摘要
基于B样条曲线是分段的Bézier曲线段的集合这一数学特性,通过剖析三次均匀B样条曲线的数学表达及其几何意义,由曲线的几何特性给出了各曲线段Bézier点的几何表示。每段B样条曲线段(三次Bézier曲线段)对应的4个Bézier特征顶点,可以导出该曲线段的B样条基函数。依此为基础,描述了三次均匀B样条曲线构造的原理和过程,并给出了不同曲线段数情况下曲线特征构造和插值构造的相关公式。
Based on the mathematic properties, the B-spline is the sets of the Bezier curve segments. Through analyzing the mathematic expressions and geometric properties of cubic uniform B-spline, the geometric expressions of the Bezier points of curve segments are given according to the geometric properties of the curve. Each B-spline segment has related 4 Bezier characteristic points, by which the B-spline basis functions can be got. Based on the above, the principle and process of construction for the cubic uniform B-spline curve are presented, and the formulas for curve characteristic and interpolation in different circumstances are also presented.
出处
《工程图学学报》
CSCD
北大核心
2006年第2期96-102,共7页
Journal of Engineering Graphics
关键词
计算机应用
曲线构造
几何特性
三次均匀B样条曲线
computer application
curve construction
geometric properties
cubic uniform B-spline curve
