一类G^1连续的空间五次PH拟合曲线  

G^1-continuity spatial quintic PH fitted curve

作　　者：彭丰富 刘惠[2] PENG Fengfu;LIU Hui(School of Mathematics and Computing Science, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China;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高校数据分析与计算重点实验室,广西桂林541004 [2]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《计算机工程与应用》2017年第20期161-165,共5页Computer Engineering and Applications

基　　金：广西自然科学基金(No.2015GXNSFAA139014)

摘　　要：为了构造一种空间五次Pythagorean-hodograph G^1连续拟合曲线以重建空间曲线,对已知空间采样点数据加入中间条件确定首末端点数据,对其进行G^1Hermite插值构造拟合PH曲线。根据空间PH曲线的充分必要条件,给出由四个二次多项式组成的四次导函数,比对其与空间五次Bézier曲线的导函数在Bernstein基下分别对应的向量型系数,形成向量等式,再根据Bézier曲线导函数的系数与其控制多边形顶点的关系,引入自由参数建立五次Bézier曲线导函数的系数与首末端点的等量关系,并与前述向量等式组成方程组。通过求解方程组可得一段由G^1Hermite插值构造出的满足由中间条件给出的首末端点数据且G^1连续的PH拟合曲线,并给出了数值实例。此构造方法直观,有多个自由参数可对曲线进行拟合效果的形状控制,且通过数值实验拟合效果较好。To construct a G1continuity spatial quintic Pythagorean-hodograph fitted curve for the reconstruction of spatialcurve,through adding some intermediate conditions into the space sampling points to determine endpoints’dates,it interpolatesthese spatial discrete data with G1Hermite to construct spatial PH fitted curve.According to the sufficient and necessaryconditions of PH space curve,the quartic derived vector composed of four quadratic polynomials is given.Its coefficientsin Bernstein basis are compared with coefficients of Bézier curve’s derived vector to compose a system of equations.Following it compares Bézier curve’s derived vector coefficients with the control points of Bézier curve,by addingsome free parameters to build their equal relationships.Then it composes a system of equations with aforementioned equationsand equal relationships.By solving them,a G1continuity spatial quintic Pythagorean-hodograph fitted curve is productedwith G1Hermite interpolation,which satisfies the data of endpoints determined by intermediate conditions,and some numerical examples are presented.This construction method is intuitive,it includes multiple free parameters tocontrol the shape of curve fitting effect.

关 键 词：PH空间曲线 曲线拟合 G1Hermite插值 BERNSTEIN基函数 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]