Topology evolutions of silhouettes

We give the topology changing of the silhouette in 3D space while others study the projections in an image. Silhou- ettes play a crucial role in visualization, graphics and vision. This work focuses on the global behaviors of silhouettes, especially their topological evolutions, such as splitting, merging, appearing and disappearing. The dynamics of silhouettes are governed by the topology, the curvature of the surface, and the view point. In this paper, we work on a more theoretical level to give enu- merative properties of the silhouette including: the integration of signed geodesic curvature along a silhouette is equal to the view cone angle; in elliptic regions, no silhouette can be contained in another one; in hyperbolic regions, if a silhouette is homotopic to a point, then it has at least 4 cusps; finally, critical events can only happen when the view point is on the aspect surfaces (ruled surface of the asymptotic lines of parabolic points with surface itself). We also introduce a method to visualize the evolution of silhouettes, especially all the critical events where the topologies of the silhouettes change. The results have broad applications in computer vision for recognition, graphics for rendering and visualization.     

基于光纤光栅传感的智能内窥镜形状感知系统

Thisdissertationaimsatprovidingsteadysensingfor theshapedetectionofcolonoscopes.Theresearch especiallydealswiththekeytechniquesoffiberbragg grating(FBG)largecurvaturesensorandsensornet,integratesthetechniquesofmechatronicsandcomput ergraphics,anddevelopsrealtimeFBGshapesensing systemandincrementalshapesensingsystemfor colonoscopies.Aftertheanalysisofstate of the artforthedevelop mentoftheendoscopeandthedifficultiesofcolonos copy,theactualitiesofbothendoscopicshapesensing systemsandofFBGstru…     

Rn+1中等参超曲面

设Mn是R^n＋1的n维C^∞超曲面，λ1，λ2，…，λn为M^n的主曲率.假设Mt^n为M^n的等参超曲面，且-↑λ1（t），-↑λ2（t），…，-↑λn（t）为Mt^n的主曲率.本文证得如下的结论：M^n为R^n＋1中的等参超曲面当且仅当（nk）Ml（x，t）=∑-↑λ1（t）-↑λ2（t）…-↑λl（t）不依赖于参数t，其中Ml表示l-th平均曲率.     

柴油机凸轮－挺柱磨损分析与摩擦副匹配试验研究

凸轮与挺柱是发动机中最容易产生早期磨损的一对摩擦副,设计不当产生磨损会严重影响发动机的可靠性。通过改进凸轮型线,增大最小曲率半径以及减小弹簧刚度来降低接触应力;同时对凸轮—挺柱二者的形状结构、空间位置、材料、硬度进行了匹配优化分析。对改进后的结果设计了合理的试验方案,进行了详细的试验验证。     

A rigidity theorem for submanifolds in S^n＋p with constant scalar curvature

Let M‘ be a closed submanifold isometrically immersed in a unit sphere S^n p. Denote by R, H and S, the normalized scalar curvature, the mean curvature, and the square of the length of the second fundamental form of M‘, respectively. Suppose R is constant and ≥1. We study the pinching problem on S and prove a rigidity theorem for M‘ immersed in S^n p with parallel normalized mean curvature vector field. When n≥8 or, n=7 and p≤2, the pinching constant is best.     

黎曼几何中的某些定理在Finsler空间上的推广

本文利用空间结构方程推出了一些结果,并在此基础上无须通过繁杂的张量运算将黎曼几何中只与弧长第二变分有关的一些定理推广到Finsler空间中.     

数控车中刀尖圆弧半径对车削精度的影响

经济型数控车床,使用开环控制系统,不具备圆弧半径补偿功能,由此引起的加工误差影响产品质量。在实际生产中要加以注意,并通过编程以补偿刀尖圆弧半径的变化,消除误差,使问题得以解决。     

给定曲率和挠率为常数的空间曲线方程

通过解向量微分方程组的特解的方法，给出了曲率函数和挠率函数为常数的空间曲线的方程，并通过分析说明具有该特征的曲线就是圆柱螺线，在此基础上进一步探讨了曲率和挠率为非常数但它们的比值为常数的空间曲线的方程．     

论曲线的一种生成算法

依据曲线的曲率变化,给出了一种不均匀取点的曲线生成算法,该算法具有逼近程度好、计算量小、适用面广等特点.     

体积比较性质与Poincare不等式

证明了Ricci曲率平方渐近非负的黎曼流形上的体积比较定理和Poincare不等式,从Poincare不等式可以得到,p-Laplacian算子关于Dirichlet边界问题的第一特征值估计。