A New Shape Control and Classification for Cubic Bézier Curves

Abstract

In this paper, a new shape control method called one-point shape control is proposed for cubic Bezier curves. First, we show that a Bezier curve, with given boundary points and tangent directions, can be uniquely determined by a point called the shape point. Then the advantages of this shape control method are discussed and shape classification with respect to the shape point is also studied. Furthermore, by using this one-point shape control method, we introduce a new offset algorithm for Bezier curves. Empirical tests will be given. It shows that our offset algorithm is not only simple and direct but also effective and efficient.