Graphics Reference
In-Depth Information
α
F
α
F
2
3
α
F
α
F
α
F
α
I
α
1
q
q
x
q
q
(b)
Figure 10.22
(a) An impulse response function (IRF) and (b) an impulse response function where the
initial and persistent forces are the same. (From [James and Fatahalian 03] c
(a)
2003 ACM,
Inc. Included here by permission.)
10.3.3 Model Reduction
One problemwith general deformablemodels is the large number of points needed
to accurately describe their shape. This is a serious impediment to the precompu-
tation scheme in which the IRF orbits are indexed by state vectors, as state vector
can have thousands of components. The authors therefore had to find a way of
reducing the complexity of the deformable models without losing too much free-
dom in deformation.
4
The deformation model reduction uses information obtained from a collection
of simulations. As described above, each time step in a simulation is represented
by a state vector
x
t
, which consists of the 3D position and velocity vectors of all
points in the deformation model:
x
t
v
1
,
v
1
,...,
v
t
M
,
v
t
M
)
,
=(
where
v
denotes the velocity vector, and there are
M
points in the model. Each
position vector
v
i
represents a position on the model in a particular deformation
state; subtracting the corresponding position in a representative shape produces
a displacement vector
u
t
. The collection of
M
displacement vectors for a set of
simulated states can be arranged into a data matrix
⎡
⎤
u
1
u
1
u
1
...
⎣
.
.
.
⎦
.
.
.
u
1
u
2
u
N
A
u
=[
···
]=
u
M
u
M
u
M
...
4
The general problem of deformable model reduction has been well studied, and various reduction
methods exist. For example, an interesting general method was recently proposed in the paper “Skip-
ping Steps in Deformable Simulation with Online Model Reduction” by Theodore Kim and Doug L.
James [Kim and James 09].
