Graphics Reference
In-Depth Information
Secondary motion
is the motion of small parts of a figure relative to its root
motion; for example, the flowing of cloth and hair and the jiggling of muscle and
fat. Secondary motion is important to our perception of motion and performance,
but it is often inefficient to simulate as part of the entire system or explicitly pose.
Animators often develop special-case secondary motion simulators that create the
character of the motion detail without the full cost [PH06, BBO
+
09, JP02]. This
is analogous to modeling small-scale visual detail in texture instead of geometry.
It is often desirable to transfer an animation performance that was authored
or captured on one body to another body [BVGP09, SP04, BCWG09, BLB
+
08].
There are some cases where there is little choice but to transfer motion between
bodies. For example, to animate a centaur with motion capture, we must transfer
the motion from a human and a horse onto a single virtual creature. In other cases,
it is a matter of cost. Rather than recording the performance of actors of many
sizes wearing many costumes, with transfer we could record a single actor and
adapt the performance to multiple characters in a crowd [LBJK09].
Plausible animation
is the problem of working backward to compute the
start
state of a system, given the end state [BHW96, KKA05, YRPF09, CF00, TJ07,
MTPS04]. For example, a film shot may require a player to roll two sixes on a pair
of dice. We would like to start with the sixes facing up at the end of the shot, and
solve backward for a physically viable series of bounces as the dice roll that leads
them to that position. Since the problem may be overconstrained, we are willing to
accept any “plausible” solution in which the laws of physics are bent only in ways
that are imperceptible to the average observer. It is plausible for the momentum of
a die to be exaggerated by 5% to produce one extra tumble, but not for the die to
bounce three meters in the air off the initial throw.
The most straightforward way to represent poses is to specify a separate mesh
for each key frame. The mesh topology is usually constant over the animation so
that every key frame contains the same number of vertices. Only their positions
change, not their adjacency and ordering. To simplify the discussion, assume that
key poses
k
[
t
]
are defined at the ends of integers at time intervals, and that we want
to form a continuous expression for the pose at the fractional times
t
in between
these poses.
Sample-and-hold interpolation,
x
(
t
)=
k
[
t
]
,
(35.14)
produces substantial temporal aliasing. The character simply holds its position
until the end of the time period and then instantaneously snaps to the next pose.
This also produces infinite velocity at the frame intervals because
x
(
t
)
is discon-
tinuous.
We'd like to make smoother transitions with finite velocities. As we said
in the introduction, one solution is to linearly interpolate between key poses,
which produces continuous positions but discontinuous velocity. That is, we've
ensured
C
0
continuity but still exhibit infinite acceleration, which is unnatural
for character motion. A higher-order interpolation scheme can produce smoother
