GEOMETRIC CONSTRUCTION OF BEZIER MOTIONS

This paper deals with discrete computational geometry of motion. It co mbines concepts from the fields of kinematics and computer aided geome tric design and develops a computational geometric framework for geome tric construction of motions useful in mechanical systems animation, r obot trajectory planning and key framing in computer graphics. In part icular, screw motion interpolants are used in conjunction with deCaste ljau-type methods to construct Bezier motions. The properties of the r esulting Bezier motions are studied and it is shown that the Bezier mo tions obtained by application of the deCasteljau construction are not, in general, of polynomial type and do not possess the useful subdivis ion property of Bernstein-Bezier curves. An alternative form of deCast eljau algorithm is presented that results in Bezier motions with subdi vision property and Bernstein basis function. The results are illustra ted by examples.