一类含参的C^(3)连续单位四元数插值样条曲线  

A C^(3)-Continuous Unit Quaternion Interpolation Spline Curve with Parameters

作　　者：王倩 周奕含 徐宇飞 刘美含 周彤 WANG Qian;ZHOU Yihan;XU Yufei;LIU Meihan;ZHOU Tong(School of Mathematics,Liaoning Normal University,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《赣南师范大学学报》2023年第6期31-38,共8页Journal of Gannan Normal University

摘　　要：为调控单位四元数样条曲线的局部形状,以方便刚体关键帧动画设计,提出一种基于欧氏空间中含参七次多项式的单位四元数样条曲线.该样条曲线满足C^(3)连续性并能自动插值任意给定的一系列关键帧方向,同时样条曲线的形状可局部调控.通过数值实验具体分析了参数的改变对样条曲线形状的影响.In order to control the unit quaternion spline curve to facilitate the design of rigid body key headframes,this paper proposes a unit quaternion spline curve based on the parametric seventh-degree polynomial in Euclidean space.The spline curve preservesC^(3)continuity and interpolates a given sequence of solid orientations.Meanwhile,the unit quaternion interpolation spline curve possesses the local shape adjustability.The influence of parameter changes on the shape of spline curves was specifically analyzed through numerical experiments.

关 键 词：四元数 样条曲线 插值性 C^(3)连续 参数向量 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]