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Free Path Sampling in High
Resolution Inhomogeneous
Participating Media
Szirmay-Kalos László
Magdics Milán
Tóth Balázs
Budapest University of Technology
and Economics, Hungary
Problem statement
• GI rendering in participating media:
– Free path between scattering points
– Absorption or scattering
– Scattering direction
Free Path Sampling
1  exp(  ( s)) CDF of free path
r
s
s
 ( s )    (t )dt
Optical depth
0
r  P( s )  1  exp(  ( s )) Sampling equation
Homogeneous case is simple
1  exp(   s)
r
 (s)    s
r  P( s )  1  exp(   s )
s
s
 log( 1  r )

Ray marching
1  exp(  i s)
i
• Complexity grows with the resolution
• Independent of the density variation
• Slow in high resolution low density media
Woodcock tracking
Accept with prob: (t)/max
1  exp(  max s)
• Resolution independent
• Complexity grows with the density variation
• Slow in strongly inhomogeneous media
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”
Inhomogeneous media
Spatial density variation
Photon
Scattering lobe (albedo +
Phase function) variation
Free
path
Particle and its
scattering lobe
Collision
High density
region
Low density
region
In free path sampling only
density variation matters!
Mix virtual particles to modify the
density but to keep the radiance
Photon
Virtual
collision
Virtual particle and its
scattering lobe
Real
collision
Probability of hitting a real particle:
(t)/((t)+virtual (t))=(t)/comb(t)
Sampling with virtual particles
• Find comb(t) = (t)+virtual(t)
– upper bounding function extinction
comb(t),
s
– Analytic evaluation:  ( s)    comb (t )dt
0
• Sample with comb(t)
• Real collision with probability (t)/comb(t)
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
Procedural media (Perlin noise)
S (1)

n( p )
S ( 2)
S ( 3)

p

p
Upper bound: construction up to a
limited scale
S (1)
upper-bound

n( k ) ( p)  max Sˆ ( k 1)
S ( 2)
n(x) noise

p
S ( 3)
original
resolution
super-voxel
resolution
Line integration
scattering point where
 ( s)   log( 1  r )
super-voxels
smax
 ( s2 , s3 )
 (s1 , s2 )
 ( s0 , s1 )
optical depth

ray
sn
s3 sn1
s2
s1
s0  smin
s
real depth
original voxels
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
Perlin noise clouds, 9 million rays
Scalability
Million rays per second
Videos
• 40963 effective resolution
• 1283 super-voxel grid
• 5 million photons/frame
• 1 sec/frame
• 40963 effective resolution
• 1283 super-voxel grid
• 50 million photons/frame
• 9 sec/frame
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