Graphics Reference
In-Depth Information
1.3 Area Lighting Model
1.3.1 Radiometric Integrals and BRDF Definition
In this section we introduce basic radiometric quantities such as light intensity,
irradiance, and radiance [Pharr and Humphreys 04]. Then, we define radiometric
integrals essential to solving area lighting models.
Let
intensity
be defined as the light flux density per solid angle:
I
=
dφ
dω
,
where
dφ
is the light flux differential and
dω
is the solid angle differential. Inten-
sity is meaningful only for a point light source.
Irradiance
defines the total amount of light flux per area:
E
=
dφ
dA
,
where
dA
is the differential area receiving light flux.
Radiance
describes the light flux density per unit area, per unit solid angle:
dφ
dωdA
⊥
L
=
,
where
dA
⊥
is the projected area of
dA
on a hypothetical surface perpendicular
to the solid angle.
We also define radiance emitted
L
o
(
p,ω
) and incoming
L
i
(
p,ω
) to a point on
a surface as a function of the point and direction.
Irradiance at point
p
with normal vector
n
would be defined as
E
(
p,n
)=
L
i
(
p,ω
)
cosθdω,
H
2
(
n
)
where cos
θdω
is the projected solid angle
dω
⊥
, with
θ
the angle between
ω
and
the surface normal
n
. This term comes from the definition of radiance. In other
words, this equation integrates incoming light from all directions on a hemisphere,
around a point of integration with a given normal, with respect to the projected
solid angle.
A
bidirectional reflectance distribution function
(BRDF) defines a ratio of the
light reflecting from a surface point, in the viewer's direction, and the amount of
light incoming to a surface from a specific direction. Therefore, a basic definition
of BRDF is
f
r
(
p,ω
o
,ω
i
)=
dL
o
(
p,ω
o
)
dE
(
p,ω
i
)
.