Beta四元数样条曲线相关问题研究
Research on the Beta Quaternion Spline
摘要: 为了更加灵活地调控单位四元数样条曲线，局部控制样条曲线形状，本文基于球面Bézier曲线，将欧氏空间中的Beta样条曲线推广到四元数空间，给出Beta四元数样条曲线定义。证明了该样条曲线满足G1连续，给出了满足G2连续的充要条件及其证明。最后通过数值实验验证该方法的可行性。本文构造的四元数样条曲线是由控制多边形的顶点直接定义曲线控制顶点，只需改变某段形状参数的取值，即可局部调控样条曲线形状。
Abstract: In order to control the unit quaternion spline more flexibly locally, this paper generalizes the Beta spline in the Euclidean space to the quaternion space based on the spherical Bézier curve, and gives the definition of the Beta quaternion spline. It is proved that the spline satisfies the first-order ge-ometric continuity. The Sufficient requisites for satisfying the second-order geometric continuity and the proof are given. Finally, numerical experiments are used to verify the feasibility of the pro-posed method. The control points of quaternion spline constructed in this paper are directly de-fined by the points of the control polygon, and the spline shape can be controlled locally by simply changing the value of some shape parameters.
文章引用：何耀, 王倩, 周奕含, 陈佳惠, 刘美含. Beta四元数样条曲线相关问题研究[J]. 应用数学进展, 2022, 11(12): 8431-8441. https://doi.org/10.12677/AAM.2022.1112892

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