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中文摘要：
为了分析清楚形状参数对一类双参数三次Bézier曲线形态的影响及实现其对该曲线形状的调控,利用包络理论与拓扑映射的方法对一类双参数三次Bézier曲线进行了形状分析,明确了形状参数对曲线的影响,画出了曲线的形状特征分布图,得出了曲线上有奇点、拐点和曲线为局部凸或全局凸的充分必要条件,这些条件完全由控制多边形的相对位置表示,并进一步讨论了形状参数对曲线形状的影响。
英文摘要：
The shape features of a class of Bezier curve with two shape parameters are analyzed by using the method based on the theory of envelope and topological mapping. Investigate effects of the shape parameter on the curve shape. Necessary and sufficient conditions are derived for this curve having one or two inflection points, a loop or a cusp, or be locally or globally convex. Those conditions are completely characterized by the relative position of the edge vectors of the control polygon. Furthermore we discussed the influences of shape parameter on the shape diagram and the ability for adjusting the shape of the curve.
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