一种可调的Catmull-Clark细分曲面

通过在曲面细分过程中引入一个参数t(0≤t≤1)，使得Catmull-Clark细分曲面可调，得出一种新的算法。这种算法简单直观，通过调节参数t值，可以得到一族细分曲面。该族细分曲面不但保留了许多Catmull—Clark细分曲面的特性，而又可以方便地解决在工程中经常遇到的调整曲面位置和形状的问题。同时，还可以将这种细分算法作为Catmull-Clark细分的前置处理方法。文中详细讨论了这一算法，并给出了验证实例。     

Butterfly细分曲面的快速求值

从分析Butterfly细分曲面的局部参数化出发,通过参数二进制分解生成数列以及构造细分格式的局部加细矩阵,并利用对应矩阵序列乘积与矩阵特征分解计算出控制点权值,从而解决TButterfly细分曲面插值问题.算法独立于网格存储的数据结构,避免了求邻接关系等费时的操作,并且容易推广到其他三角网格插值细分格式的曲面求值中.     

P-nary细分多层B样条算法及曲面拟合

多层B样条方法在曲面的拟合中提供了新的途径.在证明均匀B样条基函数P-nary细分方程基础上,给出了均匀B样条曲线的P-nary细分控制点之间的计算公式,进而讨论了B样条曲面的P-nary细分问题,并将其用于层次B样条曲面拟合.提出了基于P-nary细分多层B样条曲面拟合算法.该算法加快了层次B样条曲面拟合中网格加细后曲面控制点的计算,数值实例显示所给算法的有效性.     

Loop细分曲面的加工等距面生成及误差控制算法

不同层次的Loop细分网格曲面可作为不同工序的加工模型.当判断各细分层次与极限曲面的整体误差时,若不考虑所存在的尖锐特征,则计算所得误差将高于实际误差.本文考虑了尖锐特征的存在,对现有给定误差估计所需细分次数的算法进行了改进,并针对粗加工和精加工的不同特点,给出了各工序等距面的生成及调整算法.实践验证方法可行.     

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.     

基于三角网格的ternary插值细分法

本文针对规则三角网格,首先提出了一种基于插值√3细分法的ternary插值曲面细分法,极限曲面可达C1连续.为使得细分法生成的曲面形状可调,本文进而研究了带参数的ternary插值曲面细分法的构造问题,分析了细分法的连续性.     

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。     

基于九叉树分割的曲面片上点的快速反解算法

本文针对曲面造型中，”由参数样条曲面上点的笛卡尔坐标，反求其对应参数“的反解问题，提出了一种通过曲面快速分割来逼近最终解的快速，简单，可靠的反解算法；并以Ｂ样条参数曲面为例，介绍了算法的实现过程。     

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。     

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.     

Subdivision surface-based finish machining

Subdivision surfaces combine smooth spline surfaces and polygonal meshes together, therefore, a smooth design model and discrete machining models may be unified and subdivision surfaces may be used as a common representation for geometric design and machining. Motivated by the idea, this paper presents the study of finish machining of objects represented by subdivision surfaces with emphasis on geometric error control involved in tool-path generation. First, given a design model, chordal error is controlled during finishing model building. A chordal error-driven adaptive subdivision method is used to build finishing models with less data. Second, a surface decomposition machining strategy is used to control the cusp height error. A simple iso-slope curve tracing and surface decomposition algorithm is presented to partition the model into flat and steep regions. Contour-map tool-paths are generated in the steep regions while iso-planar tool-paths are generated in the flat regions. The gouge problem is easily handled through two-dimensional (2D) tool-path correction algorithms. The implementation results demonstrate that subdivision is capable of serving as a unified representation for both geometric modelling and machining.     

基于细分网格的多分辨率几何数据压缩方法研究

提出了一种基于细分网格的多分辨率几何数据压缩算法 ,该算法是一种利用正则曲面法线向量特性及细分曲面的细分连通性的有损压缩方法 ,因此可以获得很高的压缩比     

C-Bezier曲面分割、拼接及其应用

首先在介绍了C-Bezier曲面的几何模型的基础上，给出了C-Bezier曲面在u向和w向两个方向上的任意分割算法，并对曲面所具有的特性进行了分析；同时，研究了两片C-Bezier曲面在不同方向上G^1连续的拼接条件，并通过合理选取控制参数，简化了拼接条件。最后，利用分割和拼接技术，结合C-Bezier曲面能够精确表示二次曲面的特性，将C-Bezier曲面推广到常见的工程曲面上。     

三重三角网格细分算法研究

标准的二值细分操作会在那些特殊顶点相关联处产生极大的曲率,这个缺陷可以通过对细分操作的特征值施加一个限定的曲率频谱来消除,但会扩大对那些超出了二价的顶点的支持.三重细分方案将网格的边一分为三,上述情况不会发生.该文中,作者推广了二阶连续的四次样条的三重细分到任意的三角形.该细分算法具有有界的曲率,并且被设计成能够维持凸包的属性.     

基于细分模式与能量优化的曲面混合方法

论述了用Catmull-Clark细分曲面及能量优化法对多张三次B样条曲面进行混合的方法。首先引入一种边界拓扑修改的细分规则，可生成逐段光滑的细分曲面，在此基础上构造多张三次B样条曲面的混合曲面，采用能量优化方法求解控制顶点。与现有方法相比，构造的混合曲面形状易于控制，能满足复杂的边界要求，且整个混合曲面除了在有限奇异点处为C^1连续外均达到C^2连续。     

Subdivision shells with exact boundary control and non‐manifold geometry

We introduce several new extensions to subdivision shells that provide an improved level of shape control over shell boundaries and facilitate the analysis of shells with non‐smooth and non‐manifold joints. To this end, extended subdivision schemes are used that enable to relax the continuity of the limit surface along prescribed crease edges and to create surfaces with prescribed limit positions and normals. Furthermore, shells with boundaries in the form of conic sections, such as circles or parabolas, are represented with rational subdivision schemes, which are defined in analogy to rational b‐splines. In terms of implementation, the difference between the introduced and conventional subdivision schemes is restricted to the use of modified subdivision stencils close to the mentioned geometric features. Hence, the resulting subdivision surface is in most parts of the domain identical to standard smooth subdivision surfaces. The particular subdivision scheme used in this paper constitutes an improved version of the original Loop's scheme and is as such based on triangular meshes. As in the original subdivision shells, surfaces created with the modified scheme are used for interpolating the reference and deformed shell configurations. At the integration points, the subdivision surface is evaluated using a newly developed discrete parameterization approach. In the resulting finite elements, the only degrees of freedom are the mid‐surface displacements of the nodes and additional Lagrange parameters for enforcing normal constraints. The versatility of the newly developed elements is demonstrated with a number of geometrically nonlinear shell examples. Copyright © 2011 John Wiley & Sons, Ltd.     

关于四点ternary插值细分法的进一步讨论

Hassan提出的四点ternary插值细分法当细分参数在一定范围内取值时可达C2连续。为了进一步扩展其在插值曲线造型方面的能力,作者对该细分法的C0及C1连续性条件、极限函数的一阶及二阶导数等重要特性作了进一步的讨论,给出了细分法C0及C1连续的必要条件、充分条件及极限函数的一阶及二阶导数的表达式,并讨论了细分法在函数逼近、无须辅助顶点而直接插值给定型值点的光滑插值细分曲线的构造等方面的应用。     

Subdivision based isogeometric analysis for geometric flows

We present a new isogeometric analysis (IGA) approach based on extended Loop subdivision scheme for solving various geometric flows defined on subdivision surfaces. The studied flows include the second-order, fourth-order, and sixth-order geometric flows, such as averaged mean curvature flow, constant mean curvature flow, and minimal mean-curvature-variation flow, which are generally derived by minimizing the associate energy functionals with $L^2$-gradient flow respectively. The geometric flows are discretized by means of subdivision based IGA, where the finite element space is formulated by the limit form of the extended Loop subdivision for different initial control meshes. The basis functions, consisting of quartic box-splines corresponding to each subdivided control mesh, are utilized to represent the geometry exactly. For the cases of the evolution of open surfaces with any shape boundary, high-order continuous boundary conditions derived from the mixed variational forms of the geometric flows should be implemented to be consistent with the isogeometric concept. For time discretization, we adopt an adaptive semi-implicit Euler scheme. By several numerical experiments, we study the convergence behaviors of the proposed approach for solving the geometric flows with high-order boundary conditions. Moreover, the numerical results also show the accuracy and efficiency of the proposed method.