A B-spline curve extension algorithm

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。