约束于圆弧的路线平面直线段重构算法

A recreating algorithm of straight segment of the horizontal alignment constrained by circular arc

提出一种利用一组(x,y)直角坐标点拟合与给定的圆弧相切的直线的算法。该算法遵循总体最小二乘准则来构建约束于圆弧的拟合直线的数学模型,在分析函数单调隔根区间的基础上,利用反拉格朗日插值迭代法计算出函数在定义域内的所有数值根,再经最小二乘准则检验获得数学模型的解,即拟合直线的回归参数。研究结果表明:拟合数学模型简明,基于单调隔根区间的迭代算法稳健,速度快,效果优,可用于重构路线平面的精确几何参数。

On the basis of a set of (x, y) points, this paper proposes a method for fitting a regression line that is tangent to the given arc. The algorithm, based on Holistic Least Square Method, firstly established mathematical model fitting a line constrained by circular arc. On the basis of analysis of the intervals on which a function’s null point exists, the Inverse Lagrange’s Interpolation Method was used to calculate all of the function’s numerical solutions on the domain of definition. Additionally, the least squares criterion decided which of the numerical solutions can satisfy the mathematical model which had been established. Numerical solutions satisfying the mathematical model were exactly regression parameters of the regression line. Theoretical derivation and practical application indicate that this is a fast and stable algorithm with accurate results. This feature allows it to reconstruct precise geometric parameters of the Horizontal Alignment.