三次Bézier曲线在三角域上的新扩展  

New Trigonometric Extension of Béier Curve

作　　者：葸海英 张贵仓 XI HAIYING;ZHANG GUICANG(College of Mathematics and Statistics Science, Northwest Normal University, Lanzhou 730070, Chin)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《应用数学学报》2017年第6期894-905,共12页Acta Mathematicae Applicatae Sinica

基　　金：甘肃省自然科学基金(No.0803RJZA109)资助项目

摘　　要：利用Bézier曲线和含有两个形状参数的三角αβ-TC-Bézier曲线,结合加权的思想,对Bézier曲线和αβ-TC-Bézier曲线进行了同时的扩展,得到了新的λαβ-TC-Bézier曲线·给出了新曲线的基函数,研究了曲线的性质,拼接及其应用.并且在控制多边形不变的情况下,通过调节形状参数λ,α,β的值,可以生成不同的逼近该控制多边形的曲线,并可以精确地表示或逼近抛物线弧等二次曲线,给出了表示抛物线以及花瓣图案的实例,同时还给出了新曲线及其G^1拼接后得到曲线的旋转体,这使得该曲线在自由曲线曲面设计中具有较高的应用价值.One kind of curve with there shape parameters is defined, which are both ex- tensions of Bezier curve and αβ -TC-Bezier curve. The basis functions of the new curve have been discussed. The properties, application, the G1 and G2 continuity conditions of two- piece of the curves of the curve have been studied. Meanwhile, in the case of the same control polygon, by adjusting the value of the shape parameter can generate different ap- proximate the control polygon curve. Its can also precisely represent or approach quadric curves through changing the value of the shape parameters. In addition ,conic said parabola and leaf design examples are given, at the same time also gives a new curve and curve resulting from the joining together of rotator, this makes in the design of the curve in the free curve surface has high application value.

关 键 词：BEZIER曲线 αβ-TC-Bezier曲线 λαβ-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]