三角网格模型上的四边形曲线网生成新方法

四边形网格划分是组合曲面建模技术的首要条件。针对海量流形三角网格数据,提出了基于网格简化技术与调和映射算法的四边形网格生成新方法--映射法。该方法采用基于顶点删除的网格简化技术对三角网格模型进行简化,进而借助调和映射算法将简化网格映射到二维平面上进行四边形划分,并将所获得的平面四边形节点数据逆映射回物理域,采用短程线边界形式最终得到适于组合曲面建模的空间四边形拓扑。该方法简单、实用,运行速度较快,实际的算例也验证了方法的有效性与可行性。     

基于逆√3细分的渐进网格生成算法研究

提出一种基于逆√3细分的渐进网格生成算法,用于解决图形的快速传输和显示问题.算法的基本思路是:将细密网格通过边折叠操作得到简化网格,以细分极限点逼近原始网格为准则进行网格调整,采用√3细分得到高密度网格,调整后进行逆√3细分,即逐层次删除部分顶点,生成用于重构渐进网格模型的基网格,并记录每层删除顶点在采用本层表示时相对于细分计算位置的几何调整量.√3细分过程中三角片数量增长速度较慢,采用逆√3细分利于生成多层次的渐进网格,经实例验证,逆√3细分生成渐进网格的效果能满足快速、多分辨率显示要求.     

基于向量夹角的三角网格模型简化算法

提出以顶点向量夹角为剔除准则,运用顶点去除方法进行网格简化的算法。该算法首先计算每个网格顶点与其周围相邻顶点所形成的方向向量,然后根据方向向量的平均夹角来识别和简化网格中的平面区域,之后再以该顶点所处区域是否比较平坦为顶点去除限制条件,判断该顶点是否符合安全去除原则,这样可以保留特征顶点,进而保持物体的视觉特征。在顶点去除后,还需要对因此而形成的多边形进行三角形网格重建,以填补空洞。该算法在简化质量和简化速率方面取得了较好的平衡。     

用Catmull-Clark细分及网格调整方法重构牙齿曲面

首先根据牙齿表面测量数据点,计算出其长方体包围盒;并据此构造细分曲面的初始网格;采用矩阵对角化方法,推导Catmull-Clark细分极限点的表达式,计算初始网格的顶点经过细分后的极限点;按照极限点逼近数据点的原则移动控制网格顶点,经过逐次再细分、再调整网格,使各级网格在数据点的＂引导＂下逐步变形,使网格逐步逼近牙齿表面的测量数据点集合,实现牙齿表面模型的三维重建。     

空间三角形网格优化算法

本文提出了空间三角形网格的优化算法,给定一组三维散乱点集和一个初始三角形网格,对三角形网格顶点位置优化和应用三角片局部细分方法,使该网格能更好的逼近三维散乱点,提高了网格对散乱点的逼近精度。     

用Loop细分曲面拟合点云数据的方法

将输入的点云数据进行三角剖分形成三角网格,按参考文献[1]建立求解插值细分曲面控制顶点的线性方程组.将所建立的线性方程组进行变换,使方程组的系数矩阵对称.证明了该系数矩阵正定,给出了矩阵特征值的上下界估计.将三角网格顶点作为迭代的初始控制点,提出了求解插值细分曲面控制顶点的两种迭代算法以及两个相应的盈亏修正公式.实例表明,两种迭代算法收敛速度快,拟合精度高.     

向量线性相关的三角网格自适应Loop细分方法

根据过同一起点,且线性相关的三个向量在同一平面上的原理提出了一种新的三维表面自适应Loop细分算法,即对网格模型过同一顶点1邻域上的所有三个紧邻边组成的三个向量判断其是否线性相关来断定该顶点的1邻域是否平坦,从而进一步判断该顶点是否参与细分.但是三角网格模型上的三条边不可能都严格地在同一个平面上,当这些向量组成的行列式值趋于零时,便认为它们在同一平面上.实验表明,该方法减少了细分的数据量和处理速度.     

一种Loop细分小波的边界处理方法

细分小波近年来发展迅速,在计算机图形显示、渐进网格传输和网格多分辨率编辑等领域获得了广泛的应用。Bertram提出的Loop细分小波是基于提升格式的双正交细分小波的典型范例,它所针对的对象均为网格的内部顶点。目前尚未发现相关文献提及细分小波对于边界的处理。该文在Loop细分小波算法的基础上,给出了一种Loop细分小波边界处理的方法,经验证效果令人满意。     

基于成长型神经网络以线段为基元的曲线重建

在逆向工程中,对基于散乱数据点的曲线重建研究有着重要的意义。曲线可用线段基元逼近。提出使用成长型神经网络以线段为基元的曲线重建新算法。给定某一曲线的散乱点集和一初始折线,新算法优化折线上的顶点位置,使折线更好地逼近散乱点;持续分裂折线上活动性强的顶点和删除活动性最弱的顶点,使折线上顶点的分布更符合散乱点数据的概率分布。实验结果表明,新算法能够取得良好的曲线重建效果。     

基于灰色预测GM(1,1)模型的网格孔洞填补算法

针对三角网格曲面中存在的孔洞提出了一种填补算法.在空洞曲面的投影平面上,每次寻找孔洞多边形最小内角所在顶点,用GM(1,1)模型在孔洞内部插入新点,构造三角形并生成新的孔洞边界多边形,直到所有的孔洞边界多边形全部处理完.最后将平面三角面片返回到三维空间并用基于径向基函数的平滑算法对其进行平滑处理.实例表明用本算法进行孔洞填补能避免出现错误和狭长的三角形,而且和原孔洞边界能光滑连接,对曲率变化较大的孔洞也能得到满意的填补结果.     

Automatic generation of anisotropic quadrilateral meshes on three‐dimensional surfaces using metric specifications

A new algorithm for constructing full quadrilateral anisotropic meshes on 3D surfaces is proposed in this paper. The proposed method is based on the advancing front and the systemic merging techniques. Full quadrilateral meshes are constructed by systemically converting triangular elements in the background meshes into quadrilateral elements.By using the metric specifications to describe the element characteristics, the proposed algorithm is applicable to convert both isotropic and anisotropic triangular meshes into full quadrilateral meshes. Special techniques for generating anisotropic quadrilaterals such as new selection criteria of base segment for merging, new approaches for the modifications of the background mesh and construction of quadrilateral elements, are investigated and proposed in this study. Since the final quadrilateral mesh is constructed from a background triangular mesh and the merging procedure is carried out in the parametric space, the mesh generator is robust and no expensive geometrical computation that is commonly associated with direct quadrilateral mesh generation schemes is needed. Copyright © 2002 John Wiley & Sons, Ltd.     

网格细分技术在汽车外形设计中的应用

细分造型技术因其计算规则简单、可以表示任意拓扑特性和几何特征的曲面等性质,受到造型技术领域中众多学者的关注,为复杂的汽车外形设计提供了工具.该文阐释了网格细分方法的基本思想以及两类典型的细分模式,提出了在相关几何造型、有限元分析和动态仿真软件配合下,设计复杂汽车外形曲面的细分技术方案;对车体曲面的控制网格生成、边界限定等关键技术进行了讨论.利用文中方法可以有效地缩短复杂汽车外形曲面的造型、计算和分析时间,为汽车外形设计的逆向工程应用提供方法和工具.     

基于Surfels的实时渲染技术研究

介绍了一种用于实现复杂场景高品质实时渲染的新算法。已有的研究表明，基于传统几何图元的渲染技术必然涉及到大量的求交与消隐计算，而这正是实现实时绘制的瓶颈所在。利用OpenGL虽然可以实现实时绘制，但这是建立在Z－Buffer技术的基础上，并且将场景尽可能地简化来实现实时绘制的一种基于传统几何图元的绘制技术。这样渲染而得的图像质量很低，很难再现纹理及材质的特殊光照效果。笔者将图像与体图形学技术相结合，研究并实现了基于表面元素（Surface elements,即Surfels)的渲染技术，避免了耗时的求交计算，因此大大提高了复杂几何场景的绘制时间。又因为surfels中包含完整的材质属性和纹理信息，从而确保了在快速重绘时的图像质量。     

A frontal Delaunay quad mesh generator using the L ∞ norm

In a recent work, a new indirect method to generate all‐quad meshes has been developed. It takes advantage of a well‐known algorithm of the graph theory, namely the Blossom algorithm, which computes in polynomial time the minimum cost perfect matching in a graph. In this paper, we describe a method that allows to build triangular meshes that are better suited for recombination into quadrangles. This is performed by using the infinity norm to compute distances in the meshing process. The alignment of the elements in the frontal Delaunay procedure is controlled by a cross field defined on the domain. Meshes constructed this way have their points aligned with the cross‐field directions, and their triangles are almost right everywhere. Then, recombination with the Blossom‐based approach yields quadrilateral meshes of excellent quality. Copyright © 2013 John Wiley & Sons, Ltd.     

Subdivision schemes for smooth contact surfaces of arbitrary mesh topology in 3D

This paper presents a strategy to parameterize contact surfaces of arbitrary mesh topology in 3D with at least C¹‐continuity for both quadrilateral and triangular meshes. In the regular mesh domain, four quadrilaterals or six triangles meet in one node, even C²‐continuity is attained. Therefore, we use subdivision surfaces, for which non‐physical pressure jumps are avoided for contact interactions. They are usually present when the contact kinematics is based on facet elements discretizing the interacting bodies. The properties of subdivision surfaces give rise to basically four different implementation strategies. Each strategy has specific features and requires more or less efforts for an implementation in a finite element program. One strategy is superior with respect to the others in the sense that it does not use nodal degrees of freedom of the finite element mesh at the contact surface. Instead, it directly uses the degrees of freedom of the smooth surface. Thereby, remarkably, it does not require an interpolation. We show how the proposed method can be used to parameterize adaptively refined meshes with hanging nodes. This is essential when dealing with finite element models whose geometry is generated by means of subdivision techniques. Three numerical 3D problems demonstrate the improved accuracy, robustness and performance of the proposed method over facet‐based contact surfaces. In particular, the third problem, adopted from biomechanics, shows the advantages when designing complex contact surfaces by means of subdivision techniques. Copyright © 2004 John Wiley & Sons, Ltd.     

Composite mappings for planar mesh generation

A new algorithm is presented for automatically grading meshes generated over planar triangular and quadrilateral regions using parametric mappings. Rational parametric bicubic Bézier polynomials are coupled with an element density function to concentrate elements around regions of high solution gradients.     

A new scheme for efficient and direct shape optimization of complex structures represented by polygonal meshes

In this paper, a new shape optimization approach is proposed to provide an efficient optimization solution of complex structures represented by polygonal meshes. Our approach consists of three main steps: (1) surface partitioning of polygonal meshes; (2) generation of shape design variables on the basis of partitioned surface patches; and (3) gradient‐based shape optimization of the structures by reducing a weighted compliance among all load cases. The main contributions of this paper include (i) that our approach can be directly applied on polygonal meshes with the reduction of design variables or decision variables by 10 to 1000 times, compared to the conventional design variable scheme of using each mesh node; (ii) our perturbation scheme is mathematically proven with respect to maintaining the smoothness of each surface patch, except on its boundary; and (iii) overall, our approach can be used to automate time‐consuming shape optimization of polygonal meshes to a greater extent. Numerical experiments have been conducted and the results indicate the effectiveness of the approach. Copyright © 2003 John Wiley & Sons, Ltd.     

An enthalpy control-volume—unstructured-mesh (cv—um) algorithm for solidification by conduction only

Recently, control volume methods have been developed for fluid flow and heat transfer on unstructured meshes. This approach has been extended here to implement the enthalpy based solidification algorithm on an unstructured mesh. A range of two-dimensional test problems are solved using triangular and quadrilateral cells (or elements). The accuracy of the CV–UM algorithms compare favourably with the structured-mesh algorithm, though the former algorithms require 1.5–3 times as much CPU as the latter. This overhead is associated with the extra work caused by the unstructuredness of the mesh; the number of sweeps to achieve convergence is roughly comparable for all algorithms. The CV–UM algorithms should perform well on complex geometry problems and, therefore, show potential to be a productive technique in casting solidification analysis.     

A parallel mesh generation algorithm based on the vertex label assignment scheme

In this article a new mesh generation algorithm is presented. The algorithm is based on a new approach called the vertex label assignment scheme to provide the information for the mesh generation so that parallel processing becomes possible. The algorithm generates 2D meshes of quadrilaterals on the basis of individual faces; conformity and smoothness of the resultant mesh are automatically assured. Local and selective mesh-refinements are also supported. A regular quadrilateral network which defines the geometry of the problem and an associated subdivision level assignment which specifies mesh density data on the network are the only input information.