IlluminationJason LawrenceCS445: GraphicsAcknowledgment: slides by Misha Kazhdan, Allison Klein, Tom Funkhouser,Adam Finkelstein and David DobkinOverview• Direct IlluminationoEmission at light sourcesoDirect light at surface points• Global illuminationoShadowsoInter-object reflectionsoTransmissionsRefractive BouncingOverview• Direct IlluminationoEmission at light sourcesoDirect light at surface points• Global illuminationoShadowsoInter-object reflectionsoTransmissionsIntersection TestingOverview• Direct IlluminationoEmission at light sourcesoDirect light at surface points• Global illuminationoShadowsoInter-object reflectionsoTransmissionsModeling Light Sources•IL(x,y,z,θ,φ,λ) ... odescribes the intensity of energy, oleaving a light source, …oarriving at location(x,y,z), ...ofrom direction (θ,φ), ...owith wavelength λ(x,y,z)LightEmpirical Models• Ideally measure irradiant energy for “all” situationsoToo much storageoDifficult in practiceλSimplified Light Source Models• Simple mathematical models:oPoint lightoDirectional lightoSpot lightPoint Light Source• Models omni-directional point sourceointensity (I0), oposition (px, py, pz), ofactors (kc, kl, kq) for attenuation with distance (d)dLight(px, py, pz)Directional Light Source• Models point light source at infinityointensity (I0), odirection (dx,dy,dz) (dx, dy, dz)No attenuationwith distanceSpot Light Source• Models point light source with directionointensity (I0), oposition (px, py, pz), oattenuation (kc, kl, kq) odirection (dx, dy, dz)ocut-off and drop-off (γ, α)dLight(px, py, pz) DLγHow can we modify point light to decrease as γ increases?Spot Light Source• Models point light source with directionointensity (I0), oposition (px, py, pz), oattenuation (kc, kl, kq) odirection (dx, dy, dz)ocut-off and drop-off (γ, α)dLight(px, py, pz) DLγOverview• Direct IlluminationoEmission at light sourcesoDirect light at surface points• Global illuminationoShadowsoTransmissionsoInter-object reflectionsModeling Surface Reflectance•Rs(θ,φ,λ,γ,ψ) ... odescribes the fraction of incident energy, oarriving from direction (θ,φ), ...owith wavelength λ, ...oleaving in direction (γ,ψ), …Surface(θ,φ)(ψ,λ)λEmpirical Models• Ideally measure radiant energy for “all” combinations of incident angles oToo much storageoDifficult in practiceSurface(θ,φ)(ψ,λ)λSimple Reflectance Model• Simple analytic model: odiffuse reflection +ospecular reflection +oemission +o“ambient”SurfaceBased on modelproposed by PhongSimple Reflectance Model• Simple analytic model: odiffuse reflection +ospecular reflection +oemission +o“ambient”SurfaceBased on Phong illumination modelBased on modelproposed by PhongDiffuse Reflection• Assume surface reflects equally in all directionsoExamples: chalk, claySurfaceDiffuse Reflection• How much light is reflected?oDepends on angle of incident lightoaka “Lambertian”SurfaceθDiffuse Reflection• How much light is reflected?oDepends on angle of incident lightSurfacedLdAθThink of aflashlight!Diffuse Reflection• Lambertian modelocosine law (dot product)oKD is surface propertyoIL is incoming lightSurfaceNLθDiffuse Reflection• Note that lights and surface properties have R,G, and B components!oSo amount of red light reflected is not necessarily equal to amount of green light, etc.oYou will need to run calculation below on EACH color channeloThis holds true for all lighting calculationsDiffuse Reflection• Assume surface reflects equally in all directionsoExamples: chalk, claySimple Reflectance Model• Simple analytic model: odiffuse reflection +ospecular reflection +oemission +o“ambient”SurfaceSpecular Reflection• Reflection is strongest near mirror angleoExamples: metals, shiny applesSpecular Reflection• Reflection is strongest near mirror angleoExamples: metals, shiny applesSpecularSpecular ReflectionHow much light is seen?Depends on: oangle of incident lightoangle to viewerNLRVViewerαθθSpecular Reflection• Phong Modelocos(α)nNLRVViewerαθθThis is a physically-motivated hack!Specular Reflection• Reflection is strongest near mirror angleoExamples: metals, shiny applesSimple Reflectance Model• Simple analytic model: odiffuse reflection +ospecular reflection +oemission +o“ambient”SurfaceEmissionRepresents light emanating directly from a surface that cannot be described by the three light sourcesEmission ≠ 0EmissionEmission ≠ 0Simple Reflectance Model• Simple analytic model: odiffuse reflection +ospecular reflection +oemission +o“ambient”SurfaceAmbient TermThis is a total hack (avoids complexity of global illumination)!• Represents reflection of all indirect illuminationAmbient Term• Represents reflection of all indirect illuminationSimple Reflectance Model• Simple analytic model: odiffuse reflection +ospecular reflection +oemission +o“ambient”SurfaceSimple Reflectance Model• Simple analytic model: odiffuse reflection +ospecular reflection +oemission +o“ambient”SurfaceSurface Illumination Calculation• Single light source :NLRVViewerαθθSurface Illumination Calculation• Multiple light sources:NL2VViewerL1Overview• Direct IlluminationoEmission at light sourcesoDirect light at surface points• Global illuminationoShadowsoTransmissionsoInter-object reflectionsShadows• Shadow term tells if light sources are blockedoCast ray towards each light source Li. If the ray is blocked, do not consider the contribution of the light.Shadows• Shadow term tells if light sources are blockedoCast ray towards each light source LioSi = 0 if ray is blocked, Si = 1 otherwiseL1L0ShadowTermShadows• Shadow term tells if light sources are blockedoCast ray towards each light source LioSi = 0 if ray is blocked, Si = 1 otherwiseL1L0S0=1:• L0 contributesShadowTermShadows• Shadow term tells if light sources are blockedoCast ray towards each light source LioSi = 0 if ray is blocked, Si = 1 otherwiseS0=1:• L0 contributesS1=0:• L1 does not contributeL1L0ShadowTermRay Casting• Trace primary rays from cameraoDirect illumination from unblocked lights onlyRecursive Ray Tracing• Also trace secondary rays from hit surfacesoConsider contributions from:1. Reflected Rays2. Refracted RaysMirror Reflections• Also trace secondary rays from hit surfacesoConsider contributions from:1. Reflected Rays2. Refracted RaysRadiance for mirror reflection rayL1L0Mirror Reflections• Also trace secondary rays from hit
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