二次Bézier曲线的扩展  

Extension of a quadratic Bézier curve

作　　者：韩旭里[1] 刘圣军[1] 

机构地区：[1]中南大学数学科学与计算技术学院,湖南长沙410083

出　　处：《中南工业大学学报》2003年第2期214-217,共4页Journal of Central South University of Technology(Natural Science)

基　　金：湖南省自然科学基金资助项目(01JJY2095);国家教育部回国人员科研基金资助项目(教外司留[2001]498号)

摘　　要：给出了三次带参数λi的多项式调配函数,它是二次B啨zier曲线基函数的扩展.基于给出的调配函数,建立了带形状参数的分段多项式曲线生成方法;研究了所生成曲线及其基函数的性质和连续条件.其基函数具有权性,在参数λi取值于[-2,1]区间时具有非负性;曲线的性质如端点性质、对称性、凸包性、几何不变性等与二次B啨zier曲线的性质类似.研究结果表明:通过改变形状参数λi的取值,可以调整第i段曲线接近某控制多边形的程度;所给曲线中的形状参数λi是局部的,便于进行曲线设计.A class of polynomial functions of degree 3 with parameter λ i is presented in this paper. It is an extension of the quadratic Bézier curves basis functions. Based on the functions, a method of generating piecewise polynomial curves with a shape parameter is given. The properties and continuity conditions of the curves and its basis functions are discussed. The basis functions have weighting property and they have positivity when the parameter λ i is between -2 and 1. The curves properties are similar with the degree 2 Bézier curves, such as endpoints' properties, symmetry, convex hull, and geometric invariability. By changing value of the shape parameter λ i , the approaching degree between the i th curve and the control polygon can be adjusted. The shape parameter λ i is local, then the method is very useful for curve design.

关 键 词：二次Bézier曲线 曲线设计 形状参数 计算机辅助几何设计 样条函数 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术] O18[自动化与计算机技术—计算机科学与技术]