Graphics Reference
In-Depth Information
Wavelet
basis function
Cube
Spherical
mapping
Figure 10.18
One approach to wavelet approximation on the sphere is to project a spherical function
onto a concentric cube, then expand the projected function on each face of the cube. Envi-
ronment maps are often represented as faces on a cube.
an environment map; the object itself is assumed to be stationary and rigid.
Re-
lighting
is the process of recomputing the appearance of the object under a dif-
ferent environment map. This is a more restricted problem than the general PRT
problem, in which the viewpoint can change.
The basic reflectance integral given in Equation (10.3) provides a formula for
the directly reflected radiance in direction
v
from a surface sample point
p
i
:
R
(
p
i
,
v
)=
L
(
s
)
V
(
p
i
,
s
)
f
(
p
i
,
s
,
v
)
d
s
.
(10.11)
Ω
4π
The function
f
(
p
i
s
,
v
)
is the cosine-weighted BRDF, and
L
(
s
)
is the incident radi-
ance in direction
s
. As usual, the environment map is sufficiently distant that the
incident radiance
L
does not depend on the surface position. If a set of
N
direc-
tional samples
s
j
are chosen, then the reflectance integral of Equation (10.11) can
be approximated by summing the integrand over the sample points
4
N
∑
j
L
(
s
j
)
R
(
p
i
,
v
)
≈
V
(
p
i
,
s
j
)
f
(
p
i
,
s
j
,
v
)
(10.12)
l
j
a
ij
(the constant factor 4
π
/
N
is hereafter omitted). The
L
(
s
j
)
factor depends on the
lighting;
V
v
is fixed.
Denoting the former by
l
j
and
a
ij
for the latter, Equation (10.12) becomes
(
p
i
,
s
j
)
f
(
p
i
,
s
j
,
v
)
can be precomputed, as the view direction
r
i
=
∑
j
R
(
p
i
,
v
)
≈
l
j
a
ij
which can be written as a matrix product
A
l
r
=
(10.13)
