Global Illumination - Princeton University
Global Illumination COS 426
Overview Direct Illumination Kajiya 1986 Emission at light sources Scattering at surfaces Global illumination Shadows Inter-object reflections Rendering equation Recursive ray tracing More advanced ray tracing Radiosity Greg Ward
Direct Illumination (last lecture) For each ray traced from camera Sum radiance reflected from each light Light Surfaces I0 Ii ca l a d q a d 2 Camera I I E K A I AL K D ( N Li ) K S (V Ri ) n I i i
Example Red’s Dream (Pixar Animation Studios)
Overview Direct Illumination Emission at light sources Scattering at surfaces Global illumination Shadows Inter-object reflections Rendering equation Recursive ray tracing More advanced ray tracing Radiosity Greg Ward
Overview Direct Illumination Emission at light sources Scattering at surfaces Global illumination Shadows Inter-object reflections Rendering equation Recursive ray tracing More advanced ray tracing Radiosity Greg Ward
Shadows Hard shadows from point light sources Light Surfaces Camera
Shadows Hard shadows from point light sources
Shadows Hard shadows from point light sources Camera
Shadows Hard shadows from point light sources Cast ray towards light; SL 0 if blocked, SL 1 otherwise Camera Shadow Term I I E K A I AL K i lights n ( N L ) K ( V R ) Si I i D i S i
Shadows Soft shadows from area light sources Umbra fully shadowed Penumbra partially shadowed source umbra penumbra Fredo Durand
Shadows Soft shadows from area light sources Average illumination for M sample rays per light Camera Shadow Term I i AreaLights K M 1 M j samples D ( N Li ) K S (V Ri ) Sij I ij n
Shadows Soft shadows from circular area light sources Average illumination for M sample rays per light I 0 ( D L) Ii ca l a d q a d 2 L D Camera Shadow Term I i AreaLights K M 1 M j samples D ( N Li ) K S (V Ri ) Sij I ij n
Shadows Soft shadows from circular area light sources Average illumination for M sample rays per light Generate M random sample points on area light (e.g., with rejection sampling) Compute illumination for every sample Average I i AreaLights K M 1 M j samples D ( N Li ) K S (V Ri ) Sij I ij n
Direct Illumination Illumination from polygonal area light sources Average illumination for M sample rays per light Camera Light Light 1 n ' x' I i AreaLights K M 1 M j samples D ( N Li ) K S (V Ri ) Sij I ij n
Overview Direct Illumination Emission at light sources Scattering at surfaces Global illumination Shadows Inter-object reflections Rendering equation Recursive ray tracing More advanced ray tracing Radiosity Greg Ward
Inter-Object Reflection
Inter-Object Reflection Radiance leaving point x on surface is sum of reflected irradiance arriving from other surfaces Camera n x
Solid Angle Angle in radians Length l Angle q l/r Solid angle in steradians Area A Solid angle A/r2
Light Emitted from a Surface Power per unit area per unit solid angle – Radiance (L) Measured in W/m2/sr d dA d L dA d
Rendering Equation [Kajiya 86] Compute radiance in outgoing direction by integrating reflections over all incoming directions Camera Light Surface Surface n 1 x' ' 2 Lo ( x' , ' ) Le ( x' , ' ) f r ( x' , , ' ) ( n ) Li ( x' , ) d
Rendering Equation [Kajiya 86] Compute radiance in outgoing direction by integrating reflections over all incoming directions Camera Light Surface n 1 (hemisphere) x' d Surface ' 2 Lo ( x' , ' ) Le ( x' , ' ) f r ( x' , , ' ) ( n ) Li ( x' , ) d
Overview Direct Illumination Emission at light sources Scattering at surfaces Global illumination Shadows Inter-object reflections Rendering equation Recursive ray tracing More advanced ray tracing Radiosity Greg Ward
Recursive Ray Tracing Assume only significant irradiance is in directions of light sources, specular reflection, and refraction Light Specular Reflection n S x ' Refraction R Direction of Ray Traced from Camera Area Light ' Lo ( x' , ' ) Le ( x' , ' ) f r ( x' , , ' ) ( n ) Li ( x' , ) d
Recursive Ray Tracing Compute radiance in outgoing direction by summing reflections from directions of lights specular reflections, and refractions Light Specular Reflection S n x ' Refraction R Direction of Ray Traced from Camera Area Light ' I I E K A I AL K D ( N Li ) K S (V Ri ) n S L I L K S I R KT IT L
Recursive Ray Tracing Same as ray casting, but trace secondary rays for specular (mirror) reflection and refraction I I E K A I AL K D ( N Li ) K S (V Ri ) n S L I L K S I R KT IT L
Specular Reflection Trace secondary ray in direction of mirror reflection Evaluate radiance along secondary ray and include it into illumination model Radiance for mirror reflection ray I I E K A I AL K D ( N Li ) K S (V Ri ) n S L I L K S IIRR KT IT L
Refraction Trace secondary ray in direction of refraction Evaluate radiance along secondary ray and include it into illumination model Radiance for Refraction Ray http://farm2.static.flickr.com/1109/1057760138 91cabeb391.jpg I I E K A I AL K D ( N Li ) K S (V Ri ) n S L I L K S I R KT ITT L
Recursive Ray Tracing ComputeRadiance is called recursively R3Rgb ComputeRadiance(R3Scene *scene, R3Ray *ray, R3Intersection& hit) { R3Ray specular ray SpecularRay(ray, hit); R3Ray refractive ray RefractiveRay(ray, hit); R3Rgb radiance Phong(scene, ray, hit) Ks * ComputeRadiance(scene, specular ray) Kt * ComputeRadiance(scene, refractive ray); return radiance; }
Recursive Ray Tracing Which paths?
Recursive Ray Tracing Specular reflection and refraction -- LD(S R)*E Whitted
Overview Direct Illumination Kajiya 1986 Emission at light sources Scattering at surfaces Global illumination Shadows Inter-object reflections Rendering equation Recursive ray tracing More advanced ray tracing Radiosity Greg Ward
Beyond Recursive Ray Tracing
Distributed Ray Tracing Estimate integral for each reflection by sampling incoming directions 2 4 3 n Lo ( x' , ' ) Le ( x' , ' ) 5 6 1 ' x' f r ( x' , , ' ) ( n ) Li ( x' , ) d samples
Ordinary Ray Tracing vs. Distribution Ray Tracing Ray tracing Distributed ray tracing
Monte Carlo Path Tracing Estimate integral for each pixel by sampling paths from camera Camera n n x'
Ray Tracing vs. Path Tracing Ray tracing Path tracing Kajiya
Overview Direct Illumination Emission at light sources Scattering at surfaces Global illumination Shadows Inter-object reflections Rendering equation Recursive ray tracing More advanced ray tracing Radiosity Greg Ward
Radiosity Indirect diffuse illumination – LD*E
Rendering Equation (1) n ' d x' Lo ( x' , ' ) Le ( x' , ' ) f r ( x' , , ' ) ( n ) Li ( x' , ) d
Rendering Equation (2) dA x x" o n i x' ' G ( x, x ' ) cos i cos o x x' 2 L( x' x" ) Le ( x' x" ) f r ( x x' x" ) L( x x' ) V ( x, x' ) G ( x, x' ) dA S Kajiya 1986
Radiosity Equation L( x' x" ) Le ( x' x" ) f r ( x x' x" ) L( x x' ) V ( x, x' ) G( x, x' ) dA S Assume everything is Lambertian L( x' ) Le ( x' ) ( x' ) f r ( x x' x" ) ( x' ) L( x) V ( x, x' ) G ( x, x' ) dA S Convert to Radiosities B( x' ) Be ( x' ) B Lo cos q d ( x' ) B( x) V ( x, x' ) G ( x, x' ) dA S L B
Radiosity Approximation ( x' ) B( x' ) Be ( x' ) B( x) V ( x, x' ) G ( x, x' ) dA S Aj Discretize the surfaces into “elements” o N Bi Ei i B j Fij r j 1 1 F where ij Ai Ai A j Vij cos i cos o r 2 dAj dAi i Ai
Radiosity Approximation
System of Equations N Bi Ei i B j Fij j 1 N Ei Bi i B j Fij j 1 N Bi i B j Fij Ei . 1 1 F1,1 F 1 2 F2, 2 2 2 ,1 . . . . n 1 Fn 1,1 . . n Fn ,1 . . . . . . . 1 F1,n B1 E1 . 2 F2,n B2 E 2 . . . . . . . . . n 1 Fn 1,n . . . 1 n Fn ,n Bn E n j 1 N N 1 i Fii Bi i Fij B j Ei j 1 j 1 N Bi Ai Ei Ai i Fji B j Aj j 1 This is an energy balance equation
Radiosity Application Interior lighting design LD*E Issues Computing form factors Selecting basis functions for radiosities Solving large linear system of equations Meshing surfaces into elements Rendering images
Summary Global illumination Rendering equation Solution methods Sampling Ray tracing Distributed ray tracing Monte Carlo path tracing Discretization Radiosity Photorealistic rendering with global illumination is an integration problem
Global illumination Rendering equation Solution methods Sampling Ray tracing Distributed ray tracing Monte Carlo path tracing Discretization Radiosity Photorealistic rendering with global illumination is an integration problem . Title: Introduction
Course #16: Practical global illumination with irradiance caching - Intro & Stochastic ray tracing Direct and Global Illumination Direct Global Direct Indirect Our topic On the left is an image generated by taking into account only direct illumination. Shadows are completely black because, obviously, there is no direct illumination in
indirect illumination in a bottom-up fashion. The resulting hierarchical octree structure is then used by their voxel cone tracing technique to produce high quality indirect illumination that supports both diffuse and high glossy indirect illumination. 3 Our Algorithm Our lighting system is a deferred renderer, which supports illumination by mul-
body. Global illumination in Figure 1b disam-biguates the dendrites' relative depths at crossing points in the image. Global illumination is also useful for displaying depth in isosurfaces with complicated shapes. Fig-ure 2 shows an isosurface of the brain from magnetic resonance imaging (MRI) data. Global illumination
yDepartment of Electrical Engineering, Princeton University, Princeton, NJ 08544-5263 (jdurante@princeton.edu). zDepartment of Operations Research and Financial Engineering, Princeton University, Princeton, NJ 0854
a) Classical illumination with a simple detector b) Quantum illumination with simple detectors Figure 1. Schematic showing LIDAR using classical illumination with a simple detector (a) and quantum illumination with simple detectors (b), where the signal and idler beam is photon number correlated. The presence of an object is de ned by object re
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APS 240 Interlude Ð Writing Scientific Reports Page 5 subspecies of an organism (e.g. Calopteryx splendens xanthostoma ) then the sub-species name (xanthostoma ) is formatted the same way as the species name. In the passage above you will notice that the name of the damselfly is followed by a name: ÔLinnaeusÕ. This is the authority, the name of the taxonomist responsible for naming the .
