This paper deals with discrete computational geometry of motions and develops geometric construction algorithms for interpolating in-between rigid displacements. It combines concepts from the fields of kinematics and computational geometry and develops a computational framework for constructing motion interpolants useful in mechanical systems animation, robot trajectory planning and key framing in computer graphics.
A de Casteljau type algorithm is presented for constructing Bézier and rational Bézier motion interpolants. In addition, the problem of achieving higher order of continuity in piecing together motion interpolants is studied. A geometric construction algorithm is presented for designing C2 continuous motion interpolants.