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# A B-spline curve extension algorithm

B 样条曲线延伸算法

## Abstract

B-spline curve extension is an important operation in computer aided design systems. In this paper, we present a new extension algorithm for B-spline curves. The algorithm uses curve unclamping to generate a uniform B-spline curve segment from the original curve and gradually extends the segment to pass through every target point. Algorithms of uniform B-spline curves are used such that our algorithm has a low time cost and can easily handle arbitrary-order derivative constraints at the target points. Generalization for non-uniform rational B-spline curve extension is also discussed, and examples show the efficiency of our method.

## 摘要

### 创新点

B 样条曲线延伸是计算机辅助造型系统中的一个重要操作。本文中我们提出一种 B 样条曲线延伸的新算法。算法使用曲线开支化将输入转化为均匀 B 样条曲线, 然后将其逐步延伸到各个目标点处。我们借助均匀 B 样条的求值方法加速曲线延伸操作, 使得算法拥有很高的时间效率, 并可以处理目标点处的任意阶导数约束。我们还进一步拓展算法, 以处理 NURBS 曲线延伸问题。在实验部分我们给出一些构造实例, 以验证算法有效性。

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## Author information

Correspondence to Hejin Gu.

## Rights and permissions

Reprints and Permissions

Lu, Y., Shi, K., Yong, J. et al. A B-spline curve extension algorithm. Sci. China Inf. Sci. 59, 32103 (2016). https://doi.org/10.1007/s11432-015-5322-x

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• Published:

### Keywords

• curve extension
• B-spline/NURBS
• unclamping
• clamping
• uniform

• 曲线延伸
• B 样条/有理B样条
• 闭支曲线
• 开支曲线
• 均匀节点