# Bidirectional reflection distribution function

A **bidirectional reflectance distribution function** ( English **Bidirectional Reflectance Distribution Function** , **BRDF** ) provides a function for the reflection behavior is of surfaces of a material under arbitrary angles of incidence. It provides for each of the material impinging light beam having a given entry angle the ratio of irradiance and irradiance for each emergent light beam. BRDFs are used, among other things, in realistic 3D computer graphics , where they represent part of the fundamental rendering equation and serve to represent surfaces as realistically and physically correct as possible. A generalization of the BRDF on textures , the BTF *( Bidirectional Texturing Function )* is.

A BRDF is very complex, depending on the selected accuracy: It can be determined, for example, for all angles of incidence / reflection (4-dimensional), for every wavelength (5-dimensional) or for every point on the surface (7-dimensional). Because of this complexity, simple models are mostly used as BRDFs in computer graphics.

Formula:

There are basically 2 approaches to represent the BRDF values:

- explicit storage of the ordered measured values or simulation results ( e.g. obtained by a gonioreflectometer ),
- high storage space requirements with simple storage in finely divided samples,
- high expenditure of time and hardware for data acquisition,
- poorly suited for importance sampling ,
- important for verification tasks,

- Approximation through analytical functions ( local lighting models ).

## Physically correct BRDF

The BRDF of a real object must also have the following properties:

- Positivity:
- fulfills the Helmholtz reciprocity:
- Energy conservation:

## See also

## Web links

- FE Nicodemus, JC Richmond, JJ Hsia, IW Ginsberg, T. Limperis:
*Geometrical Considerations and Nomenclature for Reflectance.*US Dept. of Commerce (1977) - original definition. (PDF; 5.33 MB) - N. Gebhardt:
*Some BRDF models.*(PDF; 1.27 MB)