This paper deals with smooth motion interpolation. It presents two geometric algorithms for synthesizing composite Be´zier motions with second-order geometric continuity (G2). The first one is a direct algorithm for constructing a G2 spline motion that approximates a set of displacements; the second one is an inverse design algorithm for a G2 spline motion that interpolates through a set of displacements. The results are useful for computer aided motion animation, and Cartesian trajectory generation for CNC machines and robot manipulators.

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