Graphics Reference
In-Depth Information
Figure 10.24
Displacement basis vectors (deformation modes).
(From [James and Fatahalian 03]
c
2003 ACM, Inc. Included here by permission.)
Σ
u
, the columns of the product
by
q
u
=
Σ
u
V
u
=
q
u
q
u
···
Q
u
Σ
u
V
u
, each column of
≈
are thereby truncated to
k
components. Because
A
u
U
u
q
u
. The matrix
A
u
is thus approximated with
the linear combination of
Nk
-dimensional basis vectors
u
j
U
u
A
u
can be approximated by
≈
q
u
,whichis
a reduction from the 3
M
-dimensional vectors in the columns of
A
u
. The vectors
q
u
,
q
u
,...,
q
u
are the
reduced shape coordinates
, and correspond to representative points in
the deformation model.
The basis vectors correspond to the representative deformed shapes. Fig-
ure 10.24 illustrates three poses of a dinosaur model corresponding to three basis
vectors. In the above approximation, every possible shape generated in the de-
formation can be approximated by a linear combination of these representative
shapes. The basis vectors are constant; only the weight changes along the time.
Therefore, a coefficient vector
q
u
can be thought as a
reduced shape coordinate
,
the computation of the dynamic precomputation or run-time simulation can thus
be performed using
q
u
instead of a displacement field vector.
10.3.4 Appearance Model
Once the reduced dynamical system has been constructed, the precomputation
of an appearance model is performed using a low-dimensional approximation to
the diffuse radiance transfer under low-frequency lighting. Precomputed radiance
transfer can be used for this purpose, but doing so directly is too costly, as it
requires a separate precomputation for every possible state. In general, the ef-
fects of diffuse global illumination under low-frequency lighting do not change
notably unless the shape changes dramatically. Therefore the appearance model
is reduced in a manner similar to the reduction of the deformation model: a set
of representative appearance states is selected, on which the radiance transfer is
