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作者在前两篇论文[1,2]中曾介绍过用综合四元数及复四元数计算平面镜系统的方法,讲述如何利用这种方法计算由两面、三面及四面镜组成的基本平面镜系统。按照这种方法,计算可以简化为算出平面镜系统的作用算子的正则形式。按此算子的正则形式,易于确定平面镜系统变换空间的方式。该法与其它方法特别是与向量矩阵法比较,优点在于它们不与选定的特殊坐标系相联系,因此在计算过程中,对计算结果不需要进行从一个坐标系到另一坐标系的换算。在论文[1,2]中讨论了一个正面问题:按已知的物体与平面镜系统的位置,确定象在平行光路或在会聚光路中的位置。
In the first two papers [1, 2], the author introduced a method of calculating a planar mirror system using a combination of quaternions and complex quaternions and how to use this method to calculate a basic plane mirror system consisting of two-sided, three-sided and four-sided mirrors . According to this method, the computation can be simplified to the regular form of the operator of action of the planar mirror system. Pressing the regular form of the operator makes it easy to determine the way in which the mirror system transforms space. Compared with other methods, especially vector matrix method, this method has the advantage that they are not associated with the selected special coordinate system, so the calculation result does not need to be converted from one coordinate system to another coordinate system . In the paper [1, 2] a positive problem is discussed: the position of a known object in the plane mirror system, as it is in a parallel light path or in a converging light path, is determined.