Radiance Transfer - The Magic of Computer Graphics - page 367

the precomputed motion clips. The precomputed orbits therefore have to be care-
fully chosen and properly indexed for easy lookup in order to give the ability to
handle run-time user interactions. The method described in the paper precom-
putes a number of simple deformation actions expected to be representative of
those applied by the user at run time. Such an action is described as an impulse
response . The idea is that a sudden action is performed at one time step, and
this is followed by a persistent forcing action constant in subsequent time steps.
The initial action is an impulse force (or collection of forces) denoted by

I ;the

α

F . In the cloth hanging on the door ex-
ample, the impulse action pushes the door, and the persistent forcing includes the
air resistance on the cloth and effect of inertia (angular momentum) as the door
swings.
An impulse response on a particular state results in an orbit of sequential
states. Starting from the initial state

persistent forcing state is denoted by α

I

x , the impulse force α is applied first, and

then the state is integrated through the remaining T − 1 time steps under the per-

F . This set of states (the orbit) is denoted by an impulse response

sistent forcing α

function (IRF),

I F ; T

ξ ( x , α , α ) , (10.14)

where T is the number of time steps. The IRF orbit is the set of states through
which the system passes. Figure 10.22(a) illustrates an impulse response orbit
schematically, where the state consists of a reduced displacement vector q and
the associated velocity vector q . The method described in the paper precomputes
a collection of IRF orbits to be used at run time. As Equation (10.14) suggests,
the IRF orbits are indexed by the initial state x and the two system parameters

F . An important part of the precomputation is the selection of a set of
representative impulse responses. The method uses a set of impulse response pairs
( α

I and

α α

i i

D for some fixed D , which the authors call an impulse
palette . This impulse palette represents a set of deformation actions the user
may take. Keeping the number D small bounds the precomputation requirements,
although it also limits the range of possible user interactions.
From the standpoint of run-time processing, an IRF is just a time series of
precomputed values that describe the displacement of each sequential state. Once
an impulse is specified by an index from the impulse palette, the system switches
to a nearby IRF of that type and continues to look up the precomputed values
until it either reaches the end or is interrupted by another impulse. When a new
impulse is applied, the system simply blends the time series of the old and new
IRFs. Figure 10.22(b) illustrates a special case where the initial and persistent
forces have the same value

, α ) , with i = 1 , 2 ,...,

, and suggests how the set of orbits can in a sense be
parameterized to respond to different user actions.

α