直线参数化方式的优化设计

THE OPTIMAL DESIGN OF LINE PARAMETERIZATION

提出了一条设计直线参数化方式的新标准——递归性标准，它和作者在“Ｔｈｒｅｅｃｏｎｄｉ－ｔｉｏｎｓｏｆａｇｏｏｄｌｉｎｅｐａｒａｍｅｔｅｒｉｚａｔｉｏｎ”文中提出的唯一性、有界性、均匀性三条标准一起构成了评价直线参数化方式优劣的新框架．根据上述四条标准，证明了不存在同时满足这四条标准的直线参数化方式和直线参数化方式ｃ＝αｘ＋（α０－｜α｜）ｙ，α∈［－α０，α０）不但满足唯一性、有界性和递归性标准，而且可以获得均匀性标准的最优近似．

In this paper, a new criterion, namely recursiveness,is introduced, which along with the three criteria previously introduced by Hu Z et al in his paper“Three conditions of a good line parameterization”, (i.e., uniqueness, boundedness and uniformness) makes up a new framework for the design of line parameterizations. By the above four criteria, it is proved that there does not exist a line parameterization which could satisfy all the four criteria at the same time, and that the line parameterization, formulated as c=ax+(a 0-|a|)y, a∈[-a 0,a 0) , where a 0 is an arbitrary positive number, can not only satisfy the uniqueness, boundedness, and recursiveness criteria, but also achieve the best goodness to the uniformness one.