The Quaternion Theory and Its Application in Coordinate Transformation
School of Surveying and Land Information Engineering, Henan Polytechnic University, 2001 Shiji Road, Jiaozuo 454003, China
Abstract The quaternion has been widely used in three dimensional space datum transformation, but its theoretical basis is not very clear. This paper studies some basic properties of the quaternion theory, and it proves that coordinate rotation transformation is equivalent to the orthogonal transformation of quaternion. Using the definition of basic quaternions, it establishes that all quaternions applied to coordinate rotational transformation are made by several basic quaternion’s Glassman product. At the same time, the theoretical relationship between quaternions and coordinate rotation matrix are given.
Key words ：
quaternion
the basic quaternion
Glassman product
coordinate transformation
Received: 22 September 2014
Published: 10 October 2015
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