PARAMETRIC CONTINUOUS AND SMOOTH MOTION INTERPOLATION

This paper deals with the synthesis of a second order parametrically c ontinuous (C-2) motion that interpolates through a given set of config urations of an object. It derives conditions for blending two motion s egments with C-2 continuity and develops an algorithm for constructing a C-2 composite Bezier type motion that has similarities to Beta-spli nes in the field of Computer Aided Geometric Design. A criterion for e valuating the smoothness of a motion is established and is used to syn thesize a ''globally smooth'' motion. The results have applications in trajectory generation in robotics, mechanical systems animation and C AD/CAM.