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A concise quaternion geometry of rotations
Author(s) -
Meister L.,
Schaeben H.
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.560
Subject(s) - quaternion , mathematics , unit (ring theory) , geometry , space (punctuation) , rotation (mathematics) , interpretation (philosophy) , unit sphere , mathematical analysis , algebra over a field , pure mathematics , computer science , mathematics education , programming language , operating system
This communication compiles propositions concerning the spherical geometry of rotations when represented by unit quaternions. The propositions are thought to establish a two‐way correspondence between geometrical objects in the space of real unit quaternions representing rotations and geometrical objects constituted by directions in the three‐dimensional space subjected to these rotations. In this way a purely geometrical proof of the spherical Ásgeirsson's mean value theorem and a geometrical interpretation of integrals related to the spherical Radon transform of a probability density functions of unit quaternions are accomplished. Copyright © 2004 John Wiley & Sons, Ltd.