一种裁剪曲面自适应三角剖分算法

本文介绍了一种裁剪曲面按精度三角剖分算法。三角剖分过程在参数域和曲面空间同时进行，参数域上控制三角片的拓扑关系，曲面空间进行精度检测。算法的核心思想是将裁剪曲面三角剖分视为约束剖分问题，从而使得三角形的细分操作拓展为有效域内插入散乱节点的三角剖分问题。算法简便、实用，三角化结果品质良好，已成功地应用于数控加工刀具轨迹干涉处理等具有精度要求的应用领域。     

一种曲面裁剪的快速新算法

曲面裁剪算法是曲面造型的关键算法之一。传统的裁剪算法是通过对重点和重边进行较复杂的特殊处理并基于环的两两并、交、差来实现的。本文首先提出并严格的定义了入点、出点等概念,在此基础上,提出了一种 对被裁剪曲面参数域进行快速组环的分裂、组环方法,从而实现了对曲面的快速裁剪,该算法已实现并用在ＳｕｐｅｒｍａｎＣＡＤ／ＣＡＭ曲面造型系统。     

面向四面体网格生成的曲面Delaunay三角化算法

提出了一种曲面域Delaunay三角网格的直接构造算法。该算法在曲面网格剖分的边界递归算法和限定Delaunay四面体化算法的基础上,利用曲面采样点集的空间Delaunay四面体网格来辅助曲面三角网格的生成,曲面上的三角网格根据最小空球最小准则由辅助四面体网格中选取,每个三角形都满足三维Delaunay空球准则,网格质量有保证,并且极大的方便了进一步的曲面边界限定下的Delaunay四面体化的进行。     

裁剪 NURBS 曲面面积计算的扫描分片积分法

本文设计了一种计算裁剪ＮＵＲＢＳ曲面面积的扫描分片高斯积分法。该方法无需求出曲面的法矢模长函数，而只需通过一阶偏导矢计算某些点处的法矢模长。该算法速度快，误差容易识别和控制。已应用于自主开发的超人ＣＡＤ／ＣＡＭ系统，效果良好。     

阀门产品CAD系统CAVDS的研究

应用参数化和复杂曲面造型设计方法，在大型ＣＡＤ软件ＥＵＣＬＩＤ上用二次开发语言研制了阀门产品ＣＡＤ系统ＣＡＶＤＳＤ。详细介绍了系统开发平台及结构、设计方法和开发中的一些技术问题。     

参数Bezier三角曲面的GC^1设计

本文从三次Ｂｅｚｉｅｒ三角曲面片边界曲线构造入手，综合分析了计算几何中有关Ｂｅｚｉｅｒ三角曲面ＧＣ＾１拼接设计的理论和方法。针对３Ｄ离散数据曲面插值问题，全面讨论了Ｂｅｚｉｅｒ三角曲面片内部Ｂｅｚｉｅｒ顶点计算。提出了一种基于三次Ｂｅｚｉｅｒ三角曲面片内部Ｂｅｚｉｅｒ顶点ｄ１１１选取优化的整体ＧＣ＾１Ｂｅｚｉｅｒ三角曲面设计方法。     

应用区域变换实现三角 Bezier 曲面分割

本文根据实际应用需要采用参数域变换方法对三角Ｂｅｚｉｅｒ曲面片进行分割，可简单地确定复杂分割模型下各子曲面片的控制顶点，避免了采用Ｃ－Ｔ分割带来的冗余计算和某些情况下的复杂处理过程，并且使分割算法统一。     

应用区域变换实现三角Bezier曲面分割

本文根据实际应用需要采用参数域变换方法对三角Ｂｅｚｉｅｒ曲面片进行分割，可简单地确定复杂分割模型下各子曲面片的控制顶点，避免了采用Ｃ－Ｔ分割带来的冗余计算和某些情况下的昨杂处理过程，并且使分割算法统一。     

三角网格曲面的球面参数化

提出了一种球面参数化三角网格曲面的方法。结合平面凸参数化和球面参数化,计算出封闭网格的切割线边界,网格边界映射到球面的凸区域边界上。然后分别参数化各子网格,最后将三角网格内部点映射到球面上。并用实例验证了此方法的可行性和有效性。     

DDE技术在参数化CAD中的应用

本文从分析现有微机参数化机械设计ＣＡＤ系统入手，指出了该类系统在进行的所谓参数化设计中所存在的问题和不足；同时推出了一项的参数化ＣＡＤ系统的设计技术－基于Ｗｉｎｄｏｗｓ应用间动态数据交换ＤＤＥ技术的参数化机械设计ＣＡＤ系统开发软件技术，文中阐述了基于ＤＤＥ技术的参数化ＣＡＤ系统开发的一般方法和应用环境。     

Efficient surface reconstruction from contours based on two‐dimensional Delaunay triangulation

This paper introduces an efficient method for surface reconstruction from sectional contours. The surface between neighbouring sections is reconstructed based on the consistent utilization of the two‐dimensional constrained Delaunay triangulation. The triangulation is used to extract the parametric domain and to solve the problems associated with correspondence, tiling and branching in a general framework. Natural distance interpolations are performed in order to complete the mapping of the added intermediate points. Surface smoothing and remeshing are conducted to optimize the initial surface triangulations. Several examples are presented to demonstrate the effectiveness and efficiency of the proposed approach. Copyright © 2005 John Wiley & Sons, Ltd.     

Efficient three-dimensional Delaunay triangulation with automatic point creation and imposed boundary constraints

A method is described which constructs three-dimensional unstructured tetrahedral meshes using the Delaunay triangulation criterion. Several automatic point creation techniques will be highlighted and an algorithm will be presented which can ensure that, given an initial surface triangulation which bounds a domain, a valid boundary conforming assembly of tetrahedra will be produced. Statistics of measures of grid quality are presented for several grids. The efficiency of the proposed procedure reduces the computer time for the generation of realistic unstructured tetrahedral grids to the order of minutes on workstations of modest computational capabilities.     

Delaunay triangulation of non-convex planar domains

This paper investigates the possibility of integrating the two currently most popular mesh generation techniques, namely the method of advancing front and the Delaunay triangulation algorithm. The merits of the resulting scheme are its simplicity, efficiency and versatility. With the introduction of ‘non-Delaunay’ line segments, the concept of using Delaunay triangulation as a means of mesh generation is clarified. An efficient algorithm is proposed for the construction of Delaunay triangulations over non-convex planar domains. Interior nodes are first generated within the planar domain. These interior nodes and the boundary nodes are then linked up together to produce a valid triangulation. In the mesh generation process, the Delaunay property of each triangle is ensured by selecting a node having the smallest associated circumcircle. In contrast to convex domains, intersection between the proposed triangle and the domain boundary has to be checked; this can be simply done by considering only the ‘non-Delaunay’ segments on the generation front. Through the study of numerous examples of various characteristics, it is found that high-quality triangular element meshes are obtained by the proposed algorithm, and the mesh generation time bears a linear relationship with the number of elements/nodes of the triangulation.     

Selective refinement: A new strategy for automatic node placement in graded triangular meshes

Automating triangular finite element mesh generation involves two interrelated tasks: generatine a distribution of well-placed nodes on the boundary and in the interior of a domain, and constructing a triangulation of these nodes. For a given distribution of nodes, the Delaunay triangulation generally provides a suitable mesh, and Watson's algorithm²⁶ provides a flexible means of constructing it. In this paper, a new method is described for automating node placement in a Delaunay triangulation by seieclive refinement of an initial triangulation. Grading of the mesh is controlled by an explicit or implicit node spacing function. Although this paper describes the technique only in the planar context, the method generalizes to three dimensions as well.     

Conformal solid T-spline construction from boundary T-spline representations

To achieve a tight integration of design and analysis, conformal solid T-spline construction with the input boundary spline representation preserved is desirable. However, to the best of our knowledge, this is still an open problem. In this paper, we provide its first solution. The input boundary T-spline surface has genus-zero topology and only contains eight extraordinary nodes, with an isoparametric line connecting each pair. One cube is adopted as the parametric domain for the solid T-spline. Starting from the cube with all the nodes on the input surface as T-junctions, we adaptively subdivide the domain based on the octree structure until each face or edge contains at most one face T-junction or one edge T-junction. Next, we insert two boundary layers between the input T-spline surface and the boundary of the subdivision result. Finally, knot intervals are calculated from the T-mesh and the solid T-spline is constructed. The obtained T-spline is conformal to the input T-spline surface with exactly the same boundary representation and continuity. For the interior region, the continuity is C ² everywhere except for the local region surrounding irregular nodes. Several examples are presented to demonstrate the performance of the algorithm.     

An investigation into design of fair surfaces over irregular domains using data-dependent triangulation

Design of fair surfaces over irregular domains is a fundamental problem in computer-aided geometric design (CAGD), and has applications in engineering sciences (in aircraft, automobile, ship science etc.). In the design of fair surfaces over irregular domains defined over scattered data, it was widely accepted till recently that the classical Delaunay triangulation be used because of its global optimum property. However, in recent times it has been shown that for continuous piecewise linear surfaces, improvements in the quality of fit can be achieved if the triangulation pattern is made dependent upon some topological or geometric property of the data set or is simply data dependent. The fair surface is desired because it ensures smooth and continuous surface planar cuts, and these in turn ensure smooth and easy production of the surface in CAD/CAM, and favourable resistance properties. In this paper, we discuss a method for construction of C¹ piecewise polynomial parametric fair surfaces which interpolate prescribed ℜ³ scattered data using spaces of parametric splines defined on H³ triangulation. We show that our method is more specific to the cases when the projection on a 2-D plane may consist of triangles of zero area, numerically stable and robust, and computationally inexpensive and fast. Numerical examples dealing with surfaces approximated on plates, and on ships have been presented.     

‘Ultimate’ robustness in meshing an arbitrary polyhedron

Given a boundary surface mesh (a set of triangular facets) of a polyhedron, the problem of deciding whether or not a triangulation exists is reported to be NP‐hard. In this paper, an algorithm to triangulate a general polyhedron is presented which makes use of a classical Delaunay triangulation algorithm, a phase for recovering the missing boundary facets by means of facet partitioning, and a final phase that makes it possible to remove the additional points defined in the previous step. Following this phase, the resulting mesh conforms to the given boundary surface mesh. The proposed method results in a discussion of theoretical interest about existence and complexity issues. In practice, however, the method should provide what we call ‘ultimate’ robustness in mesh generation methods. Copyright © 2003 John Wiley & Sons, Ltd.     

From medical images to anatomically accurate finite element grids

The successful application of computational modelling of blood flow for the planning of surgical and interventional procedures to treat cardiovascular diseases strongly depends on the rapid construction of anatomical models. The large individual variability of the human vasculature and the strong dependence of blood flow characteristics on the vessel geometry require modelling on a patient‐specific basis. Various image processing and geometrical modelling techniques are integrated for the rapid construction of geometrical surface models of arteries starting from medical images. These discretely defined surfaces are then used to generate anatomically accurate finite element grids for hemodynamic simulations. The proposed methodology operates directly in 3D and consists of three stages. In the first stage, the images are filtered to reduce noise and segmented using a region‐growing algorithm in order to obtain a properly defined boundary of the arterial lumen walls. In the second stage, a surface triangulation representing the vessel walls is generated using a direct tessellation of the boundary voxels. This surface is then smoothed and the quality of the resulting triangulation is improved. Finally, in the third stage, the triangulation is subdivided into so‐called discrete surface patches for surface gridding, the desired element size distribution is defined and the finite element grid generated. Copyright © 2001 John Wiley & Sons, Ltd.     

Automatic triangulation of arbitrary planar domains for the finite element method

The object of this paper is to describe a new algorithm for the semi-automatic triangulation of arbitrary, multiply connected planar domains. The strategy is based upon a modification of a finite element mesh genration algorithm recently developed. ¹ The scheme is designed for maximum flexibility and is capable of generating meshes of triangular elements for the decomposition of virtually any multiply connected planar domain. Moreover, the desired density of elements in various regions of the problem domain is specified by the user, thus allowing him to obtain a mesh decomposition appropriate to the physical loading and/or boundary conditions of the particular problem at hand. Several examples are presented to illustrate the applicability of the algorithm. An extension of the algorithm to the triangulation of shell structures is indicated.