坐标转换中的角度长度与面积变形定量分析

Quantitative Analysis of Angle,Length and Area Deformation in Coordinate Transformation

在实际测绘生产中,由坐标变换引起的不同程度的角度变形、长度变形和面积变形产生的影响不可忽略。本文通过公式推导在七参数变换中角度、长度和面积的变形及高斯投影后图斑椭球面积变形,并通过实验验证公式推导结果,得出在七参数变换中角度不发生变形,长度变形为m,面积变形为2 m,七参数变换中的变形与坐标和转换参数无关系,在高斯投影中,面积变形随着纬度和经差的增大而增大,纬度方向面积变形的变化率先增大后减小。

The transformation between the coordinate systems will cause angular deformation,length deformation and area deformation at different degrees,which influence surveying and mapping production.This paper deduces the deformation of angle,length,area and the ellipsoidal area of the plaque after Gaussian projection through Seven Parameter Transformation formula.and finds that the angle does not deform,the length deformation is m,the area deformation is 2 m;The deformation in the Seven Parameter Transformation is independent of the coordinates and transformation parameters,the Gaussian projection deformation increases with the increase of latitude and longitude difference,and the change rate of the area deformation in the latitude direction increases first and then decreases.