Bidirectional scattering distribution function
The definitoin of the BSDF (Bidirectional scattering distribution function) is not well standardized. The term was probably introduced in 1991 by Heckbert. Most often it is used to name the general mathematical function which describes the way that light is scattered by a surface. However in practice this phenomenon is usualy split into the reflected and transmitted components, which are then treated separately as BRDF (Bidirectional reflectance distribution function) and BTDF (Bidirectional transmittance distribution function).
- BSDF is a superset and the generalization of the BRDF and BTDF. The concept behind all BxDF functions could be described as a black box with the inputs being two angles, one for incomming (incident) ray and the second one for the outgoing (reflected or transmitted) ray. The output of this black box is the value defining the ratio between the incomming and outgoing light energy for the given couple of angles. The content of the black box may be a mathematical formula which more or less acurately tries to model and aproximate the actual surface behavior or an algorithm which produces the output based on discrete samples of measured data. This implies that the function is 4 + 1 dimensional (4 values for 2 3D angles + 1 for wave length of the light), which means that it cannot be simply represented by 2D and not even by a 3D graph. Each 2D or 3D graph, sometimes seen in the literature, shows only a slice of the function.
- The term BSDF is sometimes used in a slightly different context, for the function describing simply the amount of the scatter as a function of incident light. To illustrate this context, for perfectly lambertian surface the BSDF(angle)=const.
- Another recent usage of the term BSDF can be seen in some 3D packages, when vendors use it as a 'smart' cathegory to encompass the simple well known cg algorithms like Phong, Blinn etc.
Overview of the BxDF functions:
- BSDF (Bidirectional scattering distribution function) is the most general function.
- BSSRDF (Bidirectional surface scattering reflectance distribution function) describes the relation between outgoing radiance and the incident flux.
- BRDF (Bidirectional reflectance distribution function) is a simplified BSSRDF, assuming that light enters and leaves at the same point. (see the image on the right).
- BTDF (Bidirectional transmittance distribution function) is similar to BRDF but for the oposite side of the surface. (see the image above).