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 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
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Online-Zugang: | Volltext |
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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. |
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ISSN: | 0377-0427 1879-1778 |
DOI: | 10.1016/j.cam.2022.114280 |