Variational implicit surface meshing

In this paper, we propose a new algorithm to mesh implicit surfaces which produces meshes both with a good triangle aspect ratio as well as a good approximation quality. The number of vertices of the output mesh is defined by the end-user. For this goal, we perform a two-stage processing: an initialization step followed by an iterative optimization step. The initialization step consists in capturing the surface topology and allocating the vertex budget. The optimization algorithm is based on a variational vertices relaxation and triangulation update. In addition a gradation parameter can be defined to adapt the mesh sampling to the curvature of the implicit surface. We demonstrate the efficiency of the approach on synthetic models as well as real-world acquired data, and provide comparisons with previous approaches.     

Generating strictly binary trees at random based on convex polygon triangulations

A set of maximal non-intersecting diagonals can decompose a polygon into triangles, and the edges and diagonals can be converted into the external and internal nodes of a strictly binary tree. This paper gives algorithms to generate all types of triangulations and triangulations at random. Based on that, this paper gives an algorithm to generate strictly binary trees at random. The experimental results show that the numbers of various shapes of strictly binary trees generated are nearly equal. The algorithm to generate strictly binary trees at random can be transformed to the algorithm to randomly generate binary trees.     

Compact reconfigurable rat‐race coupler with tunable frequency and tunable power dividing ratio

A compact reconfigurable rat‐race coupler with tunable frequency and tunable power dividing ratio is proposed for the first time. Varactors and two single control voltages are used to obtain both the tunable frequency and the tunable power dividing ratio in this article. The structure of the rat‐race coupler involves 50 Ω parallel‐strip lines only and a phase inverter is used for size reduction. Theoretical equations for the relationship among S‐parameters and the capacitance of varactors are derived. The graphic method is used to choose capacitance for the desired operation frequency and the desired power dividing ratio. For demonstration, a prototype is designed and fabricated. The measured results show that the rat‐race coupler's frequency and the power dividing ratio can be effectively tuned in 0.69 GHz ～ 0.81 GHz and 3 dB ～ 14 dB, respectively with isolation better than 20 dB, phase difference less than 7°and return loss better than 20 dB. The theoretical simulation, electromagnetic simulation, and measured results show good agreement in this design.     

基于Netgen的层状地质体四面体网格划分方法

为解决三维地质建模中难以表达层状地质体内部属性的问题,将有限元网格划分方法应用于层状地质体建模中,研究基于Netgen进行层状地质体四面体网格划分的方法.以地质钻探数据为数据源,按照钻孔数据分层构建三维表面模型,用三角面片的集合构成封闭的包围壳来描述层状地质体的外部形状;结合Netgen强大的几何自适应和细部划分控制功能,用四面体网格划分方法对形成的三维表面模型进行空间区域划分,从而实现对复杂形状的层状地质体三维模型构建,并分析Netgen的输入、输出数据结构和地质钻探数据到STL格式的三维模型数据、STL格式数据到Netgen网格划分结果数据的生成过程.某矿区多个岩层的模型构建证明该方法稳定、可靠且有效.     

Direct generation of extended STL file from unorganized point data

An extended STL file format is presented in this paper. Differing with existing solutions, it proposes a new format to produce and store triangles. The format uses a cluster unit composed of several triangles. The main advantages of the format are that it contains both geometry and topological information and has improved storage capability. Direct generation of the extended STL from the scanned data has a great advantage in that it can reduce the time and error in modeling process. In order to obtain the format from unorganized point cloud, a new triangulation algorithm was introduced. The algorithm is based on reconstructing the relative Delaunay triangulation of the sample points on the surface. Other advantages of the extended STL format were also presented in this paper.     

Surface reconstruction using Delaunay triangulation for applications in life sciences

The Delaunay triangulation is an established method to define neighborhood relations in multi-particle systems. In particular, this method was employed for interacting multi-cellular systems in Biology. The extension of this method to a sub-cellular level that considers the membrane and the inner structure of cells is not straight forward and subject of this article. It is the objective to use a three-dimensional Delaunay-triangulation as a basis for the definition of a triangulation of a subset of particles that form a surface.An essential problem of this objective is the conservation of the number of particles belonging to the surface. This excludes established surface reconstruction algorithms. The presented algorithm allows the definition of a triangulation within a subset of particles attributed to a surface without the deletion of particles. A particular challenge is the deletion of connection that infer three-dimensional structures in the surface. The presented method is suitable for many configurations. Its performance and its limitations are analyzed and discussed.The developed algorithm for the reconstruction of connections in a surface is suitable to be used for simulations of biological cells because of the inherent conservation of the number of particles attributed to the membrane.     

基于几何特征和力学特性的自适应网格生成算法

为获得适合有限元分析的满意网格划分,提出了平面域的基于几何特征和力学特性相结合的自适应网络生成方法,实现了应力集中区的网格局部加密及平稳变密度的网格自动剖分,通过实例表明本方法实用性强、效果良好。     

Dividing Cubes算法生成的物体表面的法向量方向的光顺操作

在用DividingCubes算法提取的边界体素所构造的物体表面上,可能会存在法向量方向突变,使得物体表面光照图显示粗糙,文中提出了一种的领域加权平均法,对物体表面的法向量方向进行光顺处理,光顺操作只在相关边界体素间进行,并且对有多个等值面交汇的边界体素将不进行光顺操作,以避免模糊位于多个区域处的边界和保持物体表面光照图的细节,为避免在屏幕上产生孔洞,用光线投射法显示物体表面,文中所采用的光顺操作可以消除物体表面的法向量方向突变,使物体表面光照图光谱细腻,最后,给出一个医学图像的测试实例。     

几何数据压缩的一种新算法

本文提出一种几何数据压缩的新算法,其基本思想是在已知物体网格边界的条件下,首先寻找边界的凹点,然后建立网格结点的特殊树结构,即横切面树,并将横切面树中相邻节点内网格结点之间的关系表示为链表（三角形条带）,按契约数结构及链表（三角形条带）编码、存储帮传输网格结点的连接关系,这种算法不同于Gabriel Taubin算法,它具有对顶点坐标、属性坐标及三角形连接关系压缩无损等许多优点。     

一种常用的二维任意域的Delaunay三角剖分算法的健壮性补充

由于对任意给定的平面点集通过Ｄｅｌａｕｎａｙ三角剖分进行处理可得到具有整体最优性的三角形网络,因而该方法得到了广泛的重视。但研究发现,常用的二维任意域Ｄｅｌａｕｎａｙ三角剖分算法＾［１,２］是有缺陷的,它在构成Ｄｅｌａｕｎａｙ三角形候选点的选择过程中,可以使候选点出现“位置违约”的错误,即在候造节点链表中,虽然可出现依据算法的判据有条件成为Ｄｅｌａｕｎａｙ三角形的构成点,但采用该点构成Ｄｅｌａｕｎ