SIGGRAPH Talks 2014
The simplicity and performance of analytic diffusion-based BSSRDFs has led to their widespread adoption for rendering translucent materials. These approaches yield fairly accurate spatial bleeding of light within a material, but the angular variation of this energy is not well predicted by these models. We present a new approach for efficient rendering of translucent materials that reinterprets previous approaches as an approximate application of a theorem from neutron transport literature in the 1950s. In addition, we formulate both the incidence and exitance from the medium as beams and move away from the limitations of diffusion theory at boundaries and instead focus on producing accurate densities everywhere inside the material. The derivation is closely coupled to the associated BRDF for the material and the final exhibits accurate angular behaviour, allowing the model to form seamless transitions between explicit volumetric scattering up close, and BRDF approximations for distance materials. The result is the first semi-analytic reciprocal 8D BSSRDF that is validated against closed-form half-space benchmark solutions.
I recommend these slides for additional explanation of Placzek’s Lemma.