3D Coordinate Transformation by using Quaternion Algebra

One of the most significant issues in mathematics and other fields is rotation in space. One of the most well-known transformations in the world of engineering is the conversion of three-dimensional coordinates from one system to another, and more specifically, the Helmert transformation issue.

This chapter examines the mathematical setting of point rotation in space before presenting an analysis of particular data using three alternative transformation techniques. The dual-quaternion algebra, quaternion, and Euler angles methods are employed. Following investigation, the sensitivity of each technique was tested using three simulated data sets that had been constructed in a certain way and subjected to a particular set of changes. Three actual transformation issues including monitoring and deformation were also examined, to determine the most effective approach with accuracy. The issues Each technique’s findings were statistically analysed, and it was discovered that there were notable discrepancies in the rotations and translations for the dual quaternions approach and the Euler angle method, respectively.

Author (s) Details:

Stefania Ioannidou,
School of Rural, Surveying and Geoinformatics Engineering, National Technical University of Athens, 15780 Zografos, Athens, Greece.

George Pantazis,
School of Rural, Surveying and Geoinformatics Engineering, National Technical University of Athens, 15780 Zografos, Athens, Greece.

Please see the link here: https://stm.bookpi.org/TIER-V5/article/view/7460

Keywords: 3D coordinates, 3D rotation, Helmert transformation problem, Euler angles, quaternions, dual-quaternions.

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