Graphics Reference
In-Depth Information
π
2π/3
A
l
π/4
0
0
1
2
l
Figure 7.10
The SH coefficients for the clipping geometry term
A
drop to zero very quickly; the first
three terms (through
l
=
2) provide a sufficient approximation.
(Courtesy of Ravi Ra-
mamoorthi.)
which the global coordinate axes are labeled
x
,
y
,and
z
; the local axes are labeled
x
,
y
,
z
(
n
has the same direction as
z
). The coordinate systems are related by
a linear transformation. Each SH basis function
Y
l
,
m
(
θ
,
φ
)
is expressed in terms
of sines and cosines of
θ
and
φ
, and can therefore be expressed as a polyno-
L
(θ
i
,
φ
i
)
z
→
Z
'
θ
i
Y
'
Ω
'
X
'
θ
y
φ
x
Figure 7.11
The SH approximation to the environment map radiance
L
is in a global coordinate system,
with axes labeled
x
,
y
,and
z
. The irradiance needs a local coordinate system coincident
with the surface normal
n
. (After [Ramamoorthi and Hanrahan 01b].)
