Game Development Reference

In-Depth Information

z

dL
i

ω
i

u
i

u
r

L
i

ω
r

d

ω
i

y

x

ϕ
i

dA

ϕ
r

x

Figure 15.1
Local reference point on the surface of an object,
z
represents the local normal

At the macroscopic level, this interaction can be defined by functions of dimensions

that vary as per the phenomena we wish to take into account. These macroscopic

functions define a group of models that can be used in virtual reality (figure 15.2). The

most representative of these are texture-based models and BRDF models.

15.2.1.1 Bidirectional ref lectance distribution function

In simple words, the Bidirectional Reflectance Distribution Function (BRDF) describes

the reflection of a light wave on a surface. The initial radiometric definition was given

by Nicodemus et al. (1977). For an
incident
or
illumination
direction
ω
i
and a
reflection

or
observation
direction
ω
r
,
2
the BRDF is the ratio of luminance reflected at a point

x
of an infinitesimal surface of area
dA
at the illumination incident on this surface.

Generally, the BRDF is expressed for the local reference point on the surface formed

by the normal to
x
and two orthogonal tangent vectors (figure 15.1). The directions

are marked using their spherical coordinates in this reference point:

dL
r
(
x
,
θ
r
,
φ
r
,
λ
)

L
i
(
x
,
θ
i
,
φ
i
,
λ
) cos
θ
i
dω
i

f
r
(
x
,
ω
i
,
ω
r
,
λ
)

=

f
r
(
x
,
θ
i
,
φ
i
,
θ
r
,
φ
r
,
λ
)

=

(15.1)

The BRDF characterises the reflection of surfaces, i.e. the behaviour of materials that

reflect a part of the incident light energy and absorb or transmit the remaining energy.

It is thus defined on the upper hemisphere
H
2

+

surrounding point
x
.

Nevertheless, it is possible to characterise transparent materials by defining

the Bidirectional transmittance distribution function (BTDF) in the same manner

(Nicodemus et al., 1977). BTDF is defined on the lower hemisphere
H
_ at point
x
.

The two functions can be grouped together to form a single function defined on

sphere
S
2
surrounding the point
x
, making it possible to characterise semi-transparent

materials. It will be called Bidirectional scattering distribution function (BSDF). This

2
These are incoming light direction
ω
i
and outgoing light direction
ω
r
.

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