抛物线拟合的高斯投影长度比计算方法

The method for calculating the length ratio of Gauss projection based on parabolic fitting

针对传统的高斯投影长度比计算公式存在的次数高、参数多、计算过程复杂等不足,该文提出利用抛物线拟合法计算高斯投影长度比。首先,对高斯投影规律进行全面分析,得出高斯投影长度比与距离中央子午线横坐标值的变化成抛物线关系。然后,以点在高斯平面直角坐标系中距离中央子午线的横坐标值为参数计算高斯投影长度比。实验结果表明,采用该文方法计算高斯投影长度比运算简便、精度高,与传统公式计算的长度比差值在整个高斯投影带均达百万分之一量级,对完善高斯投影长度变形规律的研究以及实际计算均具有一定的参考价值。

In view of the traditional formula for calculating the length ratio of Gauss projection has thedefects including higher degree, too many parameters and complex calculation procedure, this paper usedparabolic fitting method to calculate the length ratio of Gauss projection. First, it was concluded that thelength ratio of Gauss projection had a parabolic relation with the horizontal coordinates to the central me-ridian by the comprehensive analysis of the Gauss projection law. Then, the length ratio of Gauss projec-tion was calculated based on the horizontal coordinate values of point to the central meridian in the Gaussplane coordinate system. Experimental results showed that the parabolic fitting method was simple withhigh accuracy, and the difference of the length ratio calculated by the traditional formula was at the orderof one millionth magnitude throughout the zone of Gauss projection, which had certain reference value forthe study on the improvement of Gauss projection length deformation and actual computation.