Game Development Reference
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Homogenous material
No surface scattering
Bidirectional Texture
Function (BTF)
Bidirectional Surface-Scattering
Distribution Function (BSSDF)
Fixed light
Fixed shot
Fixed position
No surface
Bidirectional Reflectance Distribution
Function (BRDF)
Luminance field
Reflectance field
Flat and diffuse
2D Texture
Isotropic BRDF
Figure 15.2 Hierarchy of reflectance functions
takes us close to the concept of phase function which defines the behaviour of a
participating environment (non-surface component like gas or vapour) vis-à-vis light
scattering (Glassner, 1995). The BRDF characterises the surfaces, whereas the phase
function characterises the volumes. A modelling approach valid for the BRDF can
naturally apply to the BTDF, BSDF or the phase function, if it is not specific from a
physical point of view.
To conclude, it is necessary to mention that in first approximation, the BRDF sup-
poses that the light energy incident on a point x of a surface is reflected from the same
point. In fact, a fraction of the light generally penetrates inside the material, is reflected
within the microscopic structure of the material and is reflected outside the surface only
at a point more or less away from x . Nonetheless, if we consider these microscopic
phenomena as completely unpredictable, approximation of the unique point is macro-
scopically exact since the energy penetrating the surface and then coming out of it
is distributed uniformly on the surface. However, this type of simplification is inade-
quate to get a perfect modelling of certain types of materials (for example, translucent).
We thus introduce the Bidirectional surface scattering reflectance distribution function
(BSSRDF) (Nicodemus et al., 1977) which includes this discrepancy between the inci-
dent point and reflection point. This function was used only recently in image synthesis
due to its complexity. We can quote Jensen et al. (2001), Jensen and Buhler (2002),
Dorsey et al. (1999), Hanrahan and Kruegar (1993), and Pharr and Hanrahan (2000),
all of which are works related to the problem of light scattering under the surface of a
Classification of BRDF models
The research of a typology of different BRDF models, i.e. the study of their charac-
teristics and classification attracted more geophysicists than image synthesis experts.
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