A B-spline curve extension algorithm  

作　　者：Yang LU Kanle SHI Junhai YONG Hejin GU Haichuan SONG 

机构地区：[1]School of Software, Tsinghua University, Beijing 100084, China [2]Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China [3]Key Laboratory for Information System Security, Ministry of Education of China, Beijing 100084, China [4]Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, China [5]Jiangxi Academy of Science, Nanchang 330096, China

出　　处：《Science China(Information Sciences)》2016年第3期33-41,共9页中国科学（信息科学）（英文版）

基　　金：supported by International Science&Technology Cooperation Program of China(Grant No.2013DFE13120);Kanle SHI was supported by National Natural Science Foundation of China(Grant No.61272235);Open Funding Project of State Key Laboratory of Virtual Reality Technology and Systems;Beihang University(Grant No.BUAA-VR-14KF-05);Junhai YONG was supported by National Natural Science Foundation of China(Grant No.91315302);Haichuan SONG was supported by National Natural Science Foundation of China(Grant No.61173077)

摘　　要：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.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.

关 键 词：curve extension B-spline/NURBS unclamping CLAMPING UNIFORM 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]