Game Development Reference
Explicitly calculated direct lighting;
Approximated indirect lighting
These assumptions make it possible to model the lighting for real time rendering
applications using the following equation:
br df ( x , ω l , ω r ) rgb g ( x , l ) Li rgb ( ωl ) rgb
L r ( x , ω r ) rgb
br df ( x , ω i , ω r ) rgb Li ( ω i ) rgb cos( θ i ) dω i
N l is the number of light sources potentially visible from x ;
g ( x , l ) is the visibility function between the source l and point x ;
L i ( ω ) is the incident luminance in direction ω ;
... is the term of global illumination;
is the space visible from point x .
The term global illumination of this equation can be modelled or calculated in different
ways depending on the constraints of application and calculation time allotted to the
rendering phase. This term also has a considerable influence on the quality of images
obtained. The most basic representation of this term, but which also requires the least
amount of resources, is fixing a constant ambient colour. We thus obtain the expression
of the lighting model used by the APIs of real time rendering OpenGL (Segal &Akeley,
2004) and DirectX. This approximation, thanks to its simplicity, is most widely used
in the currently available virtual reality applications.
The increase in the capacity of central processors and graphics processors has
helped to reduce the complexity of the representation of this term of global illumina-
tion. The first approaches were based on the use of environment textures (Heckbert,
1990; Zhukov et al., 1998). These approaches make it possible to represent a direc-
tional distribution of colour and allow the simulation of the illumination of an object
by its environment, provided that the environment is relatively far from the object
being lit. The concept of environment texture can also be used to represent any func-
tion for a discretisation of the space of directions. These environment textures can thus
be obtained after a long pre-calculation stage (Sloan et al., 2002; Sloan et al., 2003;
Kristensen et al., 2005), calculated rapidly by simplified global illumination methods
(Larsen & Christensen, 2004) or can be fixed all at once on starting the application.
Even direct illumination, responsible for the most perceptible part of the light-
ing of a scene, is also modelled in different manners depending on the applications.
The models thus cover a large range of effects, from the non-realistic approaches
(Winkenbach & Salesin, 1994; Decaudin, 1996; Kowalski et al., 1999; Eissele, 2003),
trying to bring out a global impression of the object rather than an exact represen-
tation, to the most developed models using complex BRDF (Blinn, 1977; Cook &
Torrance, 1982; Heidrich & Seidel, 1999; Kautz & McCool, 1999).
Several approaches of real-time rendering represent the BRDF by a set of 2D
textures (McCool et al., 2001; Kautz et al., 2002).