一类C^(3)连续的奇异混合四元数样条曲线  

A C^(3)singular blending quaternion interpolation spline curve

作　　者：王倩 徐宇飞 周彤 姜桐 朱佳一 WANG Qian;XU Yufei;ZHOU Tong;JIANG Tong;ZHU Jiayi(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）》2024年第4期449-457,共9页Journal of Liaoning Normal University:Natural Science Edition

摘　　要：为提高单位四元数样条曲线的连续性,对刚体运动姿态的细节进行调控.首先设计得到欧氏空间中的六次奇异混合插值样条曲线,再将其推广到四元数空间.得到的六次单位四元数插值样条曲线能够自动插值给定点列并达到C^(3)连续.最后通过数值实验与其他方法进行了对比,体现了本方法中的多个参数有利于实际应用中刚体运动姿态的即时调控.To increase the continuity of unit quaternion spline curves and regulate the details of rigid body attitude motion,this paper designs a sixth-degree singular blending interpolation spline curve in Euclidean space.Then the spline is extended to the quaternion space.The resulting sixth-degree unit quaternion interpolation spline curve can automatically interpolate the given sequence while achieving C^(3).Finally,numerical experiments are conducted to compare with other approaches,underscoring the advantage of utilizing multiple parameters in our methodology.This facilitates the regulation and control of rigid body motion attitudes in practical applications.

关 键 词：单位四元数 C^(3)连续 样条曲线 奇异混合插值 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]