Contouring Discrete Indicator Functions

We present a method for calculating the boundary of objects from Discrete Indicator Functions that store 2‐material volume fractions with a high degree of accuracy. Although Marching Cubes and its derivatives are effective methods for calculating contours of functions sampled over discrete grids, these methods perform poorly when contouring non‐smooth functions such as Discrete Indicator Functions. In particular, Marching Cubes will generate surfaces that exhibit aliasing and oscillations around the exact surface. We derive a simple solution to remove these problems by using a new function to calculate the positions of vertices along cell edges that is efficient, easy to implement, and does not require any optimization or iteration. Finally, we provide empirical evidence that the error introduced by our contouring method is significantly less than is introduced by Marching Cubes.     

SSD: Smooth Signed Distance Surface Reconstruction

We introduce a new variational formulation for the problem of reconstructing a watertight surface defined by an implicit equation, from a finite set of oriented points; a problem which has attracted a lot of attention for more than two decades. As in the Poisson Surface Reconstruction approach, discretizations of the continuous formulation reduce to the solution of sparse linear systems of equations. But rather than forcing the implicit function to approximate the indicator function of the volume bounded by the implicit surface, in our formulation the implicit function is forced to be a smooth approximation of the signed distance function to the surface. Since an indicator function is discontinuous, its gradient does not exist exactly where it needs to be compared with the normal vector data. The smooth signed distance has approximate unit slope in the neighborhood of the data points. As a result, the normal vector data can be incorporated directly into the energy function without implicit function smoothing. In addition, rather than first extending the oriented points to a vector field within the bounding volume, and then approximating the vector field by a gradient field in the least squares sense, here the vector field is constrained to be the gradient of the implicit function, and a single variational problem is solved directly in one step. The formulation allows for a number of different efficient discretizations, reduces to a finite least squares problem for all linearly parameterized families of functions, and does not require boundary conditions. The resulting algorithms are significantly simpler and easier to implement, and produce results of quality comparable with state‐of‐the‐art algorithms. An efficient implementation based on a primal‐graph octree‐based hybrid finite element‐finite difference discretization, and the Dual Marching Cubes isosurface extraction algorithm, is shown to produce high quality crack‐free adaptive manifold polygon meshes.     

Computing monodromy via continuation methods on random Riemann surfaces

We consider a Riemann surface X defined by a polynomial f(x,y) of degree d, whose coefficients are chosen randomly. Hence, we can suppose that X is smooth, that the discriminant δ(x) of f has d(d−1) simple roots, Δ, and that δ(0)≠0, i.e. the corresponding fiber has d distinct points {y₁,…,y_d}. When we lift a loop 0∈γ⊂C−Δ by a continuation method, we get d paths in X connecting {y₁,…,y_d}, hence defining a permutation of that set. This is called monodromy.Here we present experimentations in Maple to get statistics on the distribution of transpositions corresponding to loops around each point of Δ. Multiplying families of “neighbor” transpositions, we construct permutations and the subgroups of the symmetric group they generate. This allows us to establish and study experimentally two conjectures on the distribution of these transpositions and on transitivity of the generated subgroups.Assuming that these two conjectures are true, we develop tools allowing fast probabilistic algorithms for absolute multivariate polynomial factorization, under the hypothesis that the factors behave like random polynomials whose coefficients follow uniform distributions.     

破碎刚体三角网格模型的断裂面分割

针对基于断裂面匹配的破碎刚体复原,提出了一种分割断裂面的方法。首先,根据相邻三角片法矢的夹角,将碎块外表面以棱边为界限分割成多张曲面;然后,根据曲面法矢的扰动大小和扰动图像,经过二次分割,将曲面区分为原始面和断裂面。实验结果表明,所提方法能够正确快速地提取出形状较复杂碎块的断裂面。     

增量几何压缩

提出了一个几何压缩算法,用以节省三角网格模型存储和传输时间.它首先递归地以区域扩张方式将模型分解为一系列的层结构,利用层间的连贯性以及对层结构的有效编码,实现了高效的拓扑压缩.同时,还设计了一个有效的非线性预测器来实现几何位置的压缩.与以前的算法相比,它具有线性复杂度、压缩比高、执行速度快的特点.实验结果表明,存储一个三角形的拓扑信息平均只需1.42比特.     

基于空间网格表面距离的插值曲面

主要讨论基于空间网格表面距离的插值曲面.定义了一种空间网格表面距离,基于空间网格表 面距离,给出了两种定义在空间网格上的插值曲面：基于网格表面距离的径向基函数插值曲 面和基于网格表面距离的Kriging插值曲面,讨论了曲面的无穷阶光滑性,给出了一种计算网 格表面距离的折线跟踪算法.作为整体曲面,此类插值曲面与网格表面形状较为相符,比较适 合于局部插值与参数估计,如梯度、法方向的估计等计算.     

Pb_n微团簇(n=20～30)及铅晶体表面过程的计算机模拟

基于Murrell等提出的有效正体加三体展开势能函数对铅微团簇Pbn (n =2～ 3 0 )的结构及面心立方晶体铅的表面行为进行了计算机模拟。发现Pbn 微团簇的结构衍生规律为 :依次增加一个三配位的表面原子 ,分子表面为三元环所覆盖 ,整个分子为畸变的四面体的密堆积 ;f (c)铅晶体的表面层原子间内压缩最为严重 (最大达 8% ) ,从第三层开始层间距的伸缩率已经很小 ( <1 % )。     

Pbn微团簇(n=20～30)及铅晶体表面过程的计算机模拟

基于Ｍｕｒｒｅｌｌ等提出的有效正体加三体展开势能函数取铅微团簇ｐｂｎ（ｎ＝２～３０）的结构及面心立体表面心立方晶体铅的表面进行也计算机模拟。发现ｐｂｎ微团簇的结构衍生规律为：依次增加一个配位的表面原子,分子表面原子,分子表面为三元环所覆盖,整个分子为畸变的四面体的密堆积：ｆ（ｃ）铅晶体的表面层原子间内压缩最为严重（最大达８％）,从第三层开始层间距的伸缩率已经很小（〈１％）。     

表面粗糙度检查仪微机改造方法

介绍一种通过人机交互式界面选择控制设定表面粗糙度检测仪测量参数的方法。该方法可有效地消除人为因素的影响,稳定测量精度,简化操作。     

一种自由曲面的快速跟踪求交算法

自由白面的求交算法在ＣＡＤ／ＣＡＭ软件系统中占有重要的地位,并对软件运行的效率有较大的影响。目前常用的Ｂｅｚｉｅｒ曲面分割法难以满足高精度和高速度的要求。为此该文提出了利用交线的几何信息进行快速求交的算法,同时兼顾了快速和高精度两方面的要求,并已在作者自行开发的软件中得到了成功的应用。