三维离散曲线曲率挠率的微中心差分算法  

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[1] 李世林[1] MU Shengpeng;LI Hongjun;LI Shilin(College of Science,Beijing Forestry University,Beijing 100083,China)

机构地区：[1]北京林业大学理学院,北京100083

出　　处：《智能系统学报》2019年第1期194-206,共13页CAAI Transactions on Intelligent Systems

基　　金：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)

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。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.

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 

分 类 号：TP311[自动化与计算机技术—计算机软件与理论]