基于二次函数图形的归算高重新选取

Reselection of Naturalization Height Based on Quadratic Function Figure

在控制测量中,常通过对归算高的重新选取来抑制归算投影的长度综合变形。本文从使测区内最大综合变形的绝对值最小出发,利用二次函数形成正变形边界线、零变形线、负变形线并构成归算投影有效区图,利用该有效区图对新归算高的存在性、可选范围及最佳选取进行了讨论,并分别给出了图解和解析两种选取方式。算例表明,基于二次函数图形的归算高选取方法几何意义明显,方法简单,其符合最大变形的绝对值最小原则,获得的结果优于现有的归算高选取方法。

In control surveying, a proper naturalization height is usually needed to reduce length deformation of naturalization projection. In this paper, a new method to minimize the absolute value of the maximal integrated deformation of surveying region is proposed. The positive deformation borderline, the zeros deformation line and the negative ones were constructed by quadratic function. And the effective area of naturalization projection was determined. Thus, the optimal selection of naturalization height was discussed analytically and graphically. With this method, the naturalization height can be reasonably fixed and the length deformation of the Gauss projection be effectively suppressed.