University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell

Measurement Equation Ray space (throughput) measure for bundle of rays r Define F space of functions over ray space F is a Hilbert space A linear operator is a linear mapping University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell

Measurement Equation Imagine a sensor anywhere in the scene It has a response to its input So a measurement is Light paths start with an emitter and end at a measurement Can also do paths in reverse, measurement to light Call the quantity transported in reverse importance University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell

Importance transport Importance transport requires adjoint operators for each light transport operator The adjoint of an operator is its conjugate-transpose, defined wrt some inner product We’d like our transport operators to be self-adjoint Light transport and importance transport would be the same Photon tracing, reverse path tracing, etc all kinds of importance tracing University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell

Non-symmetric BSDFs When are transport operators not self adjoint? When the BSDF they use is not symmetric When 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, etc) University of Texas at Austin CS395T - Advanced Image Synthesis Spring 2006 Don Fussell