Interactive shape preserving interpolation by curvature continuous rational cubic splines

A scheme is described for interactively modifying the shape of convexity preserving planar interpolating curves. An initial curve is obtained by patching together rational cubic and straight line segments. This scheme has, in general, geometric continuity of order 2(G2 continuity) and preserves the local convexity of the data. A method for interactively modifying such curves, while maintaining their desirable properties, is discussed in detail. In particular, attention is focused upon local changes to the curve, while retaining G2 continuity and shape preserving properties. This is achieved by interactive adjustment of the Bézier control points, followed by automatic adjustment of the values of weights and curvatures in a prescribed manner. A number of examples are presented.