论区间B样条曲线的升阶与割角的关系

The Degree Elevation of Interval B-Spline Curves and Corner Cutting

为了解决区间B样条曲线的升阶理论问题,提出区间控制多边形概念,利用双次B样条基函数证明了区间B样条曲线具有升阶性质;并阐明了区间B样条曲线的升阶就是对其控制多边形的割角过程.最后证明了当升阶次数趋于无穷时,区间B样条曲线的控制多边形收敛到该曲线.

This paper investigates degree elevation of interval B-spline. Based on the concept of interval control polygon, we prove that interval B-spline curves hold the degree elevation property by using bi- degree B-spline basis functions. Further, we show that the degree elevation of interval B-spline curves is equivalent to corner cutting of control polygons. Finally, it＇s proved that the control polygon sequence by degree elevation will converge to the interval B-spline curve.