Geodesic
Discovery of Dual Quaternions for Geodesy
Journal for geometry and graphics, Tome 16 (2012) no. 2, pp. 195-209 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 51N20, 86A30
Mots-clés : Dual quaternion, datum transformation, Bursa-Wolf model 
@article{JGG_2012_16_2_JGG_2012_16_2_a6,
     author = {J. Proskov� },
     title = {Discovery of {Dual} {Quaternions} for {Geodesy}},
     journal = {Journal for geometry and graphics},
     pages = {195--209},
     year = {2012},
     volume = {16},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JGG_2012_16_2_JGG_2012_16_2_a6/}
}
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J. Proskov� . Discovery of Dual Quaternions for Geodesy. Journal for geometry and graphics, Tome 16 (2012) no. 2, pp. 195-209. http://geodesic.mathdoc.fr/item/JGG_2012_16_2_JGG_2012_16_2_a6/