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at the silhouette. Of course, this only amortizes the incoherence, because there is
still a pop when the graftal is replaced. Previously discussed strategies such as
2D composition can then reduce the incoherence of the pop.
An open question in expressive rendering is the significance of temporal coher-
ence for large objects like strokes. On the one hand, we know that their motion
is visually distracting. On the other hand, films have been made with hand-drawn
cartoons and live-action stop motion in the past. There, the incoherence can be
considered part of the style and not an artifact. Classic stop-motion animation
involves taking still images of models that are then manually posed for the next
frame. When the stills are shown in sequence, the models appear to move of their
own volition because the intermediate time in which the animator appeared in the
scene to manipulate it is not captured on film.
35.4 Representations
We now talk about animation methods, the naming of parts of animatable models,
and alternatives among which one might choose to express the parameters and
computational model of animation.
The state of an animated object or scene is all of the information needed to
uniquely specify its pose. For animation, a scene representation must encompass
both the state and a parameterization scheme for controlling it. For example, how
do we encode the shape and location of an apple and the force of gravity on it?
As is the case in rendering, one generally wants the simplest representation
that can support plausible simulation of an object. For rendering, interaction with
light is significant, so the surface geometry and its reflectance properties must be
fairly detailed. For animation, interaction with other objects is significant, so prop-
erties like mass and elasticity are important. Animation geometry may be coarse,
and different from that used for rendering. A variety of animation representations
have been designed for different applications. This chapter references many and
explores particles and fluid boundaries in depth as case studies.
We categorize schemes for parameterizing, and thus controlling, state into key
poses created by an artist, dynamics simulation by the laws of physics, and explicit
procedures created by an artist-programmer. Many systems are hybrids. These
leverage different control schemes for different aspects of the scene to accommo-
date varying simulation level of detail or artistic control.
35.4.1 Objects
The notion of an object is a defining one for an animation system. For example,
by calling an automobile an “object” one assumes a complex simulation model
that abstracts individual systems. If one instead considers an individual gear as
an “object,” then the simulation system for an automobile is simple but has many
parts. This can be pushed to extremes: Why not consider finite elements of the
gears themselves, or molecules, or progress the other way and consider all traffic
on a highway to be one “object”?
The choice of object definition controls not only the complexity of the underly-
ing simulation rules, but also what behaviors will emerge naturally versus requir-
ing explicit implementation. For example, finite-element objects might naturally
simulate breaking and deformation of gears and bricks, whereas atomic gear
 
 
 
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