POLAR FORMS FOR GEOMETRICALLY CONTINUOUS SPLINE CURVES OF ARBITRARY DEGREE

This paper studies geometrically continuous spline curves of arbitrary degree. Based on the concept of universal splines, we obtain geometric constructions for both the spline control points and for the Bezier points and give algorithms for computing locally supported basis functions and for knot insertion. The geometric constructions are based on the intersection of osculating flats. The concept of universal splines is defined in such a way that these intersections are guaranteed to exist. As a result of this development, we obtain a generalization of polar forms to geometrically continuous spline curves by intersecting osculating flats. The presented algorithms have been coded in Maple, and concrete examples illustrate the approach.