Shape preserving and shape control with interpolating Bézier curves (Q1263218)

The authors give a formal definition for a smooth shape preserving interpolation and derive a set of shape parameters for cubic Bézier interpolating curves. Based on these parameters, the necessary and sufficient shape preserving conditions for Bézier interpolations are given. A constructive algorithm which automatically generates shape preserving interpolating curves is proposed. Several examples demonstrate the quality of the method. Finally, a comparison with the natural bias approach proposed by \textit{Fletcher} and \textit{McAllister} [Computer-aided design 18, No.1, 48-52 (1986)] is given.