具有简单G^3条件的可调曲线曲面（英文）

Adjustable curves and surfaces with simple G^3 conditions

为了使曲线曲面具有可调的形状和简单的G3条件,利用递推方法定义了一种EI函数.基于EI函数构造了具有大部分Bézier曲线曲面性质的EI曲线曲面.由于EI函数的特殊性,EI曲线曲面具有2个突出优点,一是具有形状控制参数,另一个是其G3条件正好是Bézier曲线曲面的G1条件.对于给定的点集,为了生成自动光滑的组合曲线曲面,在EI函数的基础上,定义了另一组MI函数.由MI函数定义的MI曲线曲面具有形状可调性,以及简单的连续性条件.根据连续性条件,采用一种特殊方式定义了组合MI曲线曲面,此方法无需附加任何条件,可自动达到光滑连接.

In order to make curves and surfaces have adjustable shape and simple G3 conditions,a kind of EI functions is defined recursively.Based on them,we construct EI curves and surfaces,which have the most properties of Bézier curves and surfaces.Owe to the particularity of EI functions EI curves and surfaces possess two distinct advantages.（1）They have shape control parameter;（2）Their G3 conditions are just the G1 conditions for usual Bézier curves and surfaces.For a given set of points,in order to generate automatically smooth composite curves and surfaces,another kind of MI functions is defined based on EI functions.The MI curves and surfaces defined by MI functions also enjoy adjustable shape,simple continuity conditions.According to the continuity conditions,we have defined the composite MI curves and surfaces by a special way.With no need for any constraints,they can naturally achieve smooth connection.