带形状控制的二次有理三角样条曲线

系统仿真学报 ›› 2016, Vol. 28 ›› Issue (10): 2400-2406.

带形状控制的二次有理三角样条曲线

刘新儒^1,2, 魏曼曼¹, 刘圣军^1,2,*, 杨当福¹

1.中南大学数学与统计学院,长沙 410083;
2.中南大学工程建模与科学计算研究所,长沙 410083

收稿日期:2016-05-31 修回日期:2016-07-19 出版日期:2016-10-08 发布日期:2020-08-13
作者简介:刘新儒(1982-),男,湖南新化,博士,讲师,研究方向为几何造型、数值建模;魏曼曼(1991-),女,河南商丘,硕士生,研究方向为计算机辅助几何设计。
基金资助:
国家自然科学基金(61572527,11271376),中南大学创新驱动计划(2015CXS037)

Quadratic Rational Trigonometric Spline Curves with Shape Controlling

Liu Xinru^1,2, Wei Manman¹, Liu Shengjun^1,2,*, Yang Dangfu¹

1. School of Mathematics and Statistics, Central South University, Changsha 410083, China;
2. Institute of Engineering Modeling and Scientific Computing, Central South University, Changsha 410083, China

Received:2016-05-31 Revised:2016-07-19 Online:2016-10-08 Published:2020-08-13

摘要/Abstract

摘要： 利用函数值及其一阶导数来构造带形状控制的二次有理三角样条曲线.从理论上详细讨论了该插值曲线格式的值控制及拐点控制,并从最优化角度结合设计目标,给出了拐点位置计算的最优化方法.实例表明,该曲线格式及优化方法可用于造型设计.

关键词: 有理三角样条, 值控制, 拐点控制, 最优化

Abstract: A new quadratic rational trigonometric spline curve with a shape parameter was proposed. The value control and the inflection-point control of the interpolation scheme were discussed in theory. And the optimal methods for calculating the desired inflection-points was proposed, by using optimization theory. Numerical experiments show the interpolation spline and the optimization method can be used in modeling design.

Key words: rational trigonometric spline, value control, inflection-point control, optimization

中图分类号:

TP391.9

刘新儒, 魏曼曼, 刘圣军, 杨当福. 带形状控制的二次有理三角样条曲线[J]. 系统仿真学报, 2016, 28(10): 2400-2406.

Liu Xinru, Wei Manman, Liu Shengjun, Yang Dangfu. Quadratic Rational Trigonometric Spline Curves with Shape Controlling[J]. Journal of System Simulation, 2016, 28(10): 2400-2406.

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