Free Path Sampling in High Resolution Inhomogeneous Participating Media

Budapest University of Technology and Economics, Hungary

Szirmay-Kalos LászlóMagdics MilánTóth Balázs

Problem statement• GI rendering in participating media:

– Free path between scattering points– Absorption or scattering– Scattering direction

Free Path Sampling

))(exp(1)(

d)()(0

ssPr

ttss

Optical depth

CDF of free path))(exp(1 s

r s

Sampling equation

Homogeneous case is simple

)1log( r

s

)exp(1)(

)(

ssPr

ss

sr)exp(1 s

Ray marching

• Complexity grows with the resolution• Independent of the density variation• Slow in high resolution low density media

)exp(1 si

i

Woodcock tracking

• Resolution independent• Complexity grows with the density variation • Slow in strongly inhomogeneous media

Accept with prob: (t)/max

)exp(1 maxs

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”

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!

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)

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)()(

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))1(S

)2(S

)3(S

)( pn

p

p

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

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

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• 50 million photons/frame• 9 sec/frame

• 40963 effective resolution• 1283 super-voxel grid• 5 million photons/frame• 1 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