Curve-to-curve associations in spline-based inbetweening and sweeping

Abstract

We are concerned in this paper with associations between spline curves that will hold at all inbetween positions when the control points of these curves are used as key points for animation or sweeping. It is established that any association between two spline curves that can be expressed as the equality of two linear mappings will hold throughout an inbetweening process provided the inbetweening trajectories are coordinated splines that uniquely interpolate the control-point key positions. Multiple associations are possible, so long as the basic requirements of linearity and coordination are observed.