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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

theory.

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 (

Wm
−

2

). 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

to

⋅

(

)

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

A

⋅

P

Φ
E

=

NL
.

(7.41)

(

)

A

⋅

Since the flux density Φ
I
incident on the surface is equal to
P A
, we have the

relation

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