Participating Media. Part II: interactive methods, atmosphere and clouds. Oskar Elek MFF UK Prague
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1 Participating Media Part II: interactive methods, atmosphere and clouds Oskar Elek MFF UK Prague
2 Outline Motivation Introduction Properties of participating media Rendering equation Storage strategies Non-interactive rendering strategies Part I revision Interactive rendering strategies Atmospheric rendering Cloud rendering (References) Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
3 Outline Motivation Introduction Properties of participating media Rendering equation Storage strategies Non-interactive rendering strategies Part I revision Interactive rendering strategies Atmospheric rendering Cloud rendering (References) Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
4 Motivation fluids Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
5 Motivation solids Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
6 Motivation beyond rendering Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
7 Introduction What are participating media (PMa)? General meaning CG connotation Why are PMa more challenging than B-rep rendering? At lease 1 DoF more Costly representation General scattering vs. sub-surface scattering (BSSRDF) Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
8 Properties event types 4 basic event types in PMa Single vs. multiple scattering A E A E S A E S Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
9 Properties medium composition Main property medium (particle) density Derived characteristics: σ e emission coefficient [m -1 ] σ a absorption coefficient [m -1 ] σ s scattering coefficient [m -1 ] σ t extinction coefficient (σ a + σ s ) e -σ dependency (σ = % transmittance) σ a =5 σ a =10 σ a =15 σ a =30 More particle types linear combination of coefficients Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
10 Properties scattering directionality Phase function Describes directional distribution of scattered light Equivalent of BRDF for surfaces (probability density) Denotes scattering anisotropy (equivalent of diffuse vs. glossy surfaces) We recognize Rayleigh and Mie (light) scattering Uniform: Rayleigh (λ -4 -dependent): Mie (Henyey-Greenstein approximation): Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
![Defined as: 100 * σ s / (σ a + σ s ) [%]](/docs-images/95/126257592/images/11-4.jpg "Mean number of scattering events depends on")
11 Properties other PMa characteristics Albedo efficiency of a single scattering event Defined as: 100 * σ s / (σ a + σ s ) [%] Mean number of scattering events depends on it Medium homogeneousness Medium anisotropy (sundogs, parhelia) Shape complexity Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
12 Volume rendering equation Standard (areal) RE Volume RE, directional formulation Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
13 Volume rendering equation Standard (areal) RE Volume RE, directional formulation Volume RE, differential formulation (energy transport equation) Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
14 Beer-Lambert-Bouguer law Defines relation of medium composition to its light attenuating properties Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
15 Storage strategies 3D density grids Point sets Analytically defined Combined Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
16 Rendering strategies path tracing Similar to areal PT, solves directional VRE by generating random walks in the medium Evaluation Pros: simplicity, not limited to any PMa range, unbiasedness Cons: speed (in certain cases almost pathological), high variance Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
17 Rendering strategies event location generation Choose randomly Taking into account extinction Ray marching Woodcock tracking Increment x by until Pros: fast (using adaptive kd-tree scheme), unbiasedness Cons: slightly more complicated Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
18 Rendering strategies volumetric radiance transfer Similar to areal radiosity, solves energy transport equation Pros: (theoretically) unbiased, linear scaling with number of scattering orders, computes energy state of the entire scene Cons: rather slow, high storage requirements, problems with inhomogeneous media and additional objects in scene Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
19 Rendering strategies volumetric photon mapping Once again, similar to areal PM Generates random walks in the medium, stores photon on each scattering event Gathering more complicated beam radiance estimate Evaluation widely used Pros: fast, easy extension from B-rep renderers, robust Cons: biasedness, necessary storage of photons Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
20 End (part I) Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
21 Outline Motivation Introduction Properties of participating media Rendering equation Storage strategies Non-interactive rendering strategies Part I revision Interactive rendering strategies Atmospheric rendering Cloud rendering (References) Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
22 Interactive rendering strategies Non-interactive vs. interactive methods In surface rendering, these converge Not that much in volume rendering (until recently) Instant radiosity Photon streaming Photon mapping on GPU
23 Interactive rendering strategies Non-interactive vs. interactive methods In surface rendering, these converge Not that much in volume rendering (until recently) Instant radiosity Photon streaming Photon mapping on GPU Interactive methods always rely on simplifying assumptions, limitations, special cases etc.
24 Interactive rendering strategies direct ray marching Backward method
25 Interactive rendering strategies direct ray marching Backward method Practically limited to single-scattering Hardly uses anything else than 3D grids
26 Interactive rendering strategies direct ray marching Backward method Practically limited to single-scattering Hardly uses anything else than 3D grids Evaluation Pros: simplicity Cons: slow (w/o extensive optimizations), prone to aliasing, limited to single-scattering
27 Interactive rendering strategies slice-based rendering Forward method
28 Interactive rendering strategies slice-based rendering Forward method No intrinsic way to compute light propagation Even more tied to 3D grids GPU-adaptation of ray-marching
29 Interactive rendering strategies slice-based rendering Forward method No intrinsic way to compute light propagation Even more tied to 3D grids GPU-adaptation of ray-marching Pros: fast, maps well to GPU Cons: no light propagation, prone to aliasing and slicing artefacts
30 Interactive rendering strategies half-angle slicing Extension of slice-based rendering, adds light propagation computation
31 Interactive rendering strategies half-angle slicing Extension of slice-based rendering, adds light propagation computation Slicing in the direction perpendicular to half-vector
32 Interactive rendering strategies half-angle slicing Extension of slice-based rendering, adds light propagation computation Slicing in the direction perpendicular to half-vector Evaluation Pros: comparatively fast, adds light propagation scheme Cons: partly empirical
33 Interactive rendering strategies half-angle slicing Extension of slice-based rendering, adds light propagation computation Slicing in the direction perpendicular to half-vector
34 Interactive rendering strategies billboard-based rendering Forward method, widely used in game engines
35 Interactive rendering strategies billboard-based rendering Forward method, widely used in game engines Billboards correspond to units of volume Mostly use point/particle-based medium representations
36 Interactive rendering strategies billboard-based rendering Forward method, widely used in game engines Billboards correspond to units of volume Mostly use point/particle-based medium representations Evaluation Pros: simple, fast, map well to GPU, easy to animate Cons: low accuracy, again no intrinsic light propagation computation, edging artefacts
37 Interactive rendering strategies soft particles Extension of billboard-based rendering, tackles the edging artefacts problem
38 Interactive rendering strategies soft particles Extension of billboard-based rendering, tackles the edging artefacts problem
39 Interactive rendering strategies soft particles Extension of billboard-based rendering, tackles the edging artefacts problem Solution modulation of the billboard colour by depth-based factor, e.g.:
40 Interactive rendering strategies soft particles Extension of billboard-based rendering, tackles the edging artefacts problem
41 Interactive rendering strategies analytical methods Under some specific conditions, scattering might be analytically approximated
42 Interactive rendering strategies analytical methods Under some specific conditions, scattering might be analytically approximated For instance, let s assume (Sun et al.): Homogeneous medium, spanning the entire visible scene Only single scattering Isotropic point light sources
43 Interactive rendering strategies analytical methods Under some specific conditions, scattering might be analytically approximated For instance, let s assume (Sun et al.): Homogeneous medium, spanning the entire visible scene Only single scattering Isotropic point light sources
44 Interactive rendering strategies analytical methods Under some specific conditions, scattering might be analytically approximated For instance, let s assume (Sun et al.): Homogeneous medium, spanning the entire visible scene Only single scattering Isotropic point light sources
45 Interactive rendering strategies analytical methods Under some specific conditions, scattering might be analytically approximated For instance, let s assume (Sun et al.): Homogeneous medium, spanning the entire visible scene Only single scattering Isotropic point light sources
46 Interactive rendering strategies analytical methods Under some specific conditions, scattering might be analytically approximated For instance, let s assume (Sun et al.): Homogeneous medium, spanning the entire visible scene Only single scattering Isotropic point light sources
47 Interactive rendering strategies instant volume radiosity Extension of IR to participating media
48 Interactive rendering strategies instant volume radiosity Extension of IR to participating media As in areal IR, singularities appear Solution bias compensation Exact slow
49 Interactive rendering strategies instant volume radiosity Extension of IR to participating media As in areal IR, singularities appear Solution bias compensation Exact slow Approximations: using other VPLs sub-sampling random walks local visibility reuse local vertices generation limited recursion depth
50 Interactive rendering strategies instant volume radiosity Extension of IR to participating media As in areal IR, singularities appear Solution bias compensation
51 Interactive rendering strategies cascaded light propagation Adaptation of Discrete Ordinates method (VRT variant)
52 Interactive rendering strategies cascaded light propagation Adaptation of Discrete Ordinates method (VRT variant) Lattice-based uses light propagation volume (LPV) Only used for low-frequency (indirect) lighting
53 Interactive rendering strategies cascaded light propagation Adaptation of Discrete Ordinates method (VRT variant) Lattice-based uses light propagation volume (LPV) Only used for low-frequency (indirect) lighting Basic steps (per frame!): 1. LPV initialization with area lights & surfaces causing indirect lighting 2. Creation of volumetric representation of blocker geometry 3. Light propagation simulation inside LPV 4. Using LPV for lighting scene geometry
54 Interactive rendering strategies cascaded light propagation Adaptation of Discrete Ordinates method (VRT variant) Lattice-based uses light propagation volume (LPV) Only used for low-frequency (indirect) lighting Basic steps (per frame!): 1. LPV initialization with area lights & surfaces causing indirect lighting 2. Creation of volumetric representation of blocker geometry 3. Light propagation simulation inside LPV 4. Using LPV for lighting scene geometry
55 Interactive rendering strategies cascaded light propagation Adaptation of Discrete Ordinates method (VRT variant) Lattice-based uses light propagation volume (LPV) Only used for low-frequency (indirect) lighting Basic steps (per frame!): 1. LPV initialization with area lights & surfaces causing indirect lighting 2. Creation of volumetric representation of blocker geometry 3. Light propagation simulation inside LPV 4. Using LPV for lighting scene geometry
56 Interactive rendering strategies cascaded light propagation Adaptation of Discrete Ordinates method (VRT variant) Lattice-based uses light propagation volume (LPV) Only used for low-frequency (indirect) lighting Basic steps (per frame!): 1. LPV initialization with area lights & surfaces causing indirect lighting 2. Creation of volumetric representation of blocker geometry 3. Light propagation simulation inside LPV 4. Using LPV for lighting scene geometry
57 Cascaded light propagation 1. LPV initialization Every (point) light yields one reflective shadow map (RSM)
58 Cascaded light propagation 1. LPV initialization Every (point) light yields one reflective shadow map (RSM) Every texel of a RSM is treated as VPL Low-frequency lights (area lights, env. map, fuzzy lights) treated as VPLs
59 Cascaded light propagation 1. LPV initialization Every (point) light yields one reflective shadow map (RSM) Every texel of a RSM is treated as VPL Low-frequency lights (area lights, env. map, fuzzy lights) treated as VPLs VPLs are injected into LPV using spherical harmonic (SH) projection Result initial energy state of the scene in a single LPV
60 Cascaded light propagation 2. Volumetric geometry representation Surfaces are sampled from camera position and multiple RSMs (not the lighting ones!) Temporal coherence
61 Cascaded light propagation 2. Volumetric geometry representation Surfaces are sampled from camera position and multiple RSMs (not the lighting ones!) Temporal coherence Surfels are inserted into geometry volumes (GV), again using SHs Result multiple GVs, each corresponding to one surfels source These are merged in to one GV (max)
62 Cascaded light propagation 3. Propagation step Each source cell propagates light to its 6 adjacent cells (instead of 26)
63 Cascaded light propagation 3. Propagation step Each source cell propagates light to its 6 adjacent cells (instead of 26) Each destination cell reprojects the received light into its centre
64 Cascaded light propagation 3. Propagation step Each source cell propagates light to its 6 adjacent cells (instead of 26) Each destination cell reprojects the received light into its centre Each propagation step accounts for blocking from GV
65 Cascaded light propagation 3. Propagation step Each source cell propagates light to its 6 adjacent cells (instead of 26) Each destination cell reprojects the received light into its centre Each propagation step accounts for blocking from GV Iteration count ( ) Result scene energy state
66 Cascaded light propagation 4. LPV utilization Diffuse surfaces simply fetch the LPV
67 Cascaded light propagation 4. LPV utilization Diffuse surfaces simply fetch the LPV Glossy surfaces perform ray marching along reflected vector
68 Cascaded light propagation 4. LPV utilization Diffuse surfaces simply fetch the LPV Glossy surfaces perform ray marching along reflected vector Participating media ray-march through the LPV along view ray
69 Cascaded light propagation 4. LPV utilization Diffuse surfaces simply fetch the LPV Glossy surfaces perform ray marching along reflected vector Participating media ray-march through the LPV along view ray Limitations: Isotropic PF Low-frequency light Homogeneous medium (unless density volume is used)
70 Cascaded light propagation Grid hierarchy Instead of one large LPV, use several nested smaller ones (3) Centred around observer, displaced along view direction
71 Cascaded light propagation Grid hierarchy Instead of one large LPV, use several nested smaller ones (3) Centred around observer, displaced along view direction Injection inject VPLs and surfels into all LPV levels Propagation simulate all levels separately Fetching fetch the finest available level, interpolate at boundaries
72 Cascaded light propagation Grid hierarchy Instead of one large LPV, use several nested smaller ones (3) Centred around observer, displaced along view direction Injection inject VPLs and surfels into all LPV levels Propagation simulate all levels separately Fetching fetch the finest available level, interpolate at boundaries
73 Cascaded light propagation Grid hierarchy Instead of one large LPV, use several nested smaller ones (3) Centred around observer, displaced along view direction Injection inject VPLs and surfels into all LPV levels Propagation simulate all levels separately Fetching fetch the finest available level, interpolate at boundaries
74 Cascaded light propagation Results Statistics: 2 16 VPLs per primary light source 3.75MB for cascaded LPV (3x32 3 cells) and 0.75MB per GV 8 propagation iterations (!) NV GTX 285: ~100 FPS (diffuse only), ~35 FPS (participating medium)
75 Cascaded light propagation Results Statistics: 2 16 VPLs per primary light source 3.75MB for cascaded LPV (3x32 3 cells) and 0.75MB per GV 8 propagation iterations (!) NV GTX 285: ~100 FPS (diffuse only), ~35 FPS (participating medium) Evaluation: Pros: very fast, physically-based, obtains energy state of the entire scene, temporal coherence, allows fully dynamic scenes, flexible Cons: lots of hacks and potential sources of visual artefacts
76 Outline Motivation Introduction Properties of participating media Rendering equation Storage strategies Non-interactive rendering strategies Part I revision Interactive rendering strategies Atmospheric rendering Cloud rendering (References) Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
77 Atmospheric rendering Specifics Very sparse medium Spatially large and symmetrical Very little absorption (mostly urban areas) Combined Rayleigh and Mie scattering Well defined density (exponential w/r to altitude) Density may vary w/r to latitude and longitude Special phenomena (sundogs, parhelia) Stable, slowly changing
78 Atmospheric rendering Specifics Very sparse medium Spatially large and symmetrical Very little absorption (mostly urban areas) Combined Rayleigh and Mie scattering Well defined density (exponential w/r to altitude) Density may vary w/r to latitude and longitude Special phenomena (sundogs, parhelia) Stable, slowly changing Classical methods Path tracing Volumetric radiance transfer Photon mapping
79 Atmospheric rendering analytical methods Most notable Preetham s model Sky luminance Y(T,θ,θ s,δ) given as
80 Atmospheric rendering analytical methods Most notable Preetham s model Sky luminance Y(T,θ,θ s,δ) given as T turbidity (loosely how strong overcast it is ) T=2 T=6 T=10
81 Atmospheric rendering analytical methods Most notable Preetham s model Sky luminance Y(T,θ,θ s,δ) given as T turbidity (loosely how strong overcast it is ) Evaluation Pros: simple (to use), fast Cons: fixed to Earth s atmosphere, numerically unstable for T<2 and T>10, limited to zero altitude, limited to clear sky T=2 T=6 T=10
82 Atmospheric rendering precomputed scattering Basic idea 1. Precompute scattering into table of colour values 2. Fetch this table during rendering to obtain sky colour
83 Atmospheric rendering precomputed scattering Basic idea 1. Precompute scattering into table of colour values 2. Fetch this table during rendering to obtain sky colour Table dimensions Sun zenith angle δ View zenith angle φ Sun azimuth ω Observer altitude h
84 Atmospheric rendering precomputed scattering Basic idea 1. Precompute scattering into table of colour values 2. Fetch this table during rendering to obtain sky colour Table dimensions Incremental multiple scattering computation Σ
85 Precomputed scattering - rendering Atmosphere Plain sphere 4D texture lookup (emulated)
86 Precomputed scattering - rendering Atmosphere Plain sphere 4D texture lookup (emulated) Planetary surface Atmospheric scattering Ambient light or surface reflection Water scattering (if present)
87 Precomputed scattering - results Statistics Precomputation - ~1 hour (CPU) / ~10s seconds (GPU) Dataset ~10MB NV 8800GT: ~100 FPS
88 Precomputed scattering - results Statistics Precomputation - ~1 hour (CPU) / ~10s seconds (GPU) Dataset ~10MB NV 8800GT: ~100 FPS Evaluation Pros: very fast, directly usable in real-time engines, good looking results, supports multiple scattering, applicable to other media (water) Cons: fixed atmospheric parameters, doesn t account for lat/long density variations
89 Precomputed scattering - results
90 Precomputed scattering - results Algae Phytoplankton Mud 1 meter 4 meters 10 meters 100 meters Morning Afternoon Pure seawater
91 Outline Motivation Introduction Properties of participating media Rendering equation Storage strategies Non-interactive rendering strategies Part I revision Interactive rendering strategies Atmospheric rendering Cloud rendering (References) Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
92 Cloud rendering Specifics Mediocre density Large and asymmetrical shape No absorption 100% albedo High scattering anisotropy Mie scattering only Potentially strong density fluctuation Special phenomena (glory) Mediocre evolution speed
93 Cloud rendering Specifics Mediocre density Large and asymmetrical shape No absorption 100% albedo High scattering anisotropy Mie scattering only Potentially strong density fluctuation Special phenomena (glory) Mediocre evolution speed Classical methods Path tracing Volumetric radiance transfer Photon mapping
94 Cloud rendering billboard-based methods Wang
95 Cloud rendering billboard-based methods Wang
96 Cloud rendering billboard-based methods Wang Evaluation Pros: fast, maps well to gaming studios pipeline Cons: purely empirical, lengthy modelling phase
97 Cloud rendering illumination networks Szirmay-Kalos et al. Idea: discretize and reuse light paths for every particle
98 Cloud rendering illumination networks Szirmay-Kalos et al. Idea: discretize and reuse light paths for every particle
99 Cloud rendering illumination networks Evaluation Pros: maps well to GPU Cons: doesn t allow frameless behaviour, fuzzy results
100 Cloud rendering Bouthor s method And now for something completely different
101 Cloud rendering Bouthor s method And now for something completely different Method based on partial scattering precomputation
102 Cloud rendering Bouthor s method And now for something completely different Method based on partial scattering precomputation Evaluation: Pros: physically-based, accounts for multiple anisotropic scattering Cons: very complicated, limiting assumptions, slow, parts of the method a bit shady
103 The end Conclusion
104 Outline Motivation Introduction Properties of participating media Rendering equation Storage strategies Non-interactive rendering strategies Part I revision Interactive rendering strategies Atmospheric rendering Cloud rendering (References) Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
105 References Airlieau B. et al.: Photon streaming for interactive global illumination in dynamic scenes, 2010 Beer-Lambert-Bouguer law: Born M. and Wolf E.: Principles of Optics (7 th edition, corrected reprint), 2003 Bouthors A. et al.: Interactive Multiple Anisotropic Scattering in Clouds, 2008 Bruneton E. and Neyret F.: Precomputed Atmospheric Scattering, 2008 Chandrasekhar S.: Radiative Transfer, 1960 Elek O. and Kmoch P.: Real-Time Spectral Scattering in Large-Scale Natural Participating Media, 2010; Engelhardt T. et al.: Instant Multiple Scattering for Interactive Rendering of Heterogeneous Participating Media, 2010 Haber J. et al.: Physically based Simulation of Twilight Phenomena, 2005 van de Hulst H. C.: Light Scattering by Small Particles (corrected reprint), 1981 Jarosz W. et al.: Radiance Caching for Participating Media, 2008 Jarosz W. et al.: The Beam Radiance Estimate for Volumetric Photon Mapping, 2008 Jensen H. W. and Christensen P. W.: Efficient Simulation of Light Transport in Scenes with Participating Media using Photon Maps, 1998 Jensen H. W.: Realistic Image Synthesis Using Photon Mapping, 2001 Kaplanyan A. and Dachsbacher C.: Cascaded Light Propagation Volumes for Real-Time Indirect Simulation, 2010 Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
106 References Keller A.: Instant Radiosity, 1997 Keller A.: Quasi Monte Carlo Methods for Realistic Image Synthesis (PhD thesis), 1998 Kniss J. et al.: Interactive Translucent Volume Rendering and Procedural Modelling, 2002 Lafortune E. P. and Willems Y. D.: Rendering Participating Media with Bidirectional Path Tracing, 1996 Pauly M. et al.: Metropolis Light Transport for Participating Media, 2000 Preetham A. J. et al.: A Practical Analytic Model for Daylight, 1999 Purcell T. J. et al.: Photon Mapping on Programmable Graphics Hardware, 2003 Raab M. et al.: Unbiased Global Illumination with Participating Media, 2006 Riley K. et al.: Efficient Rendering of Atmospheric Phenomena, 2004 Sun B. et al.: A Practical Analytic Single Scattering Model for Real Time Rendering, 2005 Szirmay-Kalos L. et al.: Real-Time Multiple Scattering in Participating Media with Illumination Networks, 2005 Tristan L.: Soft Particles, 2007 Veach E.: Robust Monte Carlo Methods for Light Transport Simulation (PhD thesis), 1998 Wang N.: Realistic and Fast Cloud Rendering, 2003 Woodcock E. et al.: Techniques Used in the GEM Code for Monte Carlo Neutronics Calculations in Reactors and Other Systems of Complex Geometry, 1965 Yue Y. et al.: Unbiased Adaptive Stochastic Sampling for Rendering Inhomogeneous Participating Media, 2010 Zotti G. et al.: A Critical Review of the Preetham Skylight Model, 2007 Selected Topics in Global Illumination Computation Participating Media, Part I Oskar Elek
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