Geodesic
Interpolations by Rational Motions Using Dual Quaternions
Journal for geometry and graphics, Tome 21 (2017) no. 1, pp. 71-78.

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The main aim of this paper is to show an application of dual quaternions related to a rational spline motion. The interpolation by rational spline motions is an important part of technical practice, e.g., in robotics. Therefore, we will focus on most simple examples of piecewise rational motions with first and second order geometric continuity, in particular, a cubic G2 Hermite interpolation. Consequently, it is shown that the new approach to rational spline motion design based on dual quaternions is an elegant mathematical method.
Classification : 51N20, 53A17, 65D17
Mots-clés : Dual quaternion, rational spline motion, Hermite interpolation 
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     author = {J. Proskova},
     title = {Interpolations by {Rational} {Motions} {Using} {Dual} {Quaternions}},
     journal = {Journal for geometry and graphics},
     pages = {71--78},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/JGG_2017_21_1_JGG_2017_21_1_a6/}
}
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J. Proskova. Interpolations by Rational Motions Using Dual Quaternions. Journal for geometry and graphics, Tome 21 (2017) no. 1, pp. 71-78. http://geodesic.mathdoc.fr/item/JGG_2017_21_1_JGG_2017_21_1_a6/