Abstract: CE-Bézier（Cubic Extension Bézier） curve with multiple shape parameters is one of the most important extensions of the cubic Bézier curve. It not only inherits the outstanding properties of the cubic Bézier curve but also has a good performance on adjusting their local shapes by changing the shape control parameters. In order to develop the basic theory of CE-Bézier curve, index curve catenaries, focusing on CE-Bézier curve can’t accurate said index curve, catenary etc beyond curve faults, the CE-Bézier curve modeling of exponential curve, catenary beyond curve is solved by using the continuity condition of CE-Bezier curve and H-Bezier curve. Eventually, some examples are discussed. The modeling examples illustrate that the continuity condition of CE-Bézier curves and H-Bézier curves can be widely applied to the complex surfaces modeling system.

Key words: CE-Bézier curve, H-Bézier curve, shape parameters, continuity conditions

摘要： CE-Bézier曲线作为一种重要的带多形状参数的三次扩展Bézier曲线，不仅具有与三次Bézier曲线类似的性质，而且具有优良的形状可调性和更好的逼近性。为了进一步发展CE-Bézier曲线的相关理论，针对CE-Bézier曲线无法精确表示指数曲线、悬链线等超越曲线的缺点，利用CE-Bézier曲线与H-Bézier曲线间的拼接技术，来处理CE-Bézier曲线造型中指数曲线、悬链线等超越曲线的表示问题。最后，给出了具体的数值实验；造型实例表明，该方法在计算机辅助几何设计中具有一定的应用价值。

关键词: CE-Bé, zier曲线, H-Bé, zier曲线, 形状参数, 拼接条件