摘要
给出了含有参数λ的(n+1)次多项式基函数,其是n次Bernste in基函数的扩展;分析了这组基的性质,基于该组基定义了带有形状参数的(n+1)次多项式曲线。曲线不仅具有n次Bézier曲线的特性:如端点插值、端边相切、凸包性、变差缩减性、保凸性等,而且具有形状的可调性:在控制顶点不变的情况下,随着参数不同,可产生不同逼近控制多边形的曲线。当λ=0时,曲线可退化为n次Bézier曲线。运用张量积方法,可生成形状可调的曲面,曲面具有曲线类似的性质。应用实例表明,本文定义的曲线应用于曲线/曲面的设计十分有效。
Through heightening the degree of polynomial function, a class of polynomial function of （n ＋ 1 ） degree that containing an adjustable constant parameter A is presented in this paper. They are an extension of n degree Bernstein basis functions. Properties of this new basis are analyzed, which have symmetry, linear independence, weighting property and nonnegative property when the parameter A is between - 2 and 1, based on which a （ n ＋ 1 ） degree polynomial curve with a shape parameter A is defined. The curve, to be called A-Bézier curve not only inherits the most properties of n-degree Bézier curve, such as endpoints＇ properties, symmetry, convex hull property, geometric invariability, affine invariance, convex-preserving property, variation diminishing property and so on, but also can be adjusted in shape by changing the value of A without changement of control points. When A = 0, the curve degenerates to n-degree Bézier Curve. Using tensor product approach, a surface with parameter A is constructed, whose properties are similar to the curve＇ s. At last, examples illustrate the method of constructing curve is very useful for curve/surface design.
出处
《中国图象图形学报》
CSCD
北大核心
2006年第2期269-274,共6页
Journal of Image and Graphics
基金
湖南省教育厅资助项目(04C215)
