Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- CS 354 Acceleration Structures by Mark Kilgard 2097 views
- CS 354 Typography by Mark Kilgard 2480 views
- CS 354 Texture Mapping by Mark Kilgard 3773 views
- OpenGL for 2015 by Mark Kilgard 4520 views
- CS 354 Programmable Shading by Mark Kilgard 3060 views
- CS 354 Ray Casting & Tracing by Mark Kilgard 3537 views

1,604 views

Published on

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

No Downloads

Total views

1,604

On SlideShare

0

From Embeds

0

Number of Embeds

10

Shares

0

Downloads

92

Comments

0

Likes

7

No embeds

No notes for slide

- 1. CS 354Global IlluminationMark KilgardUniversity of TexasApril 19, 2012
- 2. CS 354 2 Today’s material In-class quiz On ray casting & tracing lecture Lecture topic Project 4 Global illumination
- 3. 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
- 4. 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
- 5. 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.
- 6. 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
- 7. 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
- 8. 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
- 9. 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
- 10. 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
- 11. 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
- 12. 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
- 13. CS 354 13 Measuring BRDFs Empirically Gonioreflectometer is device to measure BRDFs
- 14. CS 354 14 BRDF Decomposition Broad characterization of BRDF appearance Pure diffuse Pure specular Glossy
- 15. 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
- 16. CS 354 16 Hemisphere over a Surface Incident radiance is integrated over the hemisphere
- 17. 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
- 18. 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
- 19. 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
- 20. CS 354 20 Discrete Integral Approximation Uniform sampling Shown in 1D, but we need to integrate over hemisphere (solid angles)
- 21. CS 354 21 Hemisphere Sampling Vary Euler angles
- 22. 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
- 23. CS 354 23 Ray Casting for Initial Samples
- 24. CS 354 24 Path Tracing via Simple Stochastic Ray Tracing
- 25. 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
- 26. CS 354 26 Sufficient Shadow Ray Sampling
- 27. CS 354 27 Light Tracing Trace rays from the light Contribution rays accumulate image samples
- 28. CS 354 28 Light Tracing Needs Lots of Samples
- 29. 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
- 30. 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
- 31. CS 354 31 Radiosity Example
- 32. CS 354 32 Scene Diced into Uniform Patches
- 33. CS 354 33 Radiosity Method Self-emitted reflectivity total radiosity radiosity Form factor Approximation to general Rendering Equation
- 34. 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 >
- 35. CS 354 35 Form Factor Visualized Mutual visibility of two patches Don’t have to be same size
- 36. CS 354 36 Differential Patches and Foreshortening Cosine fall-off applies And assuming Lambertian surfaces foreshortening
- 37. 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”
- 38. CS 354 38 Interpolation of Radiosity Solution Constant Approximation “true” solution Quadratic Approximation flat smooth
- 39. CS 354 39 Iterative Radiosity Solver 1 iteration 4 iterations 16 iterations 64 iterations 252 iterations
- 40. 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]
- 41. CS 354 41 Participating Media Assumptions Simpler Single scattering Uniform Ignore shadowing More complex Multiple scatterings Non-uniform Account for shadowing
- 42. 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
- 43. CS 354 43 Photon Mapping Examples without diffuse photo map caustics interreflection visualization sub-surface scattering diffuse interreflection
- 44. 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

No public clipboards found for this slide

Be the first to comment