PowerPoint PresentationMeasurement EquationSlide 3Importance transportNon-symmetric BSDFsUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don FussellUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don FussellMeasurement EquationRay space (throughput) measurefor bundle of rays rDefine F space of functions over ray spaceF is a Hilbert spaceA linear operator is a linear mapping ddAdd )cos()(),()( xxr )'()(')'cos()cos()'()'(2xxxxxxxx dAdAVdFF :AUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don FussellMeasurement EquationImagine a sensor anywhere in the sceneIt has a response to its inputSo a measurement isLight paths start with an emitter and end at a measurementCan also do paths in reverse, measurement to lightCall the quantity transported in reverse importance),(xeW)()()(, rrrdLWLWIiReieUniversity of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don FussellImportance transportImportance transport requires adjoint operators for each light transport operatorThe adjoint of an operator is its conjugate-transpose, defined wrt some inner productWe’d like our transport operators to be self-adjointLight transport and importance transport would be the samePhoton tracing, reverse path tracing, etc all kinds of importance tracinggfgf HH ,,* HH *University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don FussellNon-symmetric BSDFsWhen are transport operators not self adjoint?When the BSDF they use is not symmetricWhen are BSDFs not symmetric?Refraction (with improper formulation)Refracted rays need to be scaled by Phong shading (with regular angle measure)Shading normals (fake normals for shading, bump mapping,
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