Gradient Computation13/35
Radiance Caching
SceneRadiance
Cache
P1
Radiance cache lookup
CacheMiss!
Samplehemisphere
Project to hemispherical
harmonics
P1
Store incache
Lo=∫ x BRDF(P1) x cos θ dωLo(P1)
P2
Radiancecachelookup
Lo(P2)=∫ x BRDF(P2) x cos θ dωLo(P2)
Improved Radiance Gradient Computation14/35
ProblemReality
P1 P2
With radiance caching
P1 P2
Li(P1) = Li(P2)Li(P1) != Li(P2)
Wrong extrapolation
Improved Radiance Gradient Computation15/35
Wrong Extrapolation How does Li(P) change with P?
( Li(P) = incoming radiance at P )
First approximation = RADIANCE GRADIENT
Our contribution New radiance gradient computation
Improved Radiance Gradient Computation16/35
Wrong Extrapolation
Improved Radiance Gradient Computation17/35
Corrected with the New Gradients
Improved Radiance Gradient Computation18/35
Radiance Gradients: Problem Definition – Prerequisites Incoming radiance Li(P) representation
Li(P) is defined over a hemisphere Represented using hemispherical harmonics
Li(P) represented by a set of coefficients
),(),;(1
0
n
l
l
lm
ml
mli HPL
Coefficients
Basis functions
Improved Radiance Gradient Computation19/35
Radiance Gradients: Problem Definition – Prerequisites Coefficients computed with Monte Carlo
quadrature Uniform hemisphere
sampling Stratification
1
0
1
0,,, ),(
2 M
j
N
kkjkj
ml
ikj
ml HL
NM
Sum over all strata
Incoming radiance from the sampled direction
Multiplied by thebasis function
Improved Radiance Gradient Computation20/35
Radiance Gradients: Problem Definition Coefficients – hemisphere sampling
Gradients from the same hemisphere sampling Something like
1
0
1
0,,, ),(
2 M
j
N
kkjkj
ml
ikj
ml HL
NM
1
0
1
0, ......
M
j
N
k
ikj
ml L
Improved Radiance Gradient Computation21/35
Previous Work - Polygonal emitters
Arvo 1994 Irradiance Jacobian due to partially occluded
polygonal emitters of constant radiosity Holzschuch and Sillion 1995
Polygonal emitters of arbitrary radiosity
Improved Radiance Gradient Computation22/35
Previous Work - Hemisphere sampling Ward and Heckbert 1992 “Irradiance gradients”
Specifically for irradiance Cosine-proportional, uniformly weighted samples over
the hemisphere We extend this to uniformly distributed, arbitrarily
weighted samples Křivánek et al. 2005, Annen 2004
Radiance gradient Works mostly fine, except when there is occlusion in
the sampled environment We improve quality of this
Improved Radiance Gradient Computation23/35
Gradient Computation
1. Compute contribution from each hemisphere cell
2. Sum it all together
Improved Radiance Gradient Computation24/35
Gradient Computation for One Cell
Improved Radiance Gradient Computation25/35
Gradient Computation for One Cell
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Gradient Computation for One Cell
Wall movement => cell area changes
Cell area change => solid angle changes
Solid angle change => incoming radiance changes
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Putting it all together Sum incoming radiance changes from all cells Use the basis functions H as a weighting factor
Basis functions do not change with displacement
Cell area change
Incoming radiance change
Weighting by thebasis function
Improved Radiance Gradient Computation28/35
Results
Old gradients New gradients - smooth
Improved Radiance Gradient Computation29/35
Results
New gradientsOld gradients
Improved Radiance Gradient Computation30/35
Results
Old gradients
Improved Radiance Gradient Computation31/35
Results
New gradients
Improved Radiance Gradient Computation32/35
Gradients for GPU-based irradiance and radiance caching Hemisphere sampling = GPU rasterization Camera position = hemisphere center
Very non-uniform density of samples over the hemisphere
The same gradient derivation still holds (and WORKS!).
P
Improved Radiance Gradient Computation33/35
Gradients for GPU-based irradiance and radiance caching Irradiance caching video Offline irradiance caching video Radiance caching video – castle, walt disney
hall
Improved Radiance Gradient Computation34/35
Conclusion New translational gradient computation Use information from hemisphere sampling Based on the Irradiance Gradients by Ward and
Heckbert Generalized to support
Arbitrary distribution of radiance samples over the hemisphere
Arbitrary weighting of radiance samples
Improved Radiance Gradient Computation35/35
Thank you
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