Game Development Reference
Figure 15.1 Local reference point on the surface of an object, z represents the local normal
At the macroscopic level, this interaction can be defined by functions of dimensions
that vary as per the phenomena we wish to take into account. These macroscopic
functions define a group of models that can be used in virtual reality (figure 15.2). The
most representative of these are texture-based models and BRDF models.
126.96.36.199 Bidirectional ref lectance distribution function
In simple words, the Bidirectional Reflectance Distribution Function (BRDF) describes
the reflection of a light wave on a surface. The initial radiometric definition was given
by Nicodemus et al. (1977). For an incident or illumination direction ω i and a reflection
or observation direction ω r , 2 the BRDF is the ratio of luminance reflected at a point
x of an infinitesimal surface of area dA at the illumination incident on this surface.
Generally, the BRDF is expressed for the local reference point on the surface formed
by the normal to x and two orthogonal tangent vectors (figure 15.1). The directions
are marked using their spherical coordinates in this reference point:
dL r ( x , θ r , φ r , λ )
L i ( x , θ i , φ i , λ ) cos θ i dω i
f r ( x , ω i , ω r , λ )
f r ( x , θ i , φ i , θ r , φ r , λ )
The BRDF characterises the reflection of surfaces, i.e. the behaviour of materials that
reflect a part of the incident light energy and absorb or transmit the remaining energy.
It is thus defined on the upper hemisphere H 2
surrounding point x .
Nevertheless, it is possible to characterise transparent materials by defining
the Bidirectional transmittance distribution function (BTDF) in the same manner
(Nicodemus et al., 1977). BTDF is defined on the lower hemisphere H _ at point x .
The two functions can be grouped together to form a single function defined on
sphere S 2 surrounding the point x , making it possible to characterise semi-transparent
materials. It will be called Bidirectional scattering distribution function (BSDF). This
2 These are incoming light direction ω i and outgoing light direction ω r .