二次Bézier曲线的扩展

来源期刊：中南大学学报(自然科学版)2003年第2期

论文作者：韩旭里 刘圣军

文章页码：214 - 217

关键词：Bézier曲线;曲线设计;形状参数

Key words：Bézier curve; curve design; shape parameter

摘    要：给出了三次带参数λ_i的多项式调配函数,它是二次Bézier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λ_i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Bézier曲线的性质类似.研究结果表明:通过改变形状参数λ_i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λ_i是局部的,便于进行曲线设计.

Abstract: 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 λi, the approaching degree between thei-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.