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Parametric keyframing is a popular animation technique where values for parameters which control the position, orientation, size, and shape of modeled objects are determined at key times, then interpolated for smooth animation. Typically the parameter values defined by the keyframes are interpolated by spline techniques with the result that the parameter change kinetics are implicitly defined by the given keyframe times and data points. Existing interpolation systems for animation are examined and found to lack certain desirable features such as continuity of acceleration or convenient kinetic control. The requirements of interpolation for animation are analyzed in order to determine the characteristics of a satisfactory system. A new interpolation system is developed and implemented which incorporates second-derivative continuity (continuity of acceleration), local control, convenient kinetic control, and joining and phrasing of successive motions. Phrasing control includes the ability to parametrically control the degree and extent of smooth motion flow between separately defined motions.
Steketee et al. (Mon,) studied this question.