Game Development Reference

In-Depth Information

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

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.

15.2.1.2 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

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