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Journal for Geometry and Graphics 16 (2012), No. 2, 195--209
Copyright Heldermann Verlag 2012

Discovery of Dual Quaternions for Geodesy

Jitka Prosková
Dept. of Mathematics, University of West Bohemia, 306 14 Plzen, Czech Republic

The main aim of this paper is to show one application of dual quaternions in one of the challenging problem of geodesy. The Bursa-Wolf similarity transformation model is presented as a seven parameter model for transforming co-located 3D Cartesian coordinates between two datums. The transformation involves three translation parameters, three rotation elements and one scale factor. We will briefly introduce the theory of quaternions and dual quaternions. Consequently, it is shown that mathematical modelling based on dual quaternions is an elegant mathematical method which is used to represent rotation and translation parameters and a compact formula is derived for the Bursa-Wolf model.

Keywords: Dual quaternion, datum transformation, Bursa-Wolf model.

MSC: 51N20; 86A30

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