结合加权的三次Bezier曲线的新扩展  

New extension of cubic Bezier curve combining weighting thought

作　　者：拓明秀 张贵仓 汪凯 TUO Ming-xiu;ZHANG Gui-cang;WANG Kai(School of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《计算机工程与设计》2020年第3期756-762,共7页Computer Engineering and Design

基　　金：国家自然科学基金项目(61861040);甘肃省教育厅科技成果转化基金项目(2017D-09);甘肃省科技基金项目(17YF1FA119);兰州市科技计划基金项目(2018-4-35)。

摘　　要：为使构造的曲线兼顾代数多项式空间和三角多项式空间的优点,利用加权思想,提出一种ωλμ-TC-Bezier曲线。将代数多项式空间的三次Bernstein基函数和三角多项式空间的三次类Bernstein基函数相结合,得到新的基函数并分析其性质;在该基函数的基础上,给出相应曲线的定义和性质;给出曲线的大量案例。结果表明,形状参数及加权思想的融入使ωλμ-TC-Bezier曲线在具有Bezier曲线实用性质的同时还具有灵活的形状可调性,能够精确地表示地抛物线弧、椭圆弧及圆弧等二次曲线。大量的分析以及实例结果表明,结合加权思想构造的ωλμ-TC-Bezier曲线在曲线设计中十分有效。To make constructed curve have the advantages of the algebraic polynomial space and the triangular polynomial space,aωλμ-TC-Bezier curve was proposed using the idea of weighting.A new base function and its properties were analyzed by combining the cubic Bernstein base function of algebraic polynomial space and cubic class Bernstein base function of trigonometric polynomial space.The definition and properties of corresponding curves were given on the basis of the new base function.A large number of cases of curves was given.The results show that the integration of shape parameters and weighting ideas makes theωλμ-TC-Bezier curve has not only the practical properties of Bezier curve,but flexible shape adjustability,and it can accurately represent the conic curves such as parabola arc,elliptical arc and arc.A large number of analysis and examples show that theωλμ-TC-Bezier curve constructed with the weighting idea is very effective in curve design.

关 键 词：BERNSTEIN基函数 ωλμ-TC-Bezier曲线 形状参数 拼接 曲线设计 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]