计算机辅助设计与图形学学报
計算機輔助設計與圖形學學報
계산궤보조설계여도형학학보
JOURNAL OF COMPUTER-AIDED DESIGN & COMPUTER GRAPHICS
2010年
2期
306-311
,共6页
区间B样条曲线%区间控制多边形%双次B样条基函数%升阶%割角
區間B樣條麯線%區間控製多邊形%雙次B樣條基函數%升階%割角
구간B양조곡선%구간공제다변형%쌍차B양조기함수%승계%할각
interval B-spline curves%interval control polygon%bi-degree B-spline basis functions%degree elevation%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.
為瞭解決區間B樣條麯線的升階理論問題,提齣區間控製多邊形概唸,利用雙次B樣條基函數證明瞭區間B樣條麯線具有升階性質; 併闡明瞭區間B樣條麯線的升階就是對其控製多邊形的割角過程.最後證明瞭噹升階次數趨于無窮時,區間B樣條麯線的控製多邊形收斂到該麯線.
위료해결구간B양조곡선적승계이론문제,제출구간공제다변형개념,이용쌍차B양조기함수증명료구간B양조곡선구유승계성질; 병천명료구간B양조곡선적승계취시대기공제다변형적할각과정.최후증명료당승계차수추우무궁시,구간B양조곡선적공제다변형수렴도해곡선.
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, its proved that the control polygon sequence by degree elevation will converge to the interval B-spline curve.
