# 曲线的弧角概念及其应用Concept of Arcangle of Curves and Its Applications

DOI: 10.12677/GST.2016.42007, PDF, HTML, XML, 下载: 1,487  浏览: 3,777

Abstract: Corresponding to arclength of curves, the concept of arcangle of curves in E3 is proposed. Arcangle of curves can be used as the index of evaluating the total curvature of wirelike objects; especially it can induce the concept of angular distance traveled of paths, which shows its potential application value.

 [1] Sullivan, J.M. (2008) Curves of Finite Total Curvature. Discrete Differential Geometry, 38, 137-161. http://dx.doi.org/10.1007/978-3-7643-8621-4_7 [2] Qin, Y.A. and Li, S.J. (2002) Total Torsion of Closed Lines of Curvature. Bulletin of the Australian Mathematical Society, 65, 73-78. http://dx.doi.org/10.1017/S0004972700020074 [3] 丁春华. 关于曲线全曲率的几个定理[J]. 安徽师大学报(自然科学版), 1993(16): 63-68. [4] Hua, L., Pan, L.B. and Lan, J. (2009) Researches on the Ring Stiffness Condition in Radial-Axial Ring Rolling. Journal of Materials Processing Technology, 209, 2570-2575. http://dx.doi.org/10.1016/j.jmatprotec.2008.06.002 [5] Dori, D. (1995) Vector-Based Arc Segmentation in the Machine Drawing Understanding System Environment. IEEE Transactions on Pattern Analysis and Machine Intelli-gence, 17, 1057-1068. http://dx.doi.org/10.1109/34.473231 [6] Landau, U.M. (1987) Estimation of a Circular Arc Center and Its Radius. Computer Vision, Graphics, and Image Processing, 38, 317-326. http://dx.doi.org/10.1016/0734-189X(87)90116-2 [7] 吴大任. 微分几何讲义[M]. 北京: 高等教育出版社, 1959: 32-34, 55-57, 168, 180-181, 268-271. [8] 庄海涛. 公路线形设计概要[M]. 南京: 东南大学出版社, 1993: 1. [9] http://www.cn-zhangjiajie.cn/action/model/name/jingqu/itemid/12.html [10] 苏步青. 微分几何学(第二版)[M]. 北京: 高等教育出版社, 1987: 74-76.