Mbius-invariant curve and surface energies and their applications

Curvature-based surface energies are frequently used in mathematics, physics, thin plate and shell engineering, and membrane chemistry and biology studies. Invariance under rotations and shifts makes curvature-based energies very attractive for modeling various phenomena. In computer-aided geometric design, the Willmore surfaces and the so-called minimum variation surfaces （MVS） are widely used for shape modeling purposes. The Willmore surfaces are invariant w.r.t conformal transformations （Mbius or conformal invariance）, and studied thoroughly in differential geometry and related disciplines. In contrast, the minimum variation surfaces are not conformal invariant. In this paper, we suggest a simple modification of the minimum variation energy and demonstrate that the resulting modified MVS enjoy Mbius invariance （so we call them conformal-invariant MVS or, shortly, CI-MVS）. We also study connections of CI-MVS with the cyclides of Dupin. In addition, we consider several other conformal-invariant curve and surface energies involving curvatures and curvature derivatives. In particular, we show how filtering with a conformal-invariant curve energy can be used for detecting salient subsets of the principal curvature extremum curves used by Hosaka and co-workers for shape quality inspection purposes.     

Almost strictly total positivity of NUAT B-spline basis

Total positivity of spline basis has been well known in the theory of computer aided geometry design, which is highly related with good shape preserving property. Almost strictly total positivity is stronger, which could determine the positive minors while the other is zero. In this paper, a geometrical approach is proposed to prove the collection matrices of NUAT B-spline basis are almost strictly totally positive. In this paper, knot insertion algorithm combined with coefficient variation of NUAT B-spline function, we put forward an intuitive and geometrical method.     

基于Kinect的无监督图像识别

现有的物体识别方法大都是有监督学习,而且主要处理的是2D图像数据,由于这类数据给出的背景信息和物体信息少于2.5D场景中的信息,传统有监督的学习方法对于非特定物体的识别效果还是不尽如人意,更别说基于无监督学习的识别系统了。随着Kinect设别的出现,获取场景的2.5D信息变得很容易。设计了一个全新的基于无监督物体识别系统。首先用平面拟合和空间聚合把物体从场景中分离以后。然后用几何基元拟合分割技术把物体分割为不同部件,在此基础上构建物体的图模型,最后把图模型嵌入为向量空间上的点集合,使用扩展陆地移动距离算法计算物体间的相似度。从实验结果来看效果不错。     

EFFECTS OF ENTRAINED AIR MANNER ON CAVITATION DAMAGE

Early in 1953 the experiments by Peterka proved that air entrainment has effects on decreasing cavitation damage.This technology has been widely used in the release works of high dams since the inception of air entrainment in the Grand Goulee Dam in 1960.Behavior,mechanism and application of air entrainment for cavitation damage control have been investigated for over half century.However,severe cavitation damage happened due to complex mechanism of air entrainment.The effects of air entrainment are related...     

几何画板在幼儿数学教学中的应用

几何画板的使用给数学教育带来了极大的便利,本文通过对国内外几何画板应用现状的分析,提出几何画板是创设情境教学的好工具,应该在幼儿教育中大力提倡和推广。     

做数学，让知识链起来——几何画板支持下初中数学专题探究式教学研究

在信息技术与课程整合的形势下,传统教学与课程改革、过程体验与考试成绩,这两项看似的冲突成为广大教师课程改革的困惑与阻碍。本文采用专题探究式教学模式,并以初中函数图像性质专题教学为例,设计了具体的教学流程与方法。旨在探讨信息技术支持下,师生。做数学”,学生朝向高能力、高分数的目标发展。     

基于多几何特征的显微视觉对准控制策略

针对特定夹持器和环形物,基于搭建的微装配实验平台,提出了一种显微视觉引导下,夹持器相对于环形物的趋近运动控制策略.在垂直显微视觉引导下,基于夹持器和环形物的几何先验知识,实现了夹持器和环形物的多几何特征提取,从而实现了二者相对位置检测,并且根据夹持器头的几何先验知识及显微视觉检测结果,实现了对夹持器头的持续跟踪.在视觉信息反馈下,采用变结构控制器控制夹持器的运动,实现了对夹持器的快速稳定运动控制.实验结果验证了该运动控制策略的有效性.     

双边几何阈值SUSAN角点提取算法

传统的单边几何阈值SUSAN算法,易将孤立噪声点以及细线段上的点误检测为角点,或者把一些像素点较少的尖锐区域的角点检测出来,在很多的应用场合这些点并非兴趣点.为了有效地消除孤立噪声点的误检测以及剔除不感兴趣点,提出一种双边几何阈值SUSAN算法.     

基于AT89S51单片机和手势识别和的智能密码锁系统

本文介绍了一款以AT89S51单片机为主控制器,计算机完成数据处理功能的智能密码锁系统。其中,基于几何特征实现手势识别功能,并根据不同识别结果分别进行密码判断,并实现报警功能。     

用圆锥体拟合线性模型点云数据的优化计算

针对采用最小圆锥形(包括圆柱、圆锥和圆台)拟合任意轴向的线性模型的点云数据这个NP-难问题,提出一种优化算法.该算法将具有n个点的点云模型自适应地分解成一些子集,并对每个子集用一个圆锥来拟合,使得圆锥包含对应子集内所有点,且拟合圆锥的体积小于最优解的(1+ε)倍.其中圆锥拟合方法的时间复杂度为O(n/ε3),ε是用户给定的拟合误差,优于已有最快拟合方法的复杂度.实验结果表明文中算法是快速有效的.