一类G~1连续的空间五次PH拟合曲线

发布时间：2018-06-21 12:58

本文选题：PH空间曲线 + 曲线拟合　；参考：《计算机工程与应用》2017年20期

【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。
[Abstract]:In order to construct a space quintic Pythagorean-hodograph continuous fitting curve to reconstruct the spatial curve, the first and last terminal point data are determined by adding intermediate conditions to the known spatial sampling point data, and the fitting PH curve is constructed by GG 1Hermite interpolation. According to the necessary and sufficient conditions of the spatial PH curve, the fourth derivative function composed of four quadratic polynomials is given. The vector equation is formed by comparing the vector type coefficients corresponding to the derivative function of the spatial quintic B 茅 zier curve under the Bernstein basis. According to the relation between the coefficient of derivative function of B 茅 zier curve and the vertex of its control polygon, the free parameter is introduced to establish the isometric relation between the coefficient of derivative function of B 茅 zier curve and the first and end point of the derivative function of B 茅 zier curve, and the equations are formed with the vector equation mentioned above. By solving the equations, we can obtain a continuous PH fitting curve which satisfies the first and last endpoints data given by the intermediate condition and the GQ 1 continuous PH fitting curve, which is constructed by the GQ 1Hermite interpolation, and a numerical example is given. This method is intuitionistic and has many free parameters to control the shape of the curve fitting effect, and the fitting effect is better by numerical experiment.
【作者单位】：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;桂林电子科技大学数学与计算科学学院;
【基金】：广西自然科学基金(No.2015GXNSFAA139014)
【分类号】：O186.11

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