A Piecewise Linear Approximation Based on Vector Slope

DOI：

 作者 单位 王明江 复旦大学电子工程系,上海,200433 唐璞山 复旦大学电子工程系,上海,200433

介绍了用统计矢量斜率进行平面数据点分段线性拟合的算法.对于欲拟合的一系列平面数据点,一般是有先后顺序的.首先给出了矢量斜率的定义,然后计算每个平面数据点的统计矢量斜率,根据各点矢量斜率值接近的情况,将数据点分割成组,拟合各组数据形成线段,把各线段首尾连接起来就得到了平面数据点的分段线性拟合.定义的矢量斜率包含大小和方向两方面信息,主值区间为（－4～＋4）,它在主值区间的变化与角度在（－180°～180°）区间中的变化一一对应,且它们的关系曲线有很好的线性度.使用传统斜率进行分段线性拟合,存在斜率值与角度的关系曲线线性度差、斜率取值有时趋向无穷等问题,这些问题影响了拟合的精度,并限制了算法的使用范围.矢量斜率克服了上述问题,从而提供了拟合曲线的质量,且算法可适用于任意曲线.算法时间复杂度为线性.

A piecewise linear approximation based on vector slope is presented in this paper. Given a set of planar data points, generally, these points have sequence.The vector slope definition is introduced at first in this paper. The slope of every points in set G is computed. The points cluster in a group, where vector slope of these points are very near. Fitting every group to a line and linking these lines, a fitting curve can be attained. The vector slope defination has the message of size and direction, basic interval is (-4～4). The varing of vector slope in basic interval with angle(-180°～180°) is in one-to-one correspondence and the relation curve has good linearity. A piecewise linear approximation based on conventional slope has some problems that the slope value is infinite in some cases and the relation curve with angle has bad linearity. All these very effect the quality of fitting curve and confine the application range. This algorithm overcome these problems, so the authors can obtain a high quality fitting curve and the algorithm can be used in every graph. The time complexity is linear.
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