二/三阶三角Bézier曲线  

Triangular Bézier Curve of Order Two/Three

作　　者：严兰兰[1,2] 韩旭里[2] 邬国根[1] 黄国辉[1] 

机构地区：[1]东华理工大学理学院,江西抚州344000 [2]中南大学数学与统计学院,湖南长沙410083

出　　处：《图学学报》2013年第5期71-75,共5页Journal of Graphics

基　　金：国家自然科学基金资助项目(11261003;11271376;60970097)

摘　　要：构造了两组由三角函数形成的基函数,并由这两组基函数定义了两种新的曲线,分别称为二阶、三阶T-Bézier曲线。这两种曲线分别具有和二次Bézier曲线、三次Bézier曲线一样简单的结构,而且都具有Bézier曲线的基本性质,如凸包性、对称性、几何不变性、端点插值和端边相切性。此外,在普通Bézier曲线的G1光滑拼接条件下,二阶T-Bézier曲线可以达到G3光滑拼接,三阶T-Bézier曲线可以达到G2光滑拼接。另外,给出了用二阶T-Bézier曲线来构造与给定多边形相切的曲线的方法,该方法简单有效,而且曲线对给定的多边形是保形的。Two sets of basic functions formed by triangular functions are constructed,and two new kinds of curves based on them are defined.We call them T-Bézier curve of order two and T-Bézier curve of order three respectively.They have the same simple structures with quadratic Bézier curve and cubic Bézier curve respectively.They have many properties of usual Bézier curve,such as convex hull property,symmetry,geometric invariance,endpoint interpolation and end edge tangent property.In addition,under theG1 continuity conditions,the T-Bézier curve of order two can achieve G3 continuity,and the T-Bézier curve of order three can achieve G2 continuity.Furthermore,the method of using the T-Bézier curve of order two to construct combination curve with given tangent polygon is also given.This method is simple and effective.The curve is conformal to the given polygon.

关 键 词：曲线设计 BÉZIER曲线 连续性 切线多边形 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]