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Main Authors: Lu, Feng, Chen, Ziqiang
Format: Preprint
Published: 2014
Subjects:
Online Access:https://arxiv.org/abs/1404.6055
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author Lu, Feng
Chen, Ziqiang
author_facet Lu, Feng
Chen, Ziqiang
contents We present algebraic projective geometry definitions of 3D rotations so as to bridge a small gap between the applications and the definitions of 3D rotations in homogeneous matrix form. A general homogeneous matrix formulation to 3D rotation geometric transformations is proposed which suits for the cases when the rotation axis is unnecessarily through the coordinate system origin given their rotation axes and rotation angles. General three-dimensional rotation formula~\eqref{eqn:3D homogeneous roation} and~\eqref{eqn:3D rotation matrix vector Euclidean} similar to the Euler-Rodrigues formula were presented. The matrix-vector form of 3D rotation in Euclidean space is especially suited for numerical applications where gimbal lock is a concern.}
format Preprint
id arxiv_https___arxiv_org_abs_1404_6055
institution arXiv
publishDate 2014
record_format arxiv
spellingShingle A General Homogeneous Matrix Formulation to 3D Rotation Geometric Transformations
Lu, Feng
Chen, Ziqiang
Computer Vision and Pattern Recognition
We present algebraic projective geometry definitions of 3D rotations so as to bridge a small gap between the applications and the definitions of 3D rotations in homogeneous matrix form. A general homogeneous matrix formulation to 3D rotation geometric transformations is proposed which suits for the cases when the rotation axis is unnecessarily through the coordinate system origin given their rotation axes and rotation angles. General three-dimensional rotation formula~\eqref{eqn:3D homogeneous roation} and~\eqref{eqn:3D rotation matrix vector Euclidean} similar to the Euler-Rodrigues formula were presented. The matrix-vector form of 3D rotation in Euclidean space is especially suited for numerical applications where gimbal lock is a concern.}
title A General Homogeneous Matrix Formulation to 3D Rotation Geometric Transformations
topic Computer Vision and Pattern Recognition
url https://arxiv.org/abs/1404.6055