Parametric continuous and smooth motion interpolation

This paper deals with the synthesis of a second order parametrically continuous (C^) motion that interpolates through a given set of configurations of an object. It derives conditions for blending two motion segments with C^ continuity and develops an algorithm for constructing a C^ composite Bezier type motion that has similarities to Beta-splines in the field of Computer Aided Geometric Design. A criterion for evaluating the smoothness of a motion is established and is used to synthesize a ' 'globally smooth'' motion. The results have applications in trajectory generation in robotics, mechanical systems animation and CAD/CAM.