| B样条曲线同时插入多个节点的快速算法 |
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| 引用本文： | 潘日晶,潘日红,姚志强.B样条曲线同时插入多个节点的快速算法[J].小型微型计算机系统,2003,24(12):2295-2298. |
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| 作者姓名： | 潘日晶 潘日红 姚志强 |
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| 作者单位： | 福建师范大学,数学与计算机科学学院,福建,福州,350007 |
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| 基金项目： | 福建省自然科学基金 (A0 2 1 0 0 1 6)资助，福建省教育厅B类科研基金项目 (JB0 1 1 1 4 )资助 |
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| 摘 要： | 基于离散B样条的一个新的递推公式，提出B样条曲线同时插入多个节点的新算法。不同于Cohen等插入节点的Oslo算法，本算法用新的方法离算离散B样条，求每个离散B样条的值只需O(1)的运算量，从而使本算法高效，其时间复杂性为O(sk n)，其中k为B样条曲线的阶，n k 1为原节点数，s为新插入节点的个数,本算法的通用性强，适用于端点插值的和非端点插值的B样条曲线，可同时在曲线定义域内外的任意位置上插入任意个节点。
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| 关 键 词： | B样条曲线 节点插入 离散B样条 快速算法 计算机辅助几何设计 |
| 文章编号： | 1000-1220(2003)12-2295-04 |
A Fast Algorithm for Inserting a Series of Knots into a B-spline Curve Simultaneously |
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| PAN Ri-jing,PAN Ri-hong,YAO Zhi-qiang.A Fast Algorithm for Inserting a Series of Knots into a B-spline Curve Simultaneously[J].Mini-micro Systems,2003,24(12):2295-2298. |
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| Authors: | PAN Ri-jing PAN Ri-hong YAO Zhi-qiang |
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| Abstract: | Based on a new recurrent formula of discrete B-splines, a fast algorithm is presented for inserting a series of knots into a B-spline curve simultaneously. The time complexity of this algorithm is O(sk+n), where k is the order of B-spline curve and n+k+1 is the number of knots before inserting knots, s is the number of inserted knots. This algorithm can be applied to both endpoints-interpolating and non-endpoints-interpolating B-spline curves . And the positions of the inserted knots can be inside or outside the domain of B-spline curves. |
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| Keywords: | B-spline curre knot insertion discrete B-spline algorithm |
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