摘要
针对工业测量中二次曲面的拟合问题,阐述了二次多项式的标准化、二次项系数矩阵的特征值和特征向量求取、测量坐标与标准坐标之间的转换关系、特征向量与旋转角的关系等问题,提出了按特征值、旋转角和平移量为参数拟合二次曲面的拟合方法。算例表明了模型的准确性。
The standardization of second order polynomial is described. The eigenvalues and eigenvectors of quadric coefficient matrix are used to describe the relation between surveying coordinates system and standardized coordinate system, in which conicoid equations are well expressed mathematically. The rotation angles are derived from eigenvector matrix. Then conicoid fitting model is developed using eigenvalues, rotation angles and shifts as parameters. The example shows the correctness of the model.
出处
《武汉大学学报（信息科学版）》
EI
CSCD
北大核心
2007年第1期47-50,共4页
Geomatics and Information Science of Wuhan University
基金
国家自然科学基金资助项目(40234039)
关键词
工业测量
二次曲面
特征值
拟合
industrial measurement
conicoid
eigenvalue
fitting
