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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 sn1 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