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{{Short description|Mathematical function}}
The definition of the '''BSDF''' ('''bidirectional scattering distribution function''') is not well standardized. The term was probably introduced in 1980 by Bartell, Dereniak, and Wolfe.<ref name=bartell1980>{{cite journal
|last1=Bartell
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|year=1980|series=Radiation Scattering in Optical Systems
|s2cid=128406154
|url-access=subscription
</ref> Most often it is used to name the general mathematical function which describes the way in which the light is scattered by a surface. However, in practice, this phenomenon is usually split into the reflected and transmitted components, which are then treated separately as '''BRDF''' ('''[[bidirectional reflectance distribution function]]''') and '''BTDF''' ('''bidirectional transmittance distribution function''').
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* '''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 any two angles, one for incoming (incident) ray and the second one for the outgoing (reflected or transmitted) ray at a given point of the surface. The output of this black box is the value defining the ratio between the incoming and the outgoing light energy for the given couple of angles. The content of the black box may be a mathematical formula which more or less accurately tries to model and approximate 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 optional for wavelength 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.
* Some tend to use the term '''BSDF''' simply as a category name covering the whole family of BxDF functions.
* The term '''BSDF''' is sometimes used in a slightly different context, for the function describing the amount of the scatter (not scattered light), simply as a function of the incident light angle. An example to illustrate this context: for perfectly [[Lambertian reflectance|lambertian surface]] the BSDF (angle)=const. This approach is used for instance to verify the output quality by the manufacturers of the glossy surfaces.{{clarify|date=November 2012}}
* Another recent usage of the term '''BSDF''' can be seen in some 3D packages, when vendors use it as a 'smart' category to encompass the simple well known cg algorithms like [[Phong reflection model|Phong]], [[Blinn–Phong reflection model|Blinn–Phong]] etc.
* Acquisition of the BSDF over the [[human face]] in 2000 by [[Paul Debevec|Debevec]] et al.<ref name="Deb2000">{{cite book
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