C1 and G1 continuous rational motions using a conformal geometric algebra

Traditional rational motion design describes separately the translation of a reference point in a body and the rotation of the body about it. This means that there is dependence upon the choice of reference point. When considering the derivative of a motion, some approaches require the transform to...

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Veröffentlicht in:Journal of Computational and Applied Mathematics 2022-10, Vol.412, Article 114280
Hauptverfasser: Cross, Ben, Cripps, Robert J.
Format: Artikel
Sprache:eng
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Zusammenfassung:Traditional rational motion design describes separately the translation of a reference point in a body and the rotation of the body about it. This means that there is dependence upon the choice of reference point. When considering the derivative of a motion, some approaches require the transform to be unitary. This paper resolves these issues by establishing means for constructing free-form motions from specified control poses using multiplicative and additive approaches. It also establishes the derivative of a motion in the more general non-unitary case. This leads to a characterization of the motion at the end of a motion segment in terms of the end pose and the linear and angular velocity and this, in turn, leads to the ability to join motion segments together with either C1- or G1-continuity.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2022.114280