摘要
针对7参数法三维坐标转换问题,对比分析了传统的基于泰勒级数展开的线性模型转换方法和基于罗德里格矩阵的三维坐标转换方法.由于在基于罗德里格矩阵的转换方法中,不需进行三角函数的计算,也不需迭代计算,因而其计算速度更快;而且其解决了线性模型对旋转角大小的限制,不仅适用于小角度的空间直角坐标转换,也能用于大角度的空间坐标转换.实验结果也表明基于罗德里格矩阵的转换方法具有更好的适用性和更高的精度.
For the problem of three dimensional coordinate transformation with seven parameters, two methods, traditional linear model transformation method based on Taylor series expansion and coordinate transformation method based on Roderick matrix, are compared in this paper. In the method based on Roderick matrix, neither trigonometric functions nor iterative process need be carried out. Thus the calculation speed of Roderick matrix method is much faster than that of the traditional method. Furthermore, it resolves the limited conditions to rotation angle in the linear model, and it is adaptable to large angel＇s spatial coordinate transformation as well as to small angle＇s spatial rectangular coordinate transformation. Experimental results also show that the method based on Roderick matrix has a higher adaptability and accuracy.
出处
《数学的实践与认识》
CSCD
北大核心
2008年第23期121-128,共8页
Mathematics in Practice and Theory
基金
全国高校博士点基金(20060319004)
江苏省高校自然科学重大基础研究项目(07KJA42005)
关键词
三维坐标转换
泰勒级数
罗德里格矩阵
转换参数
旋转矩阵
three dimensional coordinate transformation
taylor series
roderick matrix
transformation parameters
rotation matrix
