Graphics Reference
In-Depth Information
Cluster center
(representative state)
Cluster
Static simulation trajectory
Figure 10.25
Global illumination precomputation state (schematic representation).
precomputed. Ideally, the reduced appearance model would be constructed from
a full PRT computation on all the precomputed deformation states. Besides be-
ing too costly, in practice it is not necessary because of the redundancy in the
appearance of similar shapes. The reduction of the appearance model therefore
starts with the simpler problem of computing radiance transfer vectors only at the
reduced shape coordinates rather than at every point on the shape model. Also,
PRT is applied to a small subset of all the precomputed shapes.
The reflection is assumed to be diffuse, so the PRT transfer matrices reduce
to vectors (see Section 10.1.2). The transfer vectors at all the sample points in
a particular shape (deformation state) are concatenated into a single vector. The
radiance transfer is precomputed for a subset of deformations, which are interpo-
lated across the IRF orbits. The interpolation uses
radial basis functions
,which
are suitable for high-dimensional scattered data interpolation. The resulting set of
PRT vectors is then clustered using the
k
-means algorithm (see Section 7.2.2), and
model points, or mesh. This process results in a collection of properly computed
PRT vectors for a set of shapes across an IRF orbit.
The
N
a
PRT vectors are collected into the columns of a matrix
A
u
:
⎡
⎣
⎤
⎦
X
p
1
X
p
1
X
N
a
p
1
...
.
.
.
.
.
.
X
1
X
2
X
N
a
A
a
=[
···
]=
X
p
s
X
p
s
X
N
a
p
s
...
on which principal component analysis is applied. Element
X
p
i
of
A
u
represents
the radiance transfer vector at point
p
i
on shape
j
(with the mean subtracted); each
is actually a vector of dimension 3
sn
2
,where
s
is the number of surface points,
and
n
is the order of the SH approximation. The SVD is used to extract represen-
tative basis elements in the same way as in the deformation model reduction. The
result is a set of
reduced appearance coordinates q
a
,...,
q
N
a
which correspond to
points on the model surface where the radiance transfer is most significant. The
