Graphics Reference
In-Depth Information
→
→
n
ω
'
ω
θ
'
d
ω
'
Figure 1.5
Notion of a bidirectional reflectance distribution function (BRDF). Radiance coming from
ω
(in differential cone) is reflected by the surface according to the BRDF function. The
shaded area shows the relative distribution of reflection intensity, which is often largest in
the direction of mirror reflection (in this figure the outgoing direction ω lies well away
from the mirror direction).
arbitrarily large if most of the light is reflected in one direction, such as the mirror
direction. This may also seem unintuitive, but it comes from the definition of
radiance as power (irradiance) per solid angle: if radiant power is concentrated in
a thin cone, the power per solid angle in the cone can be very large.
As the name suggests, a BRDF satisfies the property of
bidirectionality
:the
BRDF value remains the same if the incoming and outgoing directions are ex-
changed; i.e.,
,
ω
,
ω
)=
,
ω
,
ω
)
.
(1.8)
This means that light paths can be traced in the opposite direction that light would
normally travel. Some of the global illumination methods described in the coming
chapters rely on this property. BRDF bidirectionality is also known as
symmetry
.
A physically plausible BRDF must also satisfy energy conservation. For each
incoming direction
f
r
(
x
f
r
(
x
ω
, the total power output, computed by integrating the cosine-
weighted BRDF value in all directions on the hemisphere, cannot exceed the
power coming in from
ω
; i.e.,
,
ω
,
ω
)(
·
ω
)
ω
≤
f
r
(
x
n
d
1
(1.9)
Ω
ω
for each outgoing direction
.
This does not bound the BRDF
f
r
(
,
ω
,
ω
)
itself, but it does mean that it
can be large only on a commensurately small set of directions ω
x
so that total
