On the Relationship of Shapes between a Class of Control Polygons and Their Cubic Bézier Curves

In this paper,the relationship of shapes between a class of control polygons and their cubic Bézier curves are studied.The necessary and sufficient conditions for cups,loops and inflection points of the cubic Bézier curves are given according to the side length of the control polygons respectively.The method of building Bézier curves with singularities(inflection point,cusp and loop) is illustrated via an example.