曲率挠率的估计算法及其工艺嵌入

摘要

几何处理和计算机视觉的很多应用依赖于几何性质,尤其是曲线的曲率和挠率.论文对非参数化的曲线提出了曲率和挠率的离散估计公式,以及消除噪音干扰的加权因子算法.还通过Maple程序,筛选统计出常见曲线的部分曲率和挠率参考值,提出理想曲率的大致范围和理想挠率的大致范围,并考虑嵌入到特定的工艺品中实验.%Many applications of geometry processing and computer vision rely on geometric properties of curves, particularly their curvatures and torsions. This paper proposes some methods to estimate the curvature and the torsion, based on some algorithms for weighted least-squares fitting and local arc-length approximation in order to eliminate noises. By Maple procedure, statistical analysis of some selected common curves is carried out to get partial values of their curvatures and torsions, and then an approximate interval about ideal curvatures and ideal torsions is put forward. Furthermore, several test models for embedding specific ideal curvature or ideal torsion in crafts are taken into account.