The Helmert transformation (named after Friedrich Robert Helmert, 1843–1917; also called a seven-parameter transformation) is a transformation method within a three-dimensional space. It is frequently used in geodesy to produce distortion-free transformations from one datum to another using:
![X_T=C+\mu RX \,](/Images/godic/202501/17/822b176085857cc5b9b20fc9d1fa05982353.png")
![C](/Images/godic/202501/17/0d61f8370cad1d412f80b84d143e12572353.png")
— 三个坐标轴的平移参数（已知量）![\mu](/Images/godic/202501/17/b72bb92668acc30b4474caff402740442353.png")
— 转换的尺度变化参数![R](/Images/godic/202501/17/e1e1d3d40573127e9ee0480caf1283d62353.png")
— 含有三个坐标轴旋转参数的旋转矩阵，为一正交矩阵。