基于四元数和Bézier方法的五次空间PH曲线  

Spatial quintic PH curve based on quaternion and Bézier method

作　　者：彭丰富[1] 庞锦荣 PENG Fengfu;PANG Jinrong(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin,Guangxi 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《中国科技论文》2023年第7期741-745,共5页China Sciencepaper

摘　　要：为保证空间Pythagorean-hodograph(PH)曲线的光顺性并使曲线最小旋转,提出了五次空间PH曲线构造。给定空间4个控制点,在给定的端点属性下,运用四元数方法构造四次Bézier曲线。对该曲线积分得到插值端点的五次PH曲线。此PH曲线的控制顶点是在原控制点的中间插入2个新节点,并且这些顶点可以用四元数运算表示。构造的五次PH曲线包含多个自由度,利用这些自由度可以对曲线进行优化调节。一方面,可以利用自由参数,根据曲线几何意义对曲线的光顺性及最小旋转进行优化;另一方面,可以通过自由参数约束曲线合理的弧长。此PH曲线本身就是Bézier曲线,且带有自由参数,能实现分段曲线的光滑拼接。To ensure the smoothness of spatial Pythagorean-hodograph(PH)curve and minimize its rotation,spatial quintic PH curve construction was proposed.Quartic Bézier curve was constructed by quaternion method based on the given four spatial control points and the endpoint attributes.Quintic PH curve of interpolated endpoint was obtained by integrating the quartic Bézier curve.Control points of PH curve can be obtained by inserting two new knots into the original control points,and both control points can be expressed by quaternion operation.The PH curve contains many degrees of freedom,which can be used for optimization and adjustment.On the one hand,free parameters can be used to optimize the fairness and minimum rotation of the curve according to the curve geometry.On the other hand,reasonable arc length can also be restricted by assigning a corresponding free parameter.Moreover,the PH curve is Bézier curve,which has the freedom to realize the smoothness splicing of these piecewise curves.

关 键 词：四元数 BÉZIER曲线 五次空间PH曲线 自由参数 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]