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 =
,
where is the light flux differential and 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 =
dA ,
where dA is the differential area receiving light flux.
Radiance describes the light flux density per unit area, per unit solid angle:
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 , 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 i )= dL o ( p,ω o )
dE ( p,ω i ) .
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