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Cited 4 time in webofscience Cited 6 time in scopus
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Visualizing Quaternion Multiplication

Title
Visualizing Quaternion Multiplication
Authors
BAEK, JONGCHANHAYEONG, JEONKIM, GWANGJINHAN, SOOHEE
POSTECH Authors
HAN, SOOHEE
Date Issued
May-2017
Publisher
Institute of Electrical and Electronics Engineers Inc.
Abstract
Quaternion rotation is a powerful tool for rotating vectors in 3-D; as a result, it has been used in various engineering fields, such as navigations, robotics, and computer graphics. However, understanding it geometrically remains challenging, because it requires visualizing 4-D spaces, which makes exploiting its physical meaning intractable. In this paper, we provide a new geometric interpretation of quaternion multiplication using a movable 3-D space model, which is useful for describing quaternion algebra in a visual way. By interpreting the axis for the scalar part of quaternion as a 1-D translation axis of 3-D vector space, we visualize quaternion multiplication and describe it as a combined effect of translation, scaling, and rotation of a 3-D vector space. We then present how quaternion rotation formulas and the derivative of quaternions can be formulated and described under the proposed approach.
Quaternion rotation is a powerful tool for rotating vectors in 3-D; as a result, it has been used in various engineering fields, such as navigations, robotics, and computer graphics. However, understanding it geometrically remains challenging, because it requires visualizing 4-D spaces, which makes exploiting its physical meaning intractable. In this paper, we provide a new geometric interpretation of quaternion multiplication using a movable 3-D space model, which is useful for describing quaternion algebra in a visual way. By interpreting the axis for the scalar part of quaternion as a 1-D translation axis of 3-D vector space, we visualize quaternion multiplication and describe it as a combined effect of translation, scaling, and rotation of a 3-D vector space. We then present how quaternion rotation formulas and the derivative of quaternions can be formulated and described under the proposed approach.
URI
http://oasis.postech.ac.kr/handle/2014.oak/40973
DOI
10.1109/ACCESS.2017.2705196
ISSN
2169-3536
Article Type
Article
Citation
IEEE Access, vol. 5, page. 8948 - 8955, 2017-05
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한수희HAN, SOOHEE
Dept of Electrical Enginrg
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