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Retrieval of Euler rotation angles from 3D similarity transformation based on quaternions
Journal of Spatial Science ( IF 1.9 ) Pub Date : 2020-07-12 , DOI: 10.1080/14498596.2020.1776170
Süreyya Özgür Uygur 1 , Cuneyt Aydin 1 , Orhan Akyilmaz 2
Affiliation  

ABSTRACT

Recently, it has been shown how quaternion-based representation of a rotation matrix has advantages over conventional Eulerian representation in 3D similarity transformations. The iterative estimation procedure in similarity transformations based on quaternions results in translations and (scaled) quaternion elements. One needs, therefore, an additional procedure for evaluating the rest of the transformation parameters (translation, scale factor and rotation angles) after this solution.This contribution shows how to evaluate the rotation angles and the full covariance matrix of the transformation parameters from the estimation results in asymmetric and symmetric 3D similarity transformations based on quaternions.



中文翻译:

基于四元数的3D相似变换欧拉旋转角检索

摘要

最近,已经证明旋转矩阵的基于四元数的表示如何在 3D 相似性变换中优于传统的欧拉表示。基于四元数的相似变换中的迭代估计过程导致平移和(缩放)四元数元素。因此,需要一个额外的过程来评估该解决方案之后的其余变换参数(平移、比例因子和旋转角度)。该贡献显示了如何从估计中评估变换参数的旋转角度和完整协方差矩阵导致基于四元数的不对称和对称 3D 相似性变换。

更新日期:2020-07-12
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