Discretization of SO(3) using recursive tesseract subdivision

机译：使用递归tesseract细分离散化SO（3）

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摘要

The group of rotations in three dimensions SO(3) plays a crucial role in applications ranging from robotics and aeronautics to computer graphics. Rotations have three degrees of freedom, but representing rotations is a nontrivial matter and different methods, such as Euler angles, quaternions, rotation matrices, and Rodrigues vectors are commonly used. Unfortunately, none of these representations allows easy discretization of orientations on evenly spaced grids. We present a novel discretization method that is based on a quaternion representation in conjunction with a recursive subdivision scheme of the four-dimensional hypercube, also known as the tesseract.

机译：三维SO（3）中的旋转组在从机器人技术，航空技术到计算机图形学的各种应用中都起着至关重要的作用。旋转具有三个自由度，但是表示旋转是一件很重要的事情，通常使用不同的方法，例如欧拉角，四元数，旋转矩阵和罗德里格斯矢量。不幸的是，这些表示都不能轻易地使均匀间隔的网格上的方向离散化。我们提出了一种新颖的离散化方法，该方法基于四元数表示与二维超立方体（也称为tesseract）的递归细分方案相结合。

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来源
《2017 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems》|2017年|49-55|共7页
会议地点 Daegu(KR)
作者
Gerhard Kurz; Florian Pfaff; Uwe D. Hanebeck;
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作者单位

Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology (KIT), Germany;

Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology (KIT), Germany;

Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Institute for Anthropomatics and Robotics, Karlsruhe Institute of Technology (KIT), Germany;

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正文语种 eng
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关键词
Quaternions; Three-dimensional displays; Robot sensing systems; Computer graphics; Hypercubes; Approximation algorithms;

机译：四元数;三维显示;机器人传感系统;计算机图形学;超立方体;逼近算法;;

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Discretization of SO(3) using recursive tesseract subdivision

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