一种保单调的有理逼近细分算子

A Monotonicity-preserving Rational Approximative Subdivision Operator

在研究插值逼近细分算法的基础上,提出一种具体的五点有理逼近算子,利用生成多项式的方法对其光滑性进行分析,其可产生C^(5)连续的极限曲线。并进一步对该算法的保单调性进行理论分析,阐述详细的推导过程。同时给出数值实验,结果表明在控制点集严格单调递增(递减)的情况下,可以保证在数据允许范围内极限曲线的单调性不发生改变。

On the basis of studying the interpolation approximation subdivision scheme,a specific five-point rational approximation operator is proposed,and its smoothness is analyzed by generating polynomial method,which can generate C^(5) continuous limit curves.The monotonicity of the algorithm is further analyzed theoretically,and the proof process is described in detail.At the same time,numerical experiments are given,and the results show that when the control point set is strictly monotonically increasing(decreasing),the parameter within a certain range can ensure that the monotonicity of the limit curve does not change.