G^(2)连续的单位四元数样条曲线  

A G^(2)-continuous unit quaternion curve

作　　者：王倩 刘美含 周彤 周奕含 徐宇飞 WANG Qian;LIU Meihan;ZHOU Tong;ZHOU Yihan;XU Yufei(School of Mathematics,Liaoning Normal University,Dalian 116081,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116081

出　　处：《辽宁师范大学学报（自然科学版）》2023年第4期438-445,共8页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：构造一种基于四次多项式的单位四元数样条曲线,并证明了其具有G^(2)连续性.首先选取带参数的四次多项式调配函数,使其生成的样条曲线能够插值给定的点列并达到C^(2)连续;然后通过将调配函数化为累和形式,把欧氏空间中的样条曲线推广到单位四元数空间中,得到的曲线不仅能插值于给定的四元数序列,而且能达到G^(2)连续;最终通过实验算例验证了该方法的有效性.所得到的构造方法添加了可以调整样条曲线形状的参数,在最终效果相似的情况下降低了样条曲线的次数,提高了计算效率.In this paper,a unit quaternion spline curve based on quartic polynomial is constructed,and proves its G^(2) continuity. Firstly,a quartic polynomial blending function with parameters is selected to generate a spline curve that can interpolate the given point series and achieve C^(2) continuity. Then,the spline curve in Euclidean space is extended to the unit quaternion space by changing the blending function into the cumulative sum form. The resulting curve can not only interpolate the given quaternion sequence,but also achieve G^(2) continuity. Finally,the effectiveness of the proposed method is verified by an experimental example. The construction method obtained in this paper adds parameters that can adjust the shape of the spline curve,which reduces the degree of the spline curve and improves the computational efficiency when the final effect is similar.

关 键 词：单位四元数 刚体运动 插值样条 G^(2)连续 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]