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)

then the radiosity equation:

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).

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