罗德里格矩阵在相似模型坐标配准中的应用

Application of Lodrigues Matrix in the Three-dimensional Coordinates Registration of Similar Model

为减小开采沉陷相似模型指定方向变形计算的误差,需要对相似模型监测点的三维坐标进行转换和配准。传统坐标配准方法需要解算三个旋转角参数,具有计算复杂等缺点。罗德里格矩阵只需解算3个独立参数,具有计算速度快等优点,可以快速解决三维坐标转换和配准计算。本文以XJTUDP三维坐标转换为例,利用罗德里格矩阵给出了平移矩阵的计算模型以及旋转矩阵的误差方程。计算结果表明,基于罗德里格矩阵的转换模型避免了三角函数和线性变化计算,提高了计算精度,降低了计算复杂度,对提高相似模型变形分析精度具有实际意义。

Conversion and registration/in three-dimensional coordinate monitoring points are required in order to reduce the deformation calculation error of specified direction in similar model of mining subsidence. The traditional coordinate registration method computes complexly, needs to calculate three rotary angle parameters, while only three independent parameters are required in Roderick Matrix, which is of a high calculation speed. Moreover, Roderick Matrix also could solve the problem of conversion and registration parameters of/in three-dimensional coordinate. This paper proposes a calculation model of translation matrix and an error equation of rotation matrix on the basis of XJTUDP three-dimensional conversion, and the calculating results demonstrate that the conversion model of Roderick Matrix not only could avoid computing trigonometric and linear change but also improve the calculation accuracy as well as minimize the calculation complexity, which has a practical significance in bettering the deformation analysis accuracy of similar model.