The designing of objects using rational splines with shape control

Interactive curve design in Computer Aided Geometric Design (CAGD) is typically accomplished through the manipulation of a control polygon. The methodology based on B-spline type basis functions results in a curve that lies in the convex hull. Changes in the control polygon only effect the curve locally. This research is oriented towards the representation of interpolatory curves and surfaces, using rational cubic splines. These interpolatory splines have been constructed through the B-spline formulation. The method for evaluating the rational cubic B-spline curve is suggested by a transformation to Bernstein-Bezier form. The method uses the cubic by quadratic functions and for given control points constructs the interpolatory spline method which enjoys all the geometric properties of B-splines. Hence the spline representation is not a spline over spline form.; The generation of interpolating spline curves and surfaces is a useful and powerful tool in CAGD. Various methods have been developed to control the shape of an interpolating curve for computer-aided design applications. Some methods are better suited for controlling the tension of the curve on an interval, while others are better suited for controlling the tension at the individual control points. This work is oriented towards investigating C{dollar}sp2{dollar} like rational interpolatory splines with point and interval tension. Shape controls are available to tighten the rational splines on intervals and/or at the interpolation points.