Angle deficit approximation of Gaussian curvature and its convergence over quadrilateral meshes

We propose a discrete approximation of Gaussian curvature over quadrilateral meshes using a linear combination of two angle deficits. Let g_ij and b_ij be the coefficients of the first and second fundamental forms of a smooth parametric surface F. Suppose F is sampled so that a surface mesh is obtained. Theoretically we show that for vertices of valence four, the considered two angle deficits are asymptotically equivalent to rational functions in g_ij and b_ij under some special conditions called the parallelogram criterion. Specifically, the numerators of the rational functions are homogenous polynomials of degree two in b_ij with closed form coefficients, and the denominators are . Our discrete approximation of the Gaussian curvature derived from the combination of the angle deficits has quadratic convergence rate under the parallelogram criterion. Numerical results which justify the theoretical analysis are also presented.     

非均匀抽样网格简化

提出了一种考虑视点空间中某些重要视点的非均匀抽样网格简化的新方法,是在借鉴了Garland-Heckbert方法的基础上提出的,是一种考虑外观相似性的简化算法。给出并证明了两个判定边界的定理,为抽样提供了理论依据。在简化过程中,该算法通过采用视点空间中某些重要视点对模型进行抽样,使抽中的顶点对（轮廓附近的顶点对）得到适当保护。该算法除具有Garland-Heckbert方法的长处外,还可以在三角面片数较少的情况下（50多个三角面片）,尽可能保持模型的重要外观特征,给出了计算0－1图像的外观相似性误差的公式,通过该公式对简化结果进行比较,证明提出的简化算法对保持模型的外观特征是行之有效的。最后对该算法的时间和空间复杂性进行了分析。     

寻找任意线段和圆弧围成区域的一种算法

寻找任意线段和圆弧围成的区域问题是建筑结构CAD软件前处理中的一个基本问题。作者通过自己的研究开发经验,提出了三个基本算法,即如何由输入的线段和圆弧得出网格点、网格线和区域表,从而得出寻找任意线段和圆弧围成区域的一种新算法。     

网格结构上图象小波变换的并行算法

为提高大图象小波变换的速度,本文设计了一种网格结构上图象小波变换的并行算法,其特点是负载平衡,且通信只在少数几个处理机间进行,通信量小,因而算法效率高。     

A parameter uniform B-spline collocation method for solving singularly perturbed turning point problem having twin boundary layers

A numerical scheme is proposed to solve singularly perturbed two-point boundary value problems with a turning point exhibiting twin boundary layers. The scheme comprises B-spline collocation method on a non-uniform mesh of Shishkin type. Asymptotic bounds are established for the derivative of the analytical solution of a turning point problem. The present method is boundary layer resolving as well as second-order accurate in the maximum norm. A brief analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter ? by decomposing the solution into smooth and singular components. Some relevant numerical examples are also illustrated to verify computationally the theoretical aspects.     

注蒸汽热采稠油油藏数值模拟自适应网法计算软件的设计开发

注蒸汽热采稠油是一个带有相变的多孔介质中多相流动问题。利用自适应网格法动态追踪油藏中的温度和饱和度锋面,以大幅度提高计算速度。在对渗透率空间分布不均匀、油藏区域分布不同种类输运性质岩石、裂缝-孔隙双重介质、非规则边界及内部含有断层油藏等复杂地层注蒸汽热采稠油问题开展自适应网格法的研究基础上,自主开发了注蒸汽热采稠油油藏数值模拟自适应网格法计算软件。该软件具有较高的计算精度和稳定性,可满足科研生产需求。     

三维网格模型水印自适应调节算法

为提高三维网格模型嵌入水印的透明性,提出一种基于模型局部几何特征的自适应水印强度调节算法。将网格模型分割为若干局部区域,根据各区域内几何数据的波动情况对水印嵌入强度进行调节。几何误差和视觉失真误差评价结果表明,与非自适应嵌入方法相比,该方法嵌入的水印透明性较高。     

A new method of mesh simplification for 3-Dimension terrain using Laplace operator

This paper proposes a new method to simplify mesh in 3D terrain.The 3D terrain is presented by digital elevation model.First,Laplace operator is introduced to calculate sharp degree of mesh point,which indicates the variation trend of the terrain.Through setting a critical value of sharp degree,feature points are selected.Second,critical mesh points are extracted by an recursive process,and constitute the simplified mesh.Third,the algorithm of linear-square interpolation is employed to restore the characteristics of the terrain.Last,the terrain is rendered with color and texture.The experimental results demonstrate that this method can compress data by 16% and the error is lower than 10%.     

基于任务树的分布式计算平台的设计与实现

针对当前网络中PC资源利用率低和大型任务的难解性，设计并实现了一个通用的基于任务树的分布式计算平台TT-DCP（Distributed Computing Platform based on Task Tree）．TT—DCP旨在利用网络中计算机的空闲时间求解可分布运行的大型任务，主要包括服务器端程序、客户端程序、后台数据库三部分．服务器端程序主要负责利用任务树描述大型任务、对树的操作以及处理客户端返回的任务结果；客户端程序采用主动式策略获取子任务，并下载任务到本地执行、将结果返回服务器；后台数据库保存任务树．任务分布化过程中，提出采用任务树结构保存任务数据，使用回溯法构建任务树并保存在后台数据库中．同时，设计并实现了平台中服务器端与客户端的应用层通信协议UPDP（Unprocessed Packet Download Protocol）和PPUP（Processed Packet Upload Protocol）．本文进一步讨论了如何利用TT—DCP求解Mesh网络连通性问题，并给出了处理结果．TT—DCP可以用来求解生物计算中的多序列比对、motif查找等问题．