基于方向余弦参量的物坐标系与世界坐标系间的坐标变换

Coordinate Transformation Based on Direction Cosine Parameters between the Object Coordinate System and the Word Coordinate System

借助物体上三点建立了物坐标系,并给出了其坐标轴的方向余弦计算式。利用矢量代数的方法,推导出以方向余弦为参量的物坐标系到世界坐标系的坐标变换矩阵;利用矩阵求逆的方法,推导出世界坐标系到物坐标系的坐标变换矩阵。作为推论,推导出两种特殊情况的坐标变换矩阵。文中推出的物坐标系与世界坐标系间的两个变换矩阵可作为任意两个坐标系间的坐标变换矩阵,故具有通用性。

A object coordinate system is built by three points in object and the method of solving the direction cosines of the axises of the coordinate system is presented. The coordinate transformation matrix based on the direction cosine parameters from the object coordinate system to the world coordinate system is derived by vector algebra. The coordinate transformation matrix from the world coordinate system to the object coordinate system is derived by finding the converse matrix. As deductions of the coordinate transformation, two special coordinate transformation and their matrices are given. The two transformation matrices between the object coordinate system and the world coordinate system presented in this article are universal coordinate transforma- tion matrices for two arbitrary coordinate systems.