GENERALIZED GEOMETRIC INTERPOLATION FOR RATIONAL CUBIC-SPLINES

A description and analysis of an interpolatory rational cubic spline curve is made for use in computer graphics. The generalized rational cubic pieces are stitched together with a most general form of continuity. The parameters in the description of rational cubics as well as the geometric continuity provide a variety of shape control. This rational spline provides not only a computationally simple alternative to the exponential-based spline under tension [1-3] but also recovers the number of spline methods like the rational spline methods [4-6]. the well-known existing GC2 or C1 methods like cubic nu-spline of Nielson[7], gamma-splines of Boehm [8] and weighted nu-splines [9], etc.