摘要:
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"Three conditions
of a good line parameterization"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t和直线参数化方式c= ax+ (ao-lal)y, a∈[-a0 ,a0)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.
Abstract:
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+ (ao-lal)y, a∈[-a0 ,a0), where a0 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.
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