Second-Order Occlusion-Aware Volumetric Radiance Caching Julio Marco - PowerPoint PPT Presentation

Second-Order Occlusion-Aware Volumetric Radiance Caching Julio Marco 1 Adrian Jarabo 1 Wojciech Jarosz 2 Diego Gutierrez 1 1 Universidad de Zaragoza, I3A 2 Dartmouth College 1

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≈ ≈ 5

[Schwarzhaupt et al. 2012] 6

OUR METHOD L + ∆ x · d L L d x ? 7

Related Work • Photon-based methods [Bitterli and Jarosz 17] [Jensen and Christensen 98] [Knaus and Zwicker 11] Higher-dimensional POINTS [Krivanek et al. 14] [Jarosz et al. 11] [Jarosz et al. 11] BEAMS POINTS + BEAMS + PATHS 8

Related Work Frequency and gradient-domain • Frequency and first-order analysis [Durand et al. 2005, Ramamoorthi et al. 2007] • Media frequency analysis [Belcour et al. 2014] • Image-space gradients for MLT [Lehtinen et al. 2013, Manzi et al. 2014] • Gradient-domain path tracing methods [Kettunen et al. 2015, Manzi et al. 2015] 9

Related Work • Irradiance/radiance caching methods [Ward and Heckbert 91] [Ward et al. 88] 10

Related Work • Irradiance/radiance caching methods [Krivanek et al. 2005] [Krivanek et al. 2006] 11

Related Work • Irradiance/radiance caching methods [Jarosz et al. 2008] • Media gradients è YES • Occlusions è NO • Higher-order è NO 12

Related Work [Jarosz et al. 2008] 13

Related Work 2nd order Occlusions SURFACES ✘ [Jarosz et al. 2008] [Schwarzhaupt et al. 2012] ✘ ✘ [Jarosz et al. 2008] MEDIA OURS 14

Radiance extrapolation 15

Radiance extrapolation TAYLOR EXPANSION Radiance value at x n-th translational derivative at x 16

Radiance extrapolation TRUNCATED TAYLOR EXPANSION Actual value Error Extrapolated value at x’ (first order) 17

Radiance extrapolation TRUNCATED TAYLOR EXPANSION Actual value Error Extrapolated value at x’ (first order) 18

Radiance extrapolation R λ 2 R λ 1 R λ 3 Eigenvalues of Hessian Error threshold 19

? L + ∆ x · d L d x How to compute them? 20

Derivative computation TRANSMITTANCE PHASE FORESHORTENING VISIBILITY INCOMING FUNCTION RADIANCE 21

Derivative computation [Jarosz et al. 2008] Ignored in gradient computation 22

Derivative computation [Jarosz et al. 2008] ? Ignored in gradient computation 23

Derivative computation [Jarosz et al. 2008] Ignored in gradient computation 24

Derivative computation [Jarosz et al. 2008] Ignored in gradient computation 25

Derivative computation Our method Gone! 26

Derivative computation Our method RAY MARCHING 27

Derivative computation Our method For a single triangle Triangle-to-medium form factor 28

Derivative computation Our method 29

Derivative computation 30

2D visualization of derivatives Reference Occ. Unaware LIGHT Ours (finite diff.) [Jarosz 2008] SINGLE Orientation SCATTERING ROI OCCLUDER Magnitude SHADOW 1 0.1 0 PENUMBRA 31

2D visualization of derivatives Reference Occ. Unaware LIGHT Ours (finite diff.) [Jarosz 2008] MULTIPLE Orientation SCATTERING ROI OCCLUDER Magnitude 0.1 PENUMBRA 0.01 0 32

Results 33

Statues – Render comparison Reference [Jarosz et al. 2008] Ours 34

Statues – Render comparison Reference [Jarosz et al. 2008] Ours 35

Statues – Cache distribution [Jarosz et al. 2008] Occlusion-unaware, 1st order metric Single scattering Multiple scattering (TOP VIEW) (TOP VIEW) 36

Statues – Cache distribution Ours Occlusion-aware, 2nd-order metric Single scattering Multiple scattering (TOP VIEW) (TOP VIEW) 37

Patio – Time performance Our computational overhead • Triangulation +9% • Hessian computation 38

Patio – Time performance Our computational overhead • Triangulation +9% • Hessian computation Ours (iso. cache) Equal-time 135 min., 32k points 39

Patio – Time performance Our computational overhead • Triangulation +9% • Hessian computation [Jarosz et al. 2008] Equal-time 136 min., 36k points 40

Patio – Time performance Our computational overhead • Triangulation +9% • Hessian computation Same error threshold Ours (aniso. cache) 30% faster 94 min., 21k points 41

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Equal-time comparison EQUAL TIME Reference Path tracing [Jarosz et al. 2011] Ours [Jarosz et al. 2008] Progressive photon Second-order Occlusion-unaware beams occlusion-aware first-order 43

Future work • Extend to support scattering from glossy materials • Limited to finite light sources • Extend to anisotropic media and heterogeneous materials 44

Conclusions • Computation of occlusion-aware media derivatives • Second-order error metric for volumetric radiance caching • … radiance derivatives useful for other applications! 45

Thanks! 46