[1]慕生鹏,李红军,李世林.三维离散曲线曲率挠率的微中心差分算法[J].智能系统学报,2019,14(1):194-206.[doi:10.11992/tis.201802008]
MU Shengpeng,LI Hongjun,LI Shilin.An algorithm for estimating curvature and torsion of discrete curve in three-dimensional space based on microcentral difference[J].CAAI Transactions on Intelligent Systems,2019,14(1):194-206.[doi:10.11992/tis.201802008]
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MU Shengpeng,LI Hongjun,LI Shilin.An algorithm for estimating curvature and torsion of discrete curve in three-dimensional space based on microcentral difference[J].CAAI Transactions on Intelligent Systems,2019,14(1):194-206.[doi:10.11992/tis.201802008]
三维离散曲线曲率挠率的微中心差分算法
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
14
期数:
2019年第1期
页码:
194-206
栏目:
学术论文—人工智能基础
出版日期:
2019-01-05
- Title:
- An algorithm for estimating curvature and torsion of discrete curve in three-dimensional space based on microcentral difference
- Keywords:
- curvature; torsion; algorithm comparison; discrete curve; microcentral difference algorithm; discrete geometry method; three-dimensional space; difference quotient; uniformly sampling
- 分类号:
- TP311
- 摘要:
- 曲率和挠率是描述三维空间离散曲线的弯曲和扭曲程度的两个微分量。为了准确计算这两个微分量，从连续曲线的导数定义出发，提出微中心差分算法进行三维空间离散曲线的曲率和挠率计算。该算法基于差商平滑策略实现对单侧差分算法的一个有效扩展。与单侧差分算法相比，微中心差分算法不增加算法执行时间，但在计算精度方面有显著提升。实验分析是通过6条曲线的均匀采样获取离散曲线数据，与5种常用的曲率和挠率计算算法相比较，对这6种算法从采样密度对算法精度的影响、计算效率和抗噪声性能这3个方面进行了对比分析。实验结果表明，微中心差分算法总体效果最好。
- Abstract:
- The curvature and torsion of a 3D discrete curve reflect the degrees of its bending and distortion. To calculate these quantities accurately, following the definition of the derivative of the continuous curve, a microcentral difference algorithm, which is an extension to the one-side difference algorithm, is proposed based on the smoothing of the difference quotient. Compared with the one-side difference algorithm, the microcentral difference algorithm fails to prolong the running time but it remarkably improves the calculation accuracy. Several experiments are conducted by uniform sampling from six continuous curves, which are then compared with the five traditional algorithms of curvature and torsion. The experimental results are analyzed from three aspects:the influence of the sampling density on the accuracy of the algorithm, the efficiency of calculation, and the anti-noise performance. The experimental results show the good performance of the proposed microcentral difference algorithm.
- 参考文献/References:
-
[1] 李杰, 彭双春, 安宏雷, 等. 基于微分几何与李群的无人机编队会合方法[J]. 国防科技大学学报, 2013, 35(6):157-164 LI Jie, PENG Shuangchun, AN Honglei, et al. UAVs formation rendezvous method based on differential geometry and Lie group[J]. Journal of national university of defense technology, 2013, 35(6):157-164
[2] 单洪春. 基于空间特性的弹道特征抽取[J]. 飞行器测控学报, 2012, 31(2):69-72 SHAN Hongchun. Trajectory characteristics extraction based on space property[J]. Journal of spacecraft TT&C technology, 2012, 31(2):69-72
[3] 葛婷, 符锌砂, 李海峰, 等. 公路三维线形设计及约束建模[J]. 华南理工大学学报(自然科学版), 2016, 44(8):91-97, 105 GE Ting, FU Xinsha, LI Haifeng, et al. Three-dimensional highway alignment design and constraints modeling[J]. Journal of South China university of technology (natural science edition), 2016, 44(8):91-97, 105
[4] 潘登, 郑应平. 路径约束条件下车辆行为的时空演化模型[J]. 物理学报, 2015, 64(7):078902 PAN Deng, ZHENG Yingping. Spatiotemporal evolution model of vehicular movement behavior under path constraints[J]. Acta physica sinica, 2015, 64(7):078902
[5] PATRIKALAKIS N M, MAEKAWA T. Shape interrogation for computer aided design and manufacturing[M]. Berlin, Heidelberg:Springer, 2002.
[6] MOKHTARIAN F, MACKWORTH A K. A theory of multiscale, curvature-based shape representation for planar curves[J]. IEEE transactions on pattern analysis and machine intelligence, 1992, 14(8):789-805.
[7] 袁修久, 王胜勇, 刘欣, 等. 推广的三维L-系统及在树木模拟中的应用[J]. 系统仿真学报, 2011, 23(11):2308-2311 YUAN Xiujiu, WANG Shengyong, LIU Xin, et al. Improvement of three-dimensional L-system and its application to trees modeling[J]. Journal of system simulation, 2011, 23(11):2308-2311
[8] 张冠军, 朱翔, 李天匀. 基于级数变换法的椭圆柱壳受迫振动分析[J]. 哈尔滨工程大学学报, 2017, 38(4):506-513 ZHANG Guanjun, ZHU Xiang, LI Tianyun. Forced vibration analysis of elliptic cylindrical shell based on the series transformation method[J]. Journal of Harbin engineering university, 2017, 38(4):506-513
[9] 孟道骥, 梁科. 微分几何[M]. 2版. 北京:科学出版社, 2004:6-28. MENG Daoji, LIANG Ke. Differential geometry[M]. 2nd ed. Beijing:Science Press, 2004:6-28.
[10] DO CARMO M P. Differential geometry of curves and surfaces[M]. Englewood Cliffs, New Jersey:Prentice Hall, 1976:175-178.
[11] BRAY H L, JAUREGUI J L. On curves with nonnegative torsion[J]. Archiv der mathematik, 2015, 104(6):561-575.
[12] LIU Huili. Curves in three dimensional riemannian space forms[J]. Results in mathematics, 2014, 66(3/4):469-480.
[13] MASSER D, ZANNIER U. Torsion points on families of products of elliptic curves[J]. Advances in mathematics, 2014, 259:116-133.
[14] 郑长波, 刘会立. 三维欧氏空间中的几类特殊球面曲线[J]. 浙江大学学报(理学版), 2013, 40(2):127-130 ZHENG Changbo, LIU Huili. Some special spherical curves in Euclidean 3-space[J]. Journal of Zhejiang university (science edition), 2013, 40(2):127-130
[15] 袁媛, 李静, 刘会立. 三维欧氏空间中的特殊曲线[J]. 东北大学学报(自然科学版), 2017, 38(11):1669-1672 YUAN Yuan, LI Jing, LIU Huili. Special curves in 3-dimensional euclidean space[J]. Journal of Northeastern university (natural science), 2017, 38(11):1669-1672
[16] CAZALS F, POUGET M. Estimating differential quantities using polynomial fitting of osculating jets[J]. Computer aided geometric design, 2005, 22(2):121-146.
[17] 赵夫群, 周明全. 一种有效的秦俑碎块匹配算法[J]. 计算机系统应用, 2017, 26(3):198-203 ZHAO Fuqun, ZHOU Mingquan. Effective blocks matching algorithm of terracotta warrior[J]. Computer systems and applications, 2017, 26(3):198-203
[18] 喻德生, 程程. 基于离散曲率的三次均匀B样条的局部光顺算法[J]. 浙江大学学报(理学版), 2011, 38(5):511-517 YU Desheng, CHENG Cheng. On local fairing algorithm for cubic B-spline with discrete curvature[J]. Journal of Zhejiang university (science edition), 2011, 38(5):511-517
[19] KEHTARNAVAZ N, DEFIGUEIREDO R J P. A 3-D contour segmentation scheme based on curvature and torsion[J]. IEEE transactions on pattern analysis and machine intelligence, 1988, 10(5):707-713.
[20] MARDIA K V. Estimation of torsion[J]. Journal of applied statistics, 1999, 26(3):373-381.
[21] BLANKENBURG C, DAUL C, OHSER J. Parameter free torsion estimation of curves in 3D images[C]//2016 IEEE International Conference on Image Processing. Phoenix, AZ, USA, 2016:1081-1085.
[22] AN Yi, SHAO Cheng, WANG Xiaoliang, et al. Geometric properties estimation from discrete curves using discrete derivatives[J]. Computers & graphics, 2011, 35(4):916-930.
[23] 陈维桓. 微分几何[M]. 北京:北京大学出版社, 2006:23-47.
[24] MA Weiyin, KRUTH J P. Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces[J]. Computer-aided design, 1995, 27(9):663-675.
[25] 周志华. 机器学习[M]. 北京:清华大学出版社, 2016:28?37.
[26] 刘伟, 王雅静, 陈文钢, 等. 动态光散射反演算法的评价指标[J]. 光学学报, 2015, 35(S1):129001 LIU Wei, WANG Yajing, CHEN Wengang, et al. Evaluation criteria of inversion algorithm for dynamic light scattering[J]. Acta optica sinica, 2015, 35(S1):129001
备注/Memo
收稿日期:2018-02-05。
基金项目:国家自然科学基金项目（61372190）；中央高校基本科研业务费专项资金项目（2015ZCQ-LY-01）.
作者简介:慕生鹏,男,1992年生,硕士研究生,中国计算机学会会员,主要研究方向为计算几何。参加国家自然科学基金1项,计算机软件著作权登记2项;李红军,男,1969年生,副教授,博士,北京数学会理事,中国计算机学会会员,主要研究方向为计算几何、计算机图形学、图像处理和植物建模。主持国家自然科学基金面上项目1项、参加2项。获中国发明专利授权9项,计算机软件著作权登记11项。发表学术论文40余篇,被SCI、EI检索20余篇;李世林,男,1992年生,硕士研究生,中国计算机学会会员,主要研究方向为计算几何。参加国家自然科学基金项目1项,计算机软件著作权登记4项。发表学术论文1篇。
通讯作者:李红军.E-mail:lihongjun69@bjfu.edu.cn
更新日期/Last Update:
1900-01-01