Graphics Reference
In-Depth Information
ticular, they solve the problem of interactions of diffuse light in a closed environment
in a theoretical way. The theoretical foundation of the radiosity method lies in the
theory of heat transfer or exchange between surfaces and the conservation of energy.
It involves radiometry and transport theory. Because the radiosity method is techni-
cally rather complicated, all we shall do in the next two sections is sketch its overall
strategy and implementation. The interested reader is directed to [CohW93],
[FVFH90], [WatW92], [CohG85], or [CCWG88] for more details.
If we assume perfect diffuse (Lambertian) surfaces, then the rate of energy leaving
a surface (the radiosity) is equal to the sum of the self-emitted energy and the ener-
gies that came as reflections from other surfaces. This leads to an equation for the
radiosity function B(
p
) at a point
p
of the form
Ú
()
=
()
+
()
() (
)
BE
pppq
r
BG A
,
q
,
(10.3)
s
where
E(
p
) is an emitted light function,
r(
p
) is a diffuse reflectivity function,
G(
p
,
q
) is a function of the geometric relationship between
p
and
q
, and
the integration is over all surfaces in the environment.
Equation (10.3) is called the
Radiosity equation
. It is a special case of the rendering
equation (9.12).
If we now subdivide all surfaces into patches A
i
over which the radiosity and
emitted energy are essentially constant with constant value B
i
and E
i
, respectively,
then equation (10.3) leads to the following equation relating the B
i
:
n
Â
BA
=
EA
+
r
BF A
,
(10.4)
ii
ii
i
j i j
j
=
1
where
E
i
is the light emitted from the ith patch,
r
i
is the reflectivity of the patch, namely, the fraction of the light that arrives at
the patch that is reflected back into the environment, and
F
ji
is the fraction of the energy leaving the jth patch which reaches the ith patch.
The factors F
ji
are called
form factors
and are assumed to depend only on the geom-
etry of the surfaces in the environment. In fact, using the identity
FA
=
F A
(10.5)
ij
i
ji
j
equation (10.4) reduces to
n
Â
BE
=+
r
BF
(10.6)
i
i
i
j
ij
j
=
1
Solving for the B
i
reduces to solving a system of linear equations that looks like
