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Journal for Geometry and Graphics 21 (2017), No. 1, 071--078
Copyright Heldermann Verlag 2017

Interpolations by Rational Motions Using Dual Quaternions

Jitka Proskova
Dept. of Mathematics, University of West Bohemia, Univerzitní 8, 306 14 Plzen, Czech Republic

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.

Keywords: Dual quaternion, rational spline motion, Hermite interpolation.

MSC: 51N20; 53A17, 65D17

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