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CS 354 Global Illumination
 

CS 354 Global Illumination

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April 19, 2012; CS 354 Computer Graphics; University of Texas at Austin

April 19, 2012; CS 354 Computer Graphics; University of Texas at Austin

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    CS 354 Global Illumination CS 354 Global Illumination Presentation Transcript

    • CS 354Global IlluminationMark KilgardUniversity of TexasApril 19, 2012
    • CS 354 2 Today’s material  In-class quiz  On ray casting & tracing lecture  Lecture topic  Project 4  Global illumination
    • CS 354 3 My Office Hours  Tuesday, before class  Painter (PAI) 5.35  8:45 a.m. to 9:15  Thursday, after class  ACE 6.302  11:00 a.m. to 12  Randy’s office hours  Monday & Wednesday  11 a.m. to 12:00  Painter (PAI) 5.33
    • CS 354 4 Last time, this time  Last lecture, we discussed  Ray casting and tracing  This lecture  Global illumination  Projects  Project 3 due yesterday  Project 4 on ray tracing on Piazza  Due May 2, 2012
    • CS 354 5 On a sheet of paper Daily Quiz • Write your EID, name, and date • Write #1, #2, #3 followed by its answer  Multiple choice: determining if a ray intersects a sphere  Multiple choice: With involves solving a distribution ray tracing, one can accomplish a) linear equation a) depth-of-field b) quadratic equation b) soft shadows c) system of linear equations c) motion blur d) cubic equation d) a. and b. but not c.  True or False: With ray tracing, the problem of anti- e) a., b., and c. aliasing doesn’t apply.
    • CS 354 6 Solving the Rendering Equation with Ray Tracing  Ray “tracing” or “shooting”  Given a point and direction, sample radiance  Building block for global illumination algorithms  Use ray traces to approximate integrals  Conceptually, solving the rendering equation  Intractable to shoot every ray  Instead use Monte Carlo techniques
    • CS 354 7 Aspects of Modeling Light  Geometric optics  Our concern  Assume light travels instantaneously  Light travels in straight lines  Light not influenced by gravity or magnetic fields  Wave optics  Diffraction, etc.  Quantum optics  Sub-microscopic
    • CS 354 8 Rendering Equation  Theory for light-surface interactions Lo (x, ω , λ , t ) = Le (x, ω , λ , t ) + ∫ f r (x, ω ′, ω , λ , t ) Li (x, ω ′, λ , t ) (−ω ′ • n) dω ′ Ω
    • CS 354 9 Rendering Equation PartsLo (x, ω , λ , t ) = Le (x, ω , λ , t ) + ∫ f r (x, ω ′, ω , λ , t ) Li (x, ω ′, λ , t ) (−ω ′ • n) dω ′ Ω  Lo = outgoing light from x in direction ω  x = point on a surface  ω = normalized outgoing light vector  λ = wavelength of light  t = time  Le = emitted light at x going towards from ω  n = surface normal at x
    • CS 354 10 Rendering Equation Integral  ∫ = integrate over a region  Ω = region of a hemisphere  Together: “integrate overall the incoming directions for a hemisphere at a point x”  ωˊ = normalized incoming light vector  Li = incoming light at x coming from ωˊ  n = surface normal at x  (-ωˊ • n) = cosine of angle between incoming light and surface normal  dωˊ = differential of incoming angle
    • CS 354 11 Bidirectional Reflectance Distribution Function  Ratio of differential outgoing (reflected) radiance to differential incoming irradiance dLr (x, ω , λ , t ) dLr (x, ω , λ , t ) f r (x, ω ′, ω , λ , t ) = = dEi (x, ω ′, λ , t ) dLi (x, ω ′, λ , t ) (−ω ′ • n) dω ′  Physically based BRDF properties L = radiance  Must be non-negative E = irradiance  Must be reciprocal  Swap incoming & relected directions generates same ratio  Conserves energy  Integrating over entire hemisphere must be ≤ 1
    • CS 354 12 Cosine Weighting for Irradiance  At shallow angles, incoming light spreads over a wider area of the surface  Thus spreading the energy  Thus dimming the received light
    • CS 354 13 Measuring BRDFs Empirically  Gonioreflectometer is device to measure BRDFs
    • CS 354 14 BRDF Decomposition  Broad characterization of BRDF appearance Pure diffuse Pure specular Glossy
    • CS 354 15 Common BRDFs  Diffuse model, a.k.a. Lambertian f diffuse (x, Ψ ↔ Θ, λ , t ) = k d ( R • Θ) n  Phongphong (x, Ψ ↔a.k.a.=Reflection dSpecular f model, Θ, λ , t ) k s +k N •Ψ ( N • H )n f blinn (x, Ψ ↔ Θ, λ , t ) = k s + kd  Blinn model, a.k.a. Half-angle Specular N •Ψ
    • CS 354 16 Hemisphere over a Surface  Incident radiance is integrated over the hemisphere
    • CS 354 17 Rendering Equation Interpretation  Recursive equation Lo (x, ω , λ , t ) = Le (x, ω , λ , t ) + ∫ f r (x, ω ′, ω , λ , t ) Li (x, ω ′, λ , t ) (−ω ′ • n) dω ′ Ω outgoing light “sums up” all incoming light for all directions on hemisphere  Integral over hemisphere (Ω)  Limitations  Treats wavelengths all independent  Treats time in Newtonian way  Ignores volumetric and subsurface scattering  More complex models can incorporate these aspects of light  Impractical for actual computer graphics rendering
    • CS 354 18 Alternate Rendering Equation  Integrate over all points in the scene  Instead of all directions for a hemisphere Lo (x, ω , λ , t ) = Le (x, ω , λ , t ) + ∫ f (x, ω y∈Γ r yx , ω , λ , t ) L(y, ωyx , λ , t ) G (x, y ) dy outgoing light “sums up” all incoming light for all surfaces, modulated by visibility  Notes  G(x,y) returns the visibility (occlusion) between points x & y  Integral over all surface points (Γ) in the scene
    • CS 354 19 Two Versions of Rendering Equation Occlusion (G) is zero o Le (x, ω , λ , t ) + Le (x, ω , λ , t ) +Lo (x, ω , λ , t ) = ∫ Ω f r (x, ω ′, ω , λ , t ) Li (x, ω ′, λ , t ) (−ω ′ • n) dω ′ Lo (x, ω , λ , t ) = ∫ f r (x, ωyx , ω , λ , t ) L(y, ωyx , λ , t ) G (x, y ) dy y∈Γ Integrate over hemisphere Integrate over all surface points
    • CS 354 20 Discrete Integral Approximation  Uniform sampling  Shown in 1D, but we need to integrate over hemisphere (solid angles)
    • CS 354 21 Hemisphere Sampling  Vary Euler angles
    • CS 354 22 Monte Carlo Integrations  Randomly sample the rendering equation integrals  Sample space based on probability distribution function  Compute estimated variance to know when to stop  Importance sampling  Try to weight probability function to match variance
    • CS 354 23 Ray Casting for Initial Samples
    • CS 354 24 Path Tracing via Simple Stochastic Ray Tracing
    • CS 354 25 Two Versions of Rendering Equation (again) Occlusion (G) is zero o Le (x, ω , λ , t ) + Le (x, ω , λ , t ) +Lo (x, ω , λ , t ) = ∫ Ω f r (x, ω ′, ω , λ , t ) Li (x, ω ′, λ , t ) (−ω ′ • n) dω ′ Lo (x, ω , λ , t ) = ∫ f r (x, ωyx , ω , λ , t ) L(y, ωyx , λ , t ) G (x, y ) dy y∈Γ Integrate over hemisphere Integrate over all surface points
    • CS 354 26 Sufficient Shadow Ray Sampling
    • CS 354 27 Light Tracing  Trace rays from the light  Contribution rays accumulate image samples
    • CS 354 28 Light Tracing Needs Lots of Samples
    • CS 354 29 How many rays to shoot?  Two approaches  Fixed number of ray evaluations  Limits the depth of recursion  Means some paths can never be explored  Implies bias in result, since favors short paths  Russian Roulette approach  Roll dice to see if ray tracing should continue  Reduces bias in rendering result  Allows “obscure” paths to be explored
    • CS 354 30 Radiosity History  Used for thermal engineering since 1960s  Introduced to computer graphics in 1984  SIGGRAPH paper: “Modeling the Interaction of Light Between Diffuse Surfaces”  Goral, Torrance, Greenberg, Battaile (Cornell)  Reduces to solving a linear system of equations  In simple formulation, just works for diffuse surfaces  OK for building interiors
    • CS 354 31 Radiosity Example
    • CS 354 32 Scene Diced into Uniform Patches
    • CS 354 33 Radiosity Method Self-emitted reflectivity total radiosity radiosity Form factor Approximation to general Rendering Equation
    • CS 354 34 Form Factors  Form factor between i,j is Fij  Tells how much of patch A is visible from patch B  Indicates how much radiance can be transferred 1 Fij = ∫ ∫ K ( x, y ) dAy dAx Ai Si Si K ( x , y ) = G ( x, y ) V ( x, y ) cos(Θ xy , N x ) cos(−Θ xy , N y ) G ( x, y ) = π rxy 2 V ( x, y ) =< visibility between x & y >
    • CS 354 35 Form Factor Visualized  Mutual visibility of two patches  Don’t have to be same size
    • CS 354 36 Differential Patches and Foreshortening  Cosine fall-off applies  And assuming Lambertian surfaces foreshortening
    • CS 354 37 Hemi-cube Approach to Sampling Form Factors  Think about drawing hemi-cube at every point  What you see is an input for radiosity  Known as “instant radiosity”
    • CS 354 38 Interpolation of Radiosity Solution Constant Approximation “true” solution Quadratic Approximation flat smooth
    • CS 354 39 Iterative Radiosity Solver 1 iteration 4 iterations 16 iterations 64 iterations 252 iterations
    • CS 354 40 Participating Media  Light doesn’t just interact with surfaces  Gaseous phenomena affects lighting  Usually handled statistically emission in-scattering [Jarosz et.al. 2008] absorption out-scattering [FogShop 2007]
    • CS 354 41 Participating Media Assumptions  Simpler  Single scattering  Uniform  Ignore shadowing  More complex  Multiple scatterings  Non-uniform  Account for shadowing
    • CS 354 42 Photon Mapping  Two-pass global illumination algorithm  Developed by Henrick Jensen (1996)  Two passes  Randomly distribute photons around the scene  Called “photon map construction”  Render treating photons as mini-light sources  Capable of efficiently generating otherwise very expensive effects  Caustics  Diffuse inter-reflections, such as color bleed  Sub-surface scattering
    • CS 354 43 Photon Mapping Examples without diffuse photo map caustics interreflection visualization sub-surface scattering diffuse interreflection
    • CS 354 44 Next Class  Next lecture  Acceleration structures  How do we make the ray trace operation faster?  Reading  Chapter 5, 297-298  Chapter 11, 569-577  Project 4  Project 4 is a simple ray tracer  Due Wednesday, May 2, 2012