Construction of G³ rational motion of degree eight

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• 作者：Karla Ferjančič ; ^c ; ^{karla.ferjancic@iam.upr.si" class="auth_mail" title="E-mail the corresponding author} ; Marjeta Krajnc^a ; ^b ; ^{marjetka.krajnc@fmf.uni-lj.si" class="auth_mail" title="E-mail the corresponding author} ; Vito Vitrih^c ; ^d ; ^{vito.vitrih@upr.si" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Motion design ; Geometric interpolation ; Rational spline motion ; Geometric continuity
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：1 January 2016
• 年：2016
• 卷：272
• 期：part_P1
• 页码：127-138
• 全文大小：894 K

文摘

The paper presents a construction of a rigid body motion with point trajectories being rational spline curves of degree eight joining together with G³ smoothness. The motion is determined through interpolation of positions and derivative data up to order three in the geometric sense. Nonlinearity in the spherical part of construction results in a single univariate quartic equation which yields solutions in a closed form. Sufficient conditions on the regions for the curvature data are derived, implying the existence of a real admissible solution. The algorithm how to choose appropriate data is proposed too. The theoretical results are substantiated with numerical examples.