Last TimeTodaySubsurface ScatteringBSSRDFPractical ModelSingle Scattering TermSlide 7Multiple ScatteringDiffuse Scattering Term (the flavor)Fitting ParametersRendering with the BSSRDFSampling ApproachesResultsMore ResultsCan’t Escape the BunnySky IlluminationAtmospheric PhenomenaSimulation ModelsCoordinate SystemCIE ModelCIE Cloud ModelPerez ModelAerial PerspectivePreetham, Shirley and SmitsSlide 25TurbidityWard’s Model vs PreethamNext Time02/28/05 © 2005 University of WisconsinLast Time•Scattering theory•Integrating tranfer equations02/28/05 © 2005 University of WisconsinToday•Sub-surface scattering•Sky models02/28/05 © 2005 University of WisconsinSubsurface Scattering•Kubelka-Munk is a gross approximation to real scattering•Subsurface scattering is very important to capturing the appearance of organic materials02/28/05 © 2005 University of WisconsinBSSRDF•Bidirectional surface scattering reflectance distribution function, S•Relates the outgoing radiance at one point to the incident flux at another•BRDF makes the assumption that xi = xo•To get the total radiance leaving a point, integrate over the surface and the incoming directions•S depends on the sub-surface scattering of the material     iiooiioooxdxxSxdL,,;,, 02/28/05 © 2005 University of WisconsinPractical Model•Wann Jensen, Marschner, Levoy and Hanrahan, 2001•Handles non-isotropic media•Does not require extensive Monte-Carlo raytracing–Just a modified version of distribution ray-tracing•Approximation based on:–Multiple bounce scattering – diffuse component–Single bounce scattering – directional component     ooiiooiidooiixxSxxSxxS,;,,;,,;,)1(02/28/05 © 2005 University of WisconsinSingle Scattering Term•Assume one scattering event on the path from incoming to outgoing ray•To get outgoing radiance, integrate along refracted rayioxixos             -AiiiiiiooiiiiiisoiosoooxdAdnxLxxSdsdxLeFpxxLtc2)1(02)1(,,;,,,,02/28/05 © 2005 University of WisconsinSingle Scattering Term•S(1) is defined by this formula                   surfaceflat afor factorgeometry a is whereion terms transmissFresnel two,,,,;,,,,tc2)1(02)1(ioitotitotAiiiiiiooiiiiiisoiosooonnGGxGxFFFxdAdnxLxxSdsdxLeFpxxLtc---02/28/05 © 2005 University of WisconsinMultiple Scattering•Observation: multiple scattering tends to look diffuse–Each scattering event tends to blur the distribution of radiance, until it looks uniform•For flat, semi-infinite surfaces, the effect of multiple scattering can be approximated with two virtual light sources–One inside the medium–One “negative” light outside the medium–The diffusion approximation02/28/05 © 2005 University of WisconsinDiffuse Scattering Term (the flavor)•This equation uses the Fresnel, coefficients to scale the incoming radiance, coefficients for transmission and adsorption, and variables for the location of the virtual light sources          otoiditooiidvtdvtrvrtdrtrdFxxRFxxSdedzdedrRvtrrtr,,1,;,1143302/28/05 © 2005 University of WisconsinFitting Parameters•There are 4 material dependent parameters: ’s, a, , –Each parameter, except , depends on wavelength•Measure by taking a high dynamic range image of a sample piece illuminated by a focused light–High dynamic range imagery will be covered later     ooiiooiidooiixxSxxSxxS,;,,;,,;,)1(02/28/05 © 2005 University of WisconsinRendering with the BSSRDF•Rendering has to take into account:–Efficient integration of the BSSRDF including importance sampling–Single scattering for arbitrary geometry–Diffuse scattering for arbitrary geometry–Texture on the surface•Use a distribution ray-tracer•Each time you hit a surface point, xo, have to sample incoming points, xi to estimate integral02/28/05 © 2005 University of WisconsinSampling Approaches•For single scattering terms, sample points along the refracted outgoing ray–Cast shadow ray to light to find out incoming radiance–Push this through single scattering equation to get outgoing–Make distant light approximation to ease computations•For diffuse scattering term, sample points around the outgoing point–Then place the virtual lights and evaluate the equation–Must be careful to put virtual lights in appropriate places•For texture, use parameters from xi for diffuse, and combination of xi and xo for single scattering02/28/05 © 2005 University of WisconsinResults02/28/05 © 2005 University of WisconsinMore Results02/28/05 © 2005 University of WisconsinCan’t Escape the Bunny02/28/05 © 2005 University of WisconsinSky Illumination•The sky is obviously an important source of illumination•The atmosphere is an important participating medium over large distances (hundreds of meters)–People use atmospheric effects to judge distances (stereo and disparity effects are useless at large distances)•Three models:–CIE model–Perez model–Preetham, Shirley and Smits model02/28/05 © 2005 University of WisconsinAtmospheric Phenomena•Due to solar illumination and scattering in the atmosphere•Air molecules are modeled by Rayleigh scattering–Optical extinction coefficient varies with -4–What phenomena does this explain?•Scattering due to larger particles is modeled with Mie scattering–Scattering depends less on wavelength, so what color is haze?•Turbidity is a useful measurement: T=(tm+th)/tm–tm is vertical optical thickness of molecular atmosphere–th is vertical optical thickness of haze atmosphere02/28/05 © 2005 University of WisconsinSimulation Models•These attempt to simulate the scattering in the atmosphere to produce images–Very expensive for practical use–But work with any atmospheric conditions02/28/05 © 2005 University of WisconsinCoordinate System02/28/05 ©