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Free Path Sampling in High Resolution Inhomogeneous Participating Media
Budapest University of Technology and Economics, Hungary
Szirmay-Kalos LászlóMagdics MilánTóth Balázs
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Problem statement• GI rendering in participating media:
– Free path between scattering points– Absorption or scattering– Scattering direction
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Free Path Sampling
))(exp(1)(
d)()(0
ssPr
ttss
Optical depth
CDF of free path))(exp(1 s
r s
Sampling equation
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Homogeneous case is simple
)1log( r
s
)exp(1)(
)(
ssPr
ss
sr)exp(1 s
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Ray marching
• Complexity grows with the resolution• Independent of the density variation• Slow in high resolution low density media
)exp(1 si
i
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Woodcock tracking
• Resolution independent• Complexity grows with the density variation • Slow in strongly inhomogeneous media
Accept with prob: (t)/max
)exp(1 maxs
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Contribution of this paper• Sampling scheme for inhomogeneous media
– Generalization of Woodcock tracking and ray marching
– Involves them as two extreme cases– Offers new possibilities between them
• Application for high resolution voxel arrays• Application for procedurally generated media
of ”unlimited resolution”
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High densityregion Low density
region
PhotonFreepath
Inhomogeneous media
Particle and itsscattering lobe
Spatial density variation Scattering lobe (albedo +Phase function) variation
Collision
In free path sampling onlydensity variation matters!
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PhotonVirtualcollision
Realcollision
Virtual particle and itsscattering lobe
Mix virtual particles to modify the density but to keep the radiance
Probability of hitting a real particle:
(t)/((t)+virtual (t))=(t)/comb(t)
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Sampling with virtual particles
• Find comb(t) = (t)+virtual(t)
– upper bounding function extinction comb(t),
– Analytic evaluation:
• Sample with comb(t)
• Real collision with probability (t)/comb(t)
s
tts0
comb d)()(
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Challenges• For the volume density find an analytically
integrable sharp upperbound• Voxel arrays: constant or linear upper-bound
in super-voxels• Procedural definition: depends on the actual
procedure– We demonstrate it with Perlin noise
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Procedural media (Perlin noise))1(S
)2(S
)3(S
)( pn
p
p
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Upper bound: construction up to a limited scale
)1(max
)( ˆ)( kk Spn upper-bound
noise)(xn
p
original resolution
super-voxelresolution
)1(S
)2(S
)3(S
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Line integration
super-voxels
original voxels
ray
min0 ss s
1s2s
3s
maxs
real depth
optical depth
),( 10 ss),( 21 ss
),( 32 ss
scattering point where )1log()( rs
ns
1ns
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5123 voxel array, 32 million rays
Ray marching: 9 sec: Woodcock: 7 sec: New: 1.4 sec:
Million rays per second with respect to the super voxel resolution
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Perlin noise clouds, 9 million rays
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Scalability
Million rays per second
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Videos
• 40963 effective resolution• 1283 super-voxel grid• 50 million photons/frame• 9 sec/frame
• 40963 effective resolution• 1283 super-voxel grid• 5 million photons/frame• 1 sec/frame
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Conclusions• Handling of inhomogeneous media by mixing virtual
particles that– Simplify free path length sampling– Do not change the radiance
• Compromise between ray marching and Woodcock tracking– Much better than ray marching in high resolution media– Much better than Woodcock tracking in strongly
inhomogeneous media