Abstract: This paper extends the representation of quartic Bezier curve called quasi quartic bezier curve by introducing Bernstein basis function with three shape parameters and discusses the basis properties and the inner relations between quasi quartic bezier curves and quintic bezier curves. Taking different values of the shape parameters, shape of the curves can be modified easily. Without adjusting the control points, it can realize G2 merging of quasi quartic bezier curves by changing the values of the shape parameters locally which can better meet the practical applications. Finally, some specific examples are provided.

Key words: Bernstein basis functions, Bezier curves, continuity

摘要： 通过引入带三参数的Bernstein基函数，对四次Bezier曲线进行了多参数的扩展，得到了一种类四次Bezier曲线，讨论了曲线的基本性质以及与五次Bezier曲线之间的关系。通过对三参数的调节使曲线更具可调控性以及对圆锥曲线较好的逼近性。能够在不改变控制点的情况下，仅仅通过局部调节部分形状参数的值便能实现曲线间的G2拼接，从而更能满足实际应用的需要。最后给出了部分具体的实例。

关键词: Bernstein基函数, Bezier曲线, 拼接