Abstract—Photo realistic visualization of a huge number of individual filaments like in the case of hair, fur, or knitwear is a challenging task: Explicit rendering approaches for simulating radiance transfer at a filament get totally impracticable with respect to rendering performance and it is also not obvious how to derive efficient scattering functions for different levels of (geometric) abstraction or how to deal with very complex scattering mechanisms. We present a novel uniform formalism for light scattering from filaments in terms of radiance, which we call the Bidirectional Fiber Scattering Distribution Function (BFSDF). We show that previous specialized approaches, which have been developed in the context of hair rendering, can be seen as instances of the BFSDF. Similar to the role of the BSSRDF for surface scattering functions, the BFSDF can be seen as a general approach for light scattering from filaments, which is suitable for deriving approximations in a canonic and systematic way. For the frequent cases of distant light sources and observers, we deduce an efficient far field approximation (Bidirectional Curve Scattering Distribution Function, BCSDF). We show that on the basis of the BFSDF, parameters for common rendering techniques can be estimated in a non-ad-hoc, but physically-based way.