摘要
B-样条曲线的升阶算法是CAD系统相互沟通必不可少的手段之一。B-样条曲线的控制多边形经过不断升阶以后,和Bézier曲线一样都会收敛到初始B-样条曲线。根据双次数B-样条的升阶算法,得到了B-样条曲线升阶的收敛性证明。与以往升阶算法不同的是,双次数B-样条的升阶算法具有割角的性质,这就使B-样条曲线升阶有了鲜明的几何意义。得到的结论可以使B-样条曲线像Bézier曲线一样,通过几何割角法生成。
Degree elevation of B-spline curves is an essential measure for communication between CAD systems. The sequence of B-spline’s control polygon convergences to initial B-spline curve is similar to the Bézier curve. The convergence proof of B-spline curve is obtained based on the degree elevation algorithm by the bi-degree B-spline. In contrast to traditional methods, degree elevation algorithm by bi-degree B-spline can be interpreted as corner cutting process, so degree elevation of B-spline curve has obvious...
出处
《工程图学学报》
CSCD
北大核心
2010年第1期100-103,共4页
Journal of Engineering Graphics
基金
国家自然科学基金资助项目(60773179)
973国家重点基础研究发展资助项目(G2004CB318000)
国家自然科学青年基金资助项目(60904070)
关键词
计算机应用
几何收敛性
积分估计
B-样条曲线
升阶
computer application
geometric convergence
integral estimation
B-spline curves
degree elevation
