PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Blurred Highlights and Surface Roughness - RECAPSlide 32Slide 33Slide 34Torrance-Sparrow BRDF – Different Factors (RECAP)Slide 36Slide 37Slide 38Oren-Nayar Model – Different FactorsSlide 40Oren-Nayar Model – Different Factors (contd.)Oren-Nayar Model – Final ExpressionSlide 43Slide 44Slide 45Slide 46Torrance Sparrow Model of Reflectance+Oren Nayar Model of ReflectanceTorrance-Sparrow Model – Main Points•Physically Based Model for Surface Reflection.•Based on Geometric Optics.•Explains off-specular lobe (wider highlights).•Works for only rough surfaces.•For very smooth surfaces, electromagnetic nature of light must be usedBeckmann-Spizzichinno model.Beyond the scope of this course.Modeling Rough Surfaces - Microfacets• Roughness simulated by Symmetric V-groves at Microscopic level.• Distribution on the slopes of the V-grove faces are modeled.• Each microfacet assumed to behave like a perfect mirror.Coordinate System needed to derive T-S modelTorrance-Sparrow or Cook-Torrance BRDFPhysically based model of a reflecting surface. Assumes a surface is a collection of planar microscopic facets, microfacets. Each microfacet is a perfectly smooth reflector. • D describes the distribution of microfacet orientations. • G describes the masking and shadowing effects between the microfacets. • F term is a Fresnel reflection term related to material’s index of refraction.Torrance-Sparrow or Cook-Torrance BRDFMicrofacet Distribution Function • Statistical model of the microfacet variation in the halfway-vector H direction• Based on a Beckman distribution function• Consistent with the surface variations of rough surfaces• β - the angle between N and H• m - the root-mean-square slope of the microfacetsBeckman’s Distribution:Torrance-Sparrow or Cook-Torrance BRDFTorrance-Sparrow or Cook-Torrance BRDFGeometric Attenuation Factor:The geometric attenuation factor G accounts for microfacet shadowing. The factor G is in the range from 0 (total shadowing) to 1 (no shadowing). There are many different ways that an incoming beam of light can interact with the surface locally. The entire beam can simply reflect, shown here.Torrance-Sparrow or Cook-Torrance BRDFGeometric Attenuation Factor:A portion of the outgoing beam can be blocked. This is called masking.Torrance-Sparrow or Cook-Torrance BRDFGeometric Attenuation Factor:A portion of the incoming beam can be blocked. This is called shadowing.Torrance-Sparrow or Cook-Torrance BRDFGeometric Attenuation Factor:In each case, the geometric configurations can be analyzed to compute the percentage of light that actually escapes from the surface.Geometric Attenuation FactorTorrance-Sparrow or Cook-Torrance BRDFFresnel Factor:The Fresnel effect is wavelength dependent. It behavior is determined by the index-of-refraction of the material (taken as a complex value to allow for attenuation). This effect explains the variation in colors seen in specular regions particular on metals (conductors). It also explains why most surfaces approximate mirror reflectors when the light strikes them at a grazing angle.Coordinate System needed to derive T-S modelComponents of Surface Reflection – Moving Light SourceComponents of Surface Reflection – Moving CameraSplit off-specular Reflections in Woven SurfacesNext Class – Rough Diffuse SurfacesSame Analysis of Roughness for Diffuse Objects – Oren Nayar ModelDror, Adelson, WilskyDiffuse Reflections from Rough SurfacesDiffuse Reflection and Lambertian BRDF - Recapviewingdirectionsurfaceelementnormalincidentdirectioninvsdrriif ),;,(• Lambertian BRDF is simply a constant :albedo• Surface appears equally bright from ALL directions! (independent of )• Surface Radiance :v• Commonly used in Vision and Graphics!snIILdid.cossource intensitysource intensity IDiffuse Reflection and Lambertian BRDF - RecapRadiance decreases with increase in angle between surface normal and sourceRendered Sphere with Lambertian BRDF• Edges are dark (N.S = 0) when lit head-on• See shading effects clearly.Why does the Full Moon have a flat appearance? • The moon appears matte (or diffuse)• But still, edges of the moon look bright(not close to zero).Why does the Full Moon have a flat appearance? Lambertian Spheres and Moon Photos illuminated similarlySurface Roughness Causes Flat AppearanceActual Vase Lambertian VaseSurface Roughness Causes Flat Appearance – More ExamplesSurface Roughness Causes Flat Appearance Increasing surface roughnessLambertian modelValid for only SMOOTH MATTE surfaces.Bad for ROUGH MATTE surfaces.Blurred Highlights and Surface Roughness - RECAPRoughnessOren-Nayar Model – Main Points•Physically Based Model for Diffuse Reflection.•Based on Geometric Optics.•Explains view dependent appearance in Matte Surfaces•Take into account partial interreflections.•Roughness represented like in Torrance-Sparrow Model•Lambertian model is simply an extreme case withroughness equal to zero.Modeling Rough Surfaces - Microfacets•Roughness simulated by Symmetric V-groves at Microscopic level.•Distribution on the slopes of the V-grove faces are modeled.•Each microfacet assumed to behave like a perfect Lambertian surface.View Dependence of Matte Surfaces - Key Observation• Overall brightness increases as the angle between the source and viewing direction decreases. WHY?• Pixels have finite areas. As the viewing direction changes, different mixes between dark and bright are added up to give pixel brightness.Torrance-Sparrow BRDF – Different Factors (RECAP)( ) ( , ) ( )4cos( ) cos( )i i r hi rF G Df 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 viewerSlope Distribution Model• Model the distribution of slopes as Gaussian.• Mean is Zero, Variance
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