一种一阶连续分段曲线拟合方法

Method of First-order Continuous Piecewise Curve-fitting

分段曲线拟合是一种常用的数据处理方法,但在分段点处拟合曲线往往不能满足连续性要求。提出一种一阶连续分段曲线拟合方法,即在确定每个拟合区间的原始数据个数之后,采用最小二乘法进行拟合,并在分段点处重复使用前一段末端数据,且对每段数据的起始点进行加权,使分段拟合曲线在分段点处更加逼近,减小拟合误差,根据拟合曲线重合部分的端点信息,采用三次Hermite插值的方法构造一条连接分段拟合曲线的插值曲线,使分段点处满足一阶连续,逐段处理,得到一条全局光滑连续的拟合曲线。将一阶连续分段曲线拟合方法应用于处理齿轮视觉检测中提取的齿廓边缘数据,证明拟合曲线在分段点处一阶连续,且拟合误差减小,易于编程实现。

Piecewise curve-fitting is a commonly used processing method of data, but at sub-point fitting curve often does not meet the requirement for continuity. This paper present a method of first-order continuous piecewise curve-fitting. Firstly, The method determining the number of original data in each fitting interval, using piecewise curve-fitting to process data, and reusing data at the end of the previous period in the subsection point, weighting the starting point of each piece of data, which can make a piecewise fitting curve in the subsection point more approaching, and reduce the fitting error, according to the fitting curve o- verlapping part of the endpoint information, utilizing cubic Hermite interpolation to structure a interpolation curve that links the two piecewise fitting curves, making sub-point satisfy the first-order continuous, piece- wise processing, getting a global smooth continuous fitting curve. The method of first-order continuous piecewise curve fitting is applied to process extracted tooth profile edge data in gear vision inspection, which proved that the fitting curve in the subsection point is first-order continuous, and fitting error is reduced, also it is easy to program.