关键词: 计算机应用, 几何收敛性, 积分估计, B-样条曲线, 升阶

Abstract: 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 geometric meaning. The result makes B-spline curve obtained by geometric corner cutting algorithm as Bézier curve.

Key words: computer application, geometric convergence, integral estimation, B-spline curves, degree elevation