Free path sampling in high resolution inhomogeneous participating media
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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

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Free Path Sampling in High Resolution Inhomogeneous Participating Media

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Free Path Sampling in High Resolution Inhomogeneous Participating Media

Szirmay-Kalos László

Magdics Milán

Tóth Balázs

BudapestUniversity 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

CDF of free path

r

s

Optical depth

Sampling equation


Homogeneouscase is simple

r

s


Ray marching

  • Complexity grows with the resolution

  • Independent of the density variation

  • Slow in high resolution low density media

Reject

Reject

Accept


Woodcock tracking

Acceptwith prob: (t)/max

  • 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”


Inhomogeneousmedia

Scattering lobe (albedo +

Phase function) variation

Spatial density variation

Free

path

Photon

Particle and its

scattering lobe

Collision

High density

region

In free path sampling only

density variation matters!

Low density

region


Mix virtual particles to modify the density but to keep the radiance

Virtual

collision

Virtual particle and its

scattering lobe

Photon

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),

    • Analytic evaluation:

  • 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)


Upper bound: construction up to a limited scale

upper-bound

noise

original

resolution

super-voxel

resolution


Line integration

scattering point where

super-voxels

ray

optical depth

real depth

original voxels


5123voxel 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


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