Game Development Reference
In-Depth Information
hand, this approach is compatible with the graphical API such as OpenGL (Segal &
Akeley, 2004) and DirectX used for real time rendering.
On the other hand, as we will see in section 15.2.2.2, a number of simplifications
can be made to offer best quality images in real time.
The calculation of lighting in the space of a scene is less used in virtual reality and
is often seen as a pre-processing of global illumination calculation in stationary scenes
and in walkthrough type of applications. This surface formula, as we will see it in
section 15.2.2.1, can also be used directly in radiosity algorithms for instance, or even
in methods based on the estimation of density to offer a reconstruction of lighting in
the space of a scene, directly on the meshes or in the form of textures.
15.2.2.1 Global illumination and virtual reality
The method of radiosity is the first physically realistic approach to have tried resolv-
ing the rendering equation (Goral et al., 1984). Strong hypotheses were necessary to
simplify the problem considerably:
Isotropic and homogenous light sources
Perfectly diffuse surfaces
In this manner, the directional component of the rendering equation is deleted:
f r ( x ) L i ( x ) g ( x , x ) v ( x , x ) dA
L r ( x )
=
L e ( x )
+
x
Moreover, we can note that for a diffuse surface, the luminance is in fact equal to
radiosity divided by a factor π (due to the integration in all directions). For the record,
the energy emitted by a unit surface is called exitance and not radiosity (we will mark
it by E ). Similarly, the BRDF is equal to the reflectance divided by a factor π , thus
constant. It can be removed from the integral, therefore for a fixed wavelength:
ρ ( x )
π
B ( x ) g ( x , x ) v ( x , x ) dA
B ( x )
=
E ( x )
+
(15.11)
x
By grouping g , v and the factor π together, we obtain the geometrical core :
g ( x , x ) v ( x , x )
π
K ( x , x )
=
(15.12)
ρ ( x )
x
B ( x ) K ( x , x ) dA
B ( x )
=
E ( x )
+
(15.13)
This equation is generally solved by the finite elements method and particularly by the
Galerkin method (base of orthogonal functions).