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7.9 A Physical Reflection Model
The manner in which we have calculated the reflection of light on a surface be-
fore this point is computationally cheap and produces visually pleasing results in
many cases, but it is not an accurate model of the physically correct distribution
of reflected light. Achieving greater realism requires that we use a better model
of a surface's microscopic structure and that we apply a little electromagnetic
7.9.1 Bidirectional Reflectance Distribution Functions
In general, our goal is to model the way in which the radiant energy contained in
a beam of light is redistributed when it strikes a surface. Some of the energy is
absorbed by the surface, some may be transmitted through the surface, and what-
ever energy remains is reflected. The reflected energy is usually scattered in eve-
ry direction, but not in a uniform manner. A function that takes the direction L to
a light source and a reflection direction R , and returns the amount of incident
light from the direction L that is reflected in the direction R is called a bidirec-
tional reflectance distribution function (BRDF).
The precise definition of a BRDF requires that we first introduce some ter-
minology from the field of radiometry , the study of the transfer of energy via
radiation. The radiant power (energy per unit time) emitted by a light source or
received by a surface is called flux and is measured in watts (W). The power
emitted by a light source or received by a surface per unit area is called flux den-
sity and is measured in watts per square meter (
). The flux density emitted
by a surface is called the surface's radiosity , and the flux density incident on a
surface is called the irradiance of the light.
Figure 7.17 illustrates a situation in which a light source is emitting P watts
of power toward a surface of area A . The power received by the surface is equal
to the power emitted by the light source, but the flux densities received and emit-
ted are different because of the Lambertian effect. The area of the beam is equal
NL , where N is the unit surface normal and L is the unit direction-to-light
vector. The flux density Φ E emitted by the light source is thus given by
NL .
Since the flux density Φ I incident on the surface is equal to P A , we have the
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