二维任意域内点集的Delaunay三角划分生成算法

本文研究二维任意域内点集的Ｄｅｌａｕｎａｙ三角划分（简记为ＤＴＡＤ）的生成算法只有边界点的ＤＴＡＤ用环切边界的方法生成．本文讨论了ＤＴＡＤ的插入、删除性质，提出了以此为基础的生成核插入算法．     

一种基于图的平面点集Delaunay三角剖分算法

本文提出了一种基于图的平面点集Ｄｅｌａｕｎａｙ三角剖分算法。该算法首先求出平面点集的欧几里得最小生成树，然后逐次加入一边构造三角形网格，最后按最小内角最大的三角化准则，通过局部变换，得到平面点集的Ｄｅｌａｕｎａｙ三角剖分。本文同时阐述了它的对偶图；平面点集的Ｖｏｒｏｎｏｉ图的概念和性质。     

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     

基于几何造型的有限元网格的自适应生成

介绍一个基于几何造型系统的有限元分析的前处理系统。该系统可对几何造型的二维任意形体进行快速可靠的Ｄｅｌａｕｎａｙ三角剖分，提出网格自动生成的网格密度的控制和基于误差估计的自适应有限元网格生成算法，并给出了应用实例。     

任意多边形的Delaunay三角剖分

任意多边形的三角剖分是计算机图形学领域中的一个基本算法，其用途非常广泛，本文利用著名的Ｄｅｌａｕｎａｙ三角剖分的优化性质，提出了一个简洁、通用的任意多边形Ｄｅｌａｕｎａｙ三角剖分算法，并给出了该算法在有限元网络自动生成过程的应用。     

任意形状平面域的通用三角化算法

基于平面上散乱数据点的Ｄｅｌａｕｎａｙ三角剖分准则，提出了任意形状平面域的通用三角剖分算法。该算法不仅能用于Ｔｒｉｍｍｅｄ曲面的消隐显示及加工，也能用于有限元网格自动生成及其它领域。该算法已经成功应用于ＨＵＳＴＣＡＤＭ曲面造型及加工系统。     

基于几何造型的有限元网络自适应生成

介绍一个基于几何造型系统的有限元分析的前处理系统。该系统可对几何造型的二维任意形体进行快速可靠的Ｄｅｌａｕｎａｙ三角剖分，提出网络自动生成的网络密度的控制和基于误差估计的自适应有限元网格生成算法，并给出了应用实例。     

三维任意区域中点集的三角剖分算法

本文在已有算法基础上，发展了一种三维任意区域中点集的三角剖分算法。该算法不仅可用于三维点集的标准Ｄｅｌａｕｎａｙ三角剖分，而且可用于带有约束表面及内部含有孔洞情况，可以处理非凸区域的三角剖分问题。算法对点在空间的位置滑任何限制。     

散乱点集Delaunay三角剖分的分布并行算法

为了加快大数据集Ｄｅｌａｕｎａｙ三角剖分的速度,提出了一种能对任意散乱点集进行Ｄｅｌａｕｎａｙ三角剖分的分布并行算法,算法具有容错性和自动负载平衡的能力,文中对其设计和实现方法进行了详细讨论,对算法的复杂性进行了分析,实验结果表明该算法的加速效果明显。     

Delaunay三角网格的一种快速生成法

１．引 言 在计算流体力学中,采用非结构网格有许多优点,如易于生成复杂区域的网格和作网格自适应．最常见的非结构网格是非结构三角网格,而生成非结构三角网格的方法主要有前沿推进法［１－４］和 Ｄｅｌａｕｎａｙ三角剖分法［５－８］两大类．本文仅考虑后者并只讨论生成给定点集的 Ｄｅｌａｕｎａｙ三角网格． 目前流行的生成Ｄｅｌａｕｎａｙ三角网格的算法是Ｂｏｗｙｅｒ－Ｗａｔｓｏｎ算法［６,７］．Ｂｏｗｙｅｒ－Ｗａｓｏｎ算法是以逐点加入的方式进行的,如何提高该算法的运算效率是一个十分重要的问题［８－１３］．用 Ｂｏ…     

二维任意域内点集的Delaunay三角划分的研究

传统的Ｄｅｌａｕｎａｙ三角划分不适合许多实际的应用，本文提出了三维任意域内点集的Ｄｅｌａｕｎａｙ三角划的概念，研究了其存储性、唯一性的条件以及一个三角划分是ＤＴＡＤ的充要条件，ＤＴＡＤ具有最小角最大以及平均形态比最大的性质，因此它是给定区域和点集的最佳三角划分，本文同时阐述了它的对偶图。     

A new front updating solution applied to some engineering problems

Summary An automatic mesh generation dealing with domains of an arbitrary shape could be realized by an advancing front method. The mesh generator based on this method creates triangle elements inside a domain starting with the polygonal (polyhedral in 3D) discretisation of its border. In this paper an original algorithm for the front updating procedures as a part of the mesh generator is presented. The proposed algorithm provides an efficient mesh generation procedure. It has been verified on the various domains with complex geometry and with nonuniform distribution of edge nodes such as the discretisation of the switched reluctance motor and power cable configuration, respectively. The related finite element calculations are carried out.     

Interactive mesh cloning driven by boundary loop

In order to copy arbitrary irregular mesh between two models continuously, this paper presents an interactive mesh cloning approach based on pyramid spherical coordinates driven by boundary loop. The approach extends an existing algorithm for computing offset membrane on mesh. A parametric paint brush is constructed to define canvas both on the source mesh and the target mesh. They are mapped onto a 2D parametric domain using discrete geodesic polar maps to register correspondingly. During cloning, the boundary loop of the region of interest (ROI) on the target mesh is fitted in real time by B-spline curve to register the boundary loop of the source ROI. Via the reconstructed boundary loop, the ROI is deformed to register the target mesh by pyramid spherical coordinates to ensure that the clone result is seamless and natural. Our approach can clone arbitrary irregular meshes between two 3D models, even if the mesh is non-manifold. The cloning process is operated in real time by GPU acceleration. Experimental results demonstrate the effectiveness of our interactive mesh cloning.     

A Frequency-Domain Approach to Watermarking 3D Shapes

This paper presents a robust watermarking algorithm with informed detection for 3D polygonal meshes. The algorithm is based on our previous algorithm [ 22 ] that employs mesh‐spectral analysis to modify mesh shapes in their transformed domain. This paper presents extensions to our previous algorithm so that (1) much larger meshes can be watermarked within a reasonable time, and that (2) the watermark is robust against connectivity alteration (e.g., mesh simplification), and that (3) the watermark is robust against attacks that combine similarity transformation with such other attacks as cropping, mesh simplification, and smoothing. Experiment showed that our new watermarks are resistant against mesh simplification and remeshing combined with resection, similarity transformation, and other operations..     

Generation of finite element mesh with variable size over an unbounded 2D domain

With the advance of the finite element, general fluid dynamic and traffic flow problems with arbitrary boundary definition over an unbounded domain are tackled. This paper describes an algorithm for the generation of finite element mesh of variable element size over an unbounded 2D domain by using the advancing front circle packing technique. Unlike the conventional frontal method, the procedure does not start from the object boundary but starts from a convenient point within an open domain. The sequence of construction of the packing circles is determined by the shortest distance from the fictitious centre in such a way that the generation front is more or less a circular loop with occasional minor concave parts due to element size variation. As soon as a circle is added to the generation front, finite elements are directly generated by properly connecting frontal segments with the centre of the new circle. In contrast to other mesh generation schemes, the domain boundary is not considered in the process of circle packing, this reduces a lot of geometrical checks for intersection with frontal segments, and a linear time complexity for mesh generation can be achieved. In case the boundary of the domain is needed, simply generate an unbounded mesh to cover the entire object. As the element adjacency relationship of the mesh has already been established in the circle packing process, insertion of boundary segments by neighbour tracing is fast and robust. Details of such a boundary recovery procedure are described, and practical meshing problems are given to demonstrate how physical objects are meshed by the unbounded meshing scheme followed by the insertion of domain boundaries.     

Generation of anisotropic mesh by ellipse packing over an unbounded domain

With the advance of the finite element method, general fluid dynamic and traffic flow problems with arbitrary boundary definition over an unbounded domain are tackled. This paper describes an algorithm for the generation of anisotropic mesh of variable element size over an unbounded 2D domain by using the advancing front ellipse packing technique. Unlike the conventional frontal method, the procedure does not start from the object boundary but starts from a convenient point within an open domain. The sequence of construction of the packing ellipses is determined by the shortest distance from the fictitious centre in such a way that the generation front is more or less a circular loop with occasional minor concave parts due to element size variation. As soon as an ellipse is added to the generation front, finite elements are directly generated by properly connecting frontal segments with the centre of the new ellipse. Ellipses are packed closely and in contact with the existing ellipses by an iterative procedure according to the specified anisotropic metric tensor. The anisotropic meshes generated by ellipse packing can also be used through a mapping process to produce parametric surface meshes of various characteristics. The size and the orientation of the ellipses in the pack are controlled by the metric tensor as derived from the principal surface curvatures. In contrast to other mesh generation schemes, the domain boundary is not considered in the process of ellipse packing, this reduces a lot of geometrical checks for intersection between frontal segments. Five examples are given to show the effectiveness and robustness of anisotropic mesh generation and the application of ellipse packing to mesh generation over various curved surfaces.     

A filter-and-fan algorithm for the capacitated minimum spanning tree problem

The capacitated minimum spanning tree (CMST) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new CMST heuristic algorithm that effectively combines the classical node-based and tree-based neighborhoods embodied in a filter-and-fan (F&F) approach, a local search procedure that generates compound moves in a tree search fashion. The overall algorithm is guided by a multi-level oscillation strategy used to trigger each type of neighborhood while allowing the search to cross feasibility boundaries. Computational results carried out on a standard set of 135 benchmark problems show that a simple F&F design competes effectively with prior CMST metaheuristics, rivaling the best methods, which are significantly more complex.     

A Colour Interpolation Scheme for Topologically Unrestricted Gradient Meshes

Gradient meshes are a 2D vector graphics primitive where colour is interpolated between mesh vertices. The current implementations of gradient meshes are restricted to rectangular mesh topology. Our new interpolation method relaxes this restriction by supporting arbitrary manifold topology of the input gradient mesh. Our method is based on the Catmull‐Clark subdivision scheme, which is well‐known to support arbitrary mesh topology in 3D. We adapt this scheme to support gradient mesh colour interpolation, adding extensions to handle interpolation of colours of the control points, interpolation only inside the given colour space and emulation of gradient constraints seen in related closed‐form solutions. These extensions make subdivision a viable option for interpolating arbitrary‐topology gradient meshes for 2D vector graphics.     

Coupling geological and numerical models to simulate groundwater flow and contaminant transport in fractured media

A new modeling approach is presented to improve numerical simulations of groundwater flow and contaminant transport in fractured geological media. The approach couples geological and numerical models through an intermediate mesh generation phase. As a first step, a platform for 3D geological modeling is used to represent fractures as 2D surfaces with arbitrary shape and orientation in 3D space. The advantage of the geological modeling platform is that 2D triangulated fracture surfaces are modeled and visualized before building a 3D mesh. The triangulated fractures are then transferred to the mesh generation software that discretizes the 3D simulation domain with tetrahedral elements. The 2D triangular fracture elements do not cut through the 3D tetrahedral elements, but they rather form interfaces with them. The tetrahedral mesh is then used for 3D groundwater flow and contaminant transport simulations in discretely fractured porous media. The resulting mesh for the 2D fractures and 3D rock matrix is checked to ensure that there are no negative transmissibilities in the discretized flow and transport equation, to avoid unrealistic results. To test the validity of the approach, flow and transport simulations for a tetrahedral mesh are compared to simulations using a block-based mesh and with results of an analytical solution. The fluid conductance matrix for the tetrahedral mesh is also analyzed and compared with known matrix values.