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In-Depth Information
sion governing surface reflection (although it does not account for transmission
or subsurface scattering).
1.2.5 Types of Reflection
The notion of a BRDF is an abstract framework for surface reflection. For prac-
tical rendering, explicit representations for BRDFs are needed. Such a represen-
tation can be constructed from actual measurements taken from real surfaces, but
most often a BRDF is expressed as a mathematical formula known as a
reflection
model
or
BRDF model
.
Surface reflection can be categorized into two basic types:
diffuse
and
specu-
lar
. Diffuse reflection occurs when incoming light is scattered, or diffused, uni-
formly in all directions. A diffusely reflecting surface looks about the same from
any viewpoint, because the reflected radiance is essentially constant. In contrast,
specular reflection is directionally dependent. Light incident on a specular surface
is reflected most strongly near the direction of mirror reflection, which makes the
object appear shiny or glossy.
In ideal diffuse reflection, which is also known as
Lambertian reflection
,the
radiance
L
r
(
reflected from a surface point
x
is identical in all directions in the
x
)
is proportional
to the radiant exitance (radiosity) at
x
, which is in turn proportional to the surface
irradiance at
x
. The fraction of irradiance that is reflected as radiant exitance is
known as the
albedo
,definedby
x
)
L
r
(
x
)(
n
·
ω
)
d
ω
B
(
x
)
L
r
(
x
)
π
Ω
ρ
d
(
x
)=
)
=
=
)
.
(1.12)
E
(
x
E
(
x
)
E
(
x
The integral in the numerator is the radiant exitance, computed as in Equation (1.6)
but with the incident radiance term
L
i
(
x
)
replaced with the reflected radiance
L
r
(
x
)
. Because
L
r
(
x
)
is constant, it factors out of the integral. The factor of
π
·
ω
=
over the hemisphere.
A surface that exhibits purely Lambertian reflection is said to be a
Lambertian
surface
.
is the result of integrating the value of
n
cos
θ
It follows from Equation (1.12) that the BRDF of a Lambertian sur-
face is
)=
ρ
d
(
x
)
f
r
,
d
(
x
(1.13)
π
and thus depends only on the surface position.
Ideal or perfect specular reflection (also known as
mirror reflection
) is exhib-
ited by a perfectly smooth surface, such as a mirror
(
Figure 1.7(b)
)
.
