中文摘要：

提出了一般的三点三重、四点三重逼近细分格式,利用稳定细分格式C^k连续的充要条件,分析了细分法各阶连续时参数的取值范围。利用提出的一般细分法,可以造型光滑逼近曲线;当某些细分参数取特殊值时,还可以用来造型插值曲线。为便于应用,还对Hassan的3点ternary逼近细分法进行了改进,使其带有一个全局张力参数,通过它更易控制曲线的形状。在全局张力参数的一定范围内可以生成C^1,C^2连续的极限曲线。

英文摘要：

Using the necessary and sufficient conditions for C k-continuity of stationary subdivision schemes,the ranges of free parameter are analyzed for C ^k-continuity of general arity-3 approximating 3-point scheme and arity-3 approximating 4-point subdivision scheme.Using this paper’s methods,smooth approximating curve can be generated;when some parameters take particular values,smooth interpolating curve can also be generated.In addition,in order to use easily,Hassan’s methods are improved by introducing a global tension parameter,which makes it much easier to control the shape of the curve.The new methods can be used to generate a family of C^1,C^2 limit curves in certain range of global tension parameter.