Animating oscillatory motion with overlap

Oscillatory motion is ubiquitous in computer graphics, yet existing animation techniques are ill-suited to its authoring. We introduce a new type of spline for this purpose, known as a "Wiggly Spline." The spline generalizes traditional piecewise cubics when its resonance and damping are set to zero, but creates oscillatory animation when its resonance and damping are changed. The spline provides a combination of direct manipulation and physical realism. To create overlapped and propagating motion, we generate phase shifts of the Wiggly Spline, and use these to control appropriate degrees of freedom in a model. The phase shifts can be created directly by procedural techniques or through a paint-like interface. A further option is to derive the phase shifts statistically by analyzing a time-series of a simulation. In this case, the Wiggly Spline makes it possible to canonicalize a simulation, generalize it by providing frequency and damping controls and control it through direct manipulation.