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Columbia COMS 4160 - Illumination and Shading 2

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1Computer Graphics (Fall 2005)COMS 4160, Lecture 17: Illumination and Shading 2http://www.cs.columbia.edu/~cs4160Lecture includes number of slides from other sources: Hence different color scheme to be compatible with these other sourcesTo Do• Submit HW 3, do well• Start early on HW 4Outline• Preliminaries• Basic diffuse and Phong shading• Gouraud, Phong interpolation, smooth shading• Formal reflection equation• Texture mapping (next week)• Global illumination (next unit)See handout (chapter 2 of Cohen and Wallace)Motivation• Lots of ad-hoc tricks for shading– Kind of looks right, but?• Study this more formally• Physics of light transport– Will lead to formal reflection equation• One of the more technical/theoretical lectures – But important to solidify theoretical frameworkBuilding up the BRDF• Bi-Directional Reflectance Distribution Function [Nicodemus 77]• Function based on incident, view direction• Relates incoming light energy to outgoing light energy• We have already seen special cases: Lambertian, Phong• In this lecture, we study all this abstractly2Radiometry• Physical measurement of electromagnetic energy• We consider light field– Radiance, Irradiance– Reflection functions: Bi-Directional Reflectance Distribution Function or BRDF– Reflection Equation– Simple BRDF modelsRadiance • Power per unit projected area perpendicular to the ray per unit solid angle in the direction of the ray • Symbol: L(x,ω)(W/m2sr)• Flux given by dΦ = L(x,ω) cos θ dω dARadiance properties• Radiance is constant as it propagates along ray– Derived from conservation of flux – Fundamental in Light Transport. 12111 22 2dLddALddAdωωΦ== =Φ2212 21ddAr ddArωω==1211 2 22dA dAddA d dArωω==12LL∴=3Radiance properties• Sensor response proportional to surface radiance (constant of proportionality is throughput)– Far away surface: See more, but subtends smaller angle– Wall is equally bright across range of viewing distancesConsequences– Radiance associated with rays in a ray tracer– All other radiometric quantities derived from radianceIrradiance, Radiosity• Irradiance E is the radiant power per unit area• Integrate incoming radiance over hemisphere– Projected solid angle (cos θ dω)– Uniform illumination: Irradiance = π [CW 24,25]– Units: W/m2• Radiosity– Power per unit area leaving surface (like irradiance)BRDF• Reflected Radiance proportional to Irradiance• Constant proportionality: BRDF [CW pp 28,29]– Ratio of outgoing light (radiance) to incoming light (irradiance)– Bidirectional Reflection Distribution Function – (4 Vars) units 1/sr()(, )()cosrririi i iLfLdωωωωθω=() ()(,)cosrr ii ir i iLLf dωωωω θω=4Isotropic vs Anisotropic• Isotropic: Most materials (you can rotate about normal without changing reflections)• Anisotropic: brushed metal etc. preferred tangential directionIsotropicAnisotropicRadiometry• Physical measurement of electromagnetic energy• We consider light field– Radiance, Irradiance– Reflection functions: Bi-Directional Reflectance Distribution Function or BRDF– Reflection Equation– Simple BRDF modelsReflection Equationiωrω() ()(,)( )rr ii ir iLLf nωωωωω= iReflected Radiance(Output Image)Incident radiance (fromlight source)BRDFCosine of Incident angleReflection EquationiωrωSum over all light sources() ()(,)( )rr ii ir iiLLf nωωωωω=∑iReflected Radiance(Output Image)Incident radiance (fromlight source)BRDFCosine of Incident angleReflection EquationiωrωReplace sum with integralidω() ()(,)( )rr ii ir i iLLf ndωωωωω ωΩ=∫iReflected Radiance(Output Image)Incident radiance (fromlight source)BRDFCosine of Incident angle5Radiometry• Physical measurement of electromagnetic energy• We consider light field– Radiance, Irradiance– Reflection functions: Bi-Directional Reflectance Distribution Function or BRDF– Reflection Equation– Simple BRDF modelsBrdf Viewer plots Diffusebv written by Szymon RusinkiewiczTorrance-SparrowAnisotropic6Analytical BRDF: TS example• One famous analytically derived BRDF is the Torrance-Sparrow model.• T-S is used to model specular surface, like the Phong model.– more accurate than Phong– has more parameters that can be set to match different materials– derived based on assumptions of underlying geometry. (instead of ‘because it works well’)Torrance-Sparrow• Assume the surface is made up grooves at the microscopic level.• Assume the faces of these grooves (called microfacets) are perfect reflectors.• Take into account 3 phenomenaShadowingMasking InterreflectionTorrance-Sparrow Result()( , )( )4cos( )cos( )iirhirFG Dfθωω θθθ=Fresnel term:allows for wavelength dependencyGeometric Attenuation:reduces the output based on the amount of shadowing or masking that occurs.Distribution:distribution function determines what percentage of microfacets are oriented to reflect in the viewer direction.How much of the macroscopic surface is visible to the light sourceHow much of the macroscopic surface is visible to the viewerOther BRDF models• Empirical: Measure and build a 4D table• Anisotropic models for hair, brushed steel• Cartoon shaders, funky BRDFs• Capturing spatial variation• Very active area of researchComplex Lighting• So far we’ve looked at simple, discrete light sources.• Real environments contribute many colors of light from many directions.• The complex lighting of a scene can be captured in an Environment map.– Just paint the environment on a sphere.Environment Maps• Instead of determining the lighting direction by knowing what lights exist, determine what light exists by knowing the lighting direction.Blinn and Newell 1976, Miller and Hoffman, 1984Later, Greene 86, Cabral et al. 877Conclusion• All this (OpenGL, physically based) are local illumination and shading models• Good lighting, BRDFs produce convincing results– Matrix movies, modern realistic computer graphics• Do not consider global effects like shadows, interreflections (from one surface on another)– Subject of next unit (global


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