Approximately arc-length parametrized C-3 quintic interpolatory splines

A quasi-global interpolation method that fits a quintic spline curve to a s et of designated data points is described in this paper. The resultant curv e has several important features. First, the curve is smooth with C-3 conti nuity and has no unwanted oscillations. Second, the generated quintic splin e is "optimally" parametrized; that is, the curve is parametrized very clos ely to its arc length. In addition, with the interpolation method, straight line segments can be preserved to generate a quintic spline of hybrid curv e segments. The properties of C-3 continuity and the "near arc length" para metrization have direct applications to trajectory planning in robotics and the development of new types of machine tool controllers for high speed an d precision machining. The encapsulation of straight line segments enhances the capability for the shape designers to design more complicated shapes, including free form curves and straight line segments in a uniform way.