Construction of low degree rational motions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:256

Article

Krajnc, Marjeta^1,2  Pockaj, Karla³  Vitrih, Vito^3,4 

[1] Univ Ljubljana, FMF, Ljubljana, Slovenia

[2] IMFM, Ljubljana, Slovenia

[3] Univ Primorska, IAM, Koper, Slovenia

[4] Univ Primorska, FAMNIT, Koper, Slovenia

关键词: Motion design;    Geometric interpolation;    Rational spline motion;    Geometric continuity;   

DOI  :  10.1016/j.cam.2013.07.014

来源: Elsevier

【 摘 要 】

Construction of rational spline motions is an important issue in robotics, animations and related fields. In this paper a geometric approach to interpolate given sequence of rigid body positions is considered, which, in contrast to standard approaches, is free of choosing parameter values in advance and it enables the lowest possible degree of the motion. A general solution to the problem how to interpolate 2n given positions by rational motion of degree 2n is presented and two particular cases, motions of degree six and eight, are studied in more detail. This interpolation scheme is further generalized to a method for constructing first order geometric continuous rational spline motions of degree six. Numerical examples are given which confirm the presented theoretical results. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free