Game Development Reference
We can also talk of an analytical approach in the mathematical sense of the term since
these models finally provide an equation of the BRDF.
Using a reverse approach on these models creates an interesting problem. It in fact
uses them, not to predict a BRDF on the basis of their physical parameters, but rather
to deduce them using a BRDF measurement.
In most of the cases, the measurement of the physical parameters is in fact
extremely difficult, or even impossible, to implement. It is thus preferable to use a
BRDF measurement (even limited) which can be much simpler to take. When it is
possible to use the direct and reverse approach at the same time, the procedure of
validation is extremely rigorous (Verstraete et al., 1990).
The strategy to develop such a model can be statistical or purely empirical.
Statistical study presents the global phenomenon observed at a scale higher than the
description of the surface. Here the surface is represented by a distribution of sim-
ple geometric components like plane surfaces, spheres, cylinders, etc. The empirical
approach consists of a statistical adjustment carried out on a series of observations.
This approach is part of a scope of validity defined by the initial data (for example, veg-
etation cover or desert surfaces). Applying these models to situations that are variable
or new compared to those used to define them is unrealistic.
This group includes the main models used in image synthesis and virtual reality.
They include, among others, the models by Lambert for diffuse materials or models by
Phong (1975), Blinn (1977), Cook and Torrance (1982), Lewis (1993) and Ashikhmin
and Shirley (2000) for more realistic materials.
Projective models attempt to use effective digital mathematical methods to optimally
represent the set of BRDF measurements. For this purpose, these models transform
this set into another space to make its manipulation more effective in terms of memory
and/or performance. Generally, it involves a projection on a collection of arbitrarily
selected functions. This approach lies in a pure mathematical abstraction of the BRDF.
It signifies that the parameters of the model have no physical or intuitive sense. This
means that it is impossible to use such a model directly.
We can also observe that a projective model is very often used along with a virtual
goniometer. In fact, assessing the surface's response is very expensive. It is thus pre-
calculated all at once and then stored as optimally as possible.
This group of models is currently being used more and more frequently in image
synthesis and virtual reality because thesemodels make it possible to efficiently consider
measured complex materials and are suitable for encoding the result of global illumi-
nation models, which we will discuss in section 15.2.2. Works conducted by McCool
et al. (2001), Kautz et al. (2002), and Kautz and McCool (1999) on factorisation of
BRDF can be mentioned as examples in this field.
188.8.131.52 Textures and Bidirectional texture functions
The functions of bidirectional reflectance characterise the behaviour of a material
vis-à-vis an incident light. However, these functions do not depend on the position on
the surface and are limited to the representation of homogenous materials. Modelling