The Signals and Systems Approach to Animation
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Animation is ubiquitous in visualization systems, and a common technique for creating these animations is the transition. In the transition approach, animations are created by smoothly interpolating a visual attribute between a start and end value, reaching the end value after a specified duration. This approach works well when each transition for an attribute is allowed to finish before the next is triggered, but performs poorly when a new transition is triggered before the current transition has finished. In particular, interruptions introduce velocity discontinuities, and frequent interruptions can slow down the resulting animation. To solve these problems, we model the problem of animation as a signal processing problem. In our technique, animations are produced by transformations of signals, or functions over time. In particular, an animation is produced by transforming an input signal, a function from time to target attribute value, into an output signal, a function from time to displayed attribute value. We show that well-known signal-processing techniques can be applied to produce animations that are free from velocity discontinuities even when interrupted.
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