[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(01):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(01):194-206.[doi:10.11992/tis.201802008]
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三维离散曲线曲率挠率的微中心差分算法(/HTML)
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《智能系统学报》[ISSN:1673-4785/CN:23-1538/TP]

卷:
第14卷
期数:
2019年01期
页码:
194-206
栏目:
出版日期:
2019-01-05

文章信息/Info

Title:
An algorithm for estimating curvature and torsion of discrete curve in three-dimensional space based on microcentral difference
作者:
慕生鹏 李红军 李世林
北京林业大学 理学院, 北京 100083
Author(s):
MU Shengpeng LI Hongjun LI Shilin
College of Science, Beijing Forestry University, Beijing 100083, China
关键词:
曲率挠率算法比较离散曲线微中心差分法离散几何法三维空间差商均匀采样
Keywords:
curvaturetorsionalgorithm comparisondiscrete curvemicrocentral difference algorithmdiscrete geometry methodthree-dimensional spacedifference quotientuniformly sampling
分类号:
TP311
DOI:
10.11992/tis.201802008
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.

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备注/Memo

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