一种改进的六角形砍边细分方法

研究了六角形网格上的曲面细分算法,改进了六角形网格砍边细分算法.在六边形网格的砍边细分过程中,利用对偶砍角法对非六角形网格进行六角形网格化预处理,然后通过计算相邻两个面片的夹角,根据预先设置的阈值,自动对初始混合控制网格上具有尖锐特征的顶点和边分别作标记,然后对这些标记过的边和点进行特殊处理,局部修改细分规则进行迭代细分.实验结果表明,该算法效果好,能更好地保持原始模型的特征.     

任意曲面的三角形网格划分

把曲面分为可展曲面和不可展曲面，对可展曲面用曲面展开算法展成平面，对不可展曲面用曲面分割算法转化成平面片，在平面上运用Ｄｅｌａｕｎａｙ三角划分法进行网格划分，然后把网格节点反映射到曲面上，从而实现任意曲面的三角形网格划分。     

隐式曲面的多分辨率法向网格逼近

法向网格是一种新型的曲面多分辨率描述方式，其中每个层次都可以表示为其前一个粗糙层次的法向偏移．文中提出一种基于法向网格表示的隐式曲面多分辨率网格逼近算法．首先通过基于空间剖分技术的多边形化算法获得隐式曲面的粗糙逼近网格，并利用网格均衡化方法对粗糙网格进行优化，消除其中的狭长三角形；然后利用法向细分规则迭代地对网格中的三角面片进行细分，并利用区间算术技术沿法向方向对隐式曲面进行逼近．最终生成的隐式曲面分片线性逼近网格为法向网格．该逼近网格为隐式曲面提供了一种多分辨率表示，网格具有细分连通性，其数据量较传统的多边形化算法所生成的网格有大幅度的压缩．该算法可用于隐式曲面的多级绘制、累进传输及相关数字几何处理．     

基于凸凹性的网格细分综合优化

实际工程中希望表示物体的三角形网格形状优良,同时拓扑逼近真实曲面。但是对非均匀离散点云重建得到的网格进行优化时,这两个标准常常是相互矛盾的。该文针对在实际工程中遇见的这个问题,提出一种结合全局特征以及局部特性的细分算法。该算法避免了一般细分方法对凹区域处理出现的折叠现象,可以获取三角形形状和空间拓扑的综合优化解。最后通过对于工程应用实例的细分计算,得到了与原始网格拓扑一致,但更逼近真实曲面的细分优化网格,表明了所提出简化算法的有效性。     

混合网格的可调细分算法

论文主要研究混合网格的曲面细分问题,提出了一种带有可调参数的细分算法。该算法适用于多边形网格、三角形网格,以及两者的混合网格情形,且对开的和闭的拓扑结构都能进行处理。由于在算法中引入了可调参数,这样既可产生光滑曲面,也可产生具有尖锐特征的曲面,且通过调整参数还可产生标准的Catmull-Clark细分和Loop细分。另外,实现该算法不需要复杂的数据结构。     

满足G~1边界条件的混合细分曲面设计

自由曲面设计从工业制造到建筑设计都有着广泛的应用.文中将细分算法与几何偏微分方程方法相结合,构建一种统一的自由曲面设计方法.该方法将曲面扩散流作为演化方程,曲面的控制网格是三角形和四边形混合型网格;数值模拟采用Loop和Catmull-Clark混合细分的有限元方法,通过方程演化得到混合细分曲面的控制网格.数值实验结果表明,文中方法能构造高质量的曲面.此研究呈现出一种新颖的构造几何偏微分方程细分曲面的技术.     

用C-C细分法和流形方法构造G2连续的自由型曲面

通过改进Cotrina等利用流形方法构造n边曲面片的算法,以C-C细分网格奇异点的5一环作为控制网构造出了带有均匀三次B样条边界的n边曲面片,使得该曲面片和C-C细分曲面G^2拼接．在此基础上,讨论了C-C细分曲面中n边域的构造和填充,从而为基于任意拓扑网格构造低次G^2连续曲面的问题给出了一个有效的解决方案,实现了用流形方法构造的曲面和C-C细分曲面的融合．最后,给出了几个具体算例．     

表驱动的细分曲面GPU绘制

为了充分利用GPU的并行计算能力高效地绘制递归定义的细分曲面,提出一种基于GPU的面分裂细分曲面的实时绘制算法.该算法通过离线预计算生成可以复用的细分查找表,它由细分矩阵组成,其大小仅与奇异点度数和最大细分深度线性相关,与输入网格无关;对于细分曲面控制网格的每个曲面片,如果包含2个或2个以上奇异点,则进行一次局部预细分;之后对于不规则曲面片,利用细分查找表由初始控制网格直接计算得到各细分层次上的控制顶点,无需逐层计算,从而最大限度地发挥GPU的并行处理能力;最后对各层次上的规则曲面片使用硬件细分着色器绘制,大大提高绘制效率.实验结果表明,文中算法可以高效地绘制细分曲面的极限曲面.     

基于边光滑度的Loop自适应细分曲面算法

首先研究了传统的Loop细分曲面算法,通过分析发现随着细分次数的增多细分算法中三角形网格片数增长过快。针对这一问题提出一种自适应细分曲面算法。算法根据相邻两个三角形面上的法向量的夹角,判断细分网格中较为光滑和非光滑的区域。实验结果表明,算法提高了数据处理速度,并且模型简单易实现。     

基于蝶形细分自适应算法的三维地形仿真

基于格网法提出了蝶形细分自适应算法进行三维地形模拟,以原网格顶点的法向量为约束条件,通过对初始三角形控制网格进行多阶曲线迭代插值的非静态细分,实现几何造型.插值点的计算依据网格的局部几何特征,根据三角形网格上顶点的平坦度进行有选择性的自适应细分,同时对细分过程中产生的曲面裂缝加以弥补.地形仿真实例显示新的自适应细分方法可以很好地继承原始网格的形状特征,在曲面的光滑度和真实性上更加完善,加快了图形处理的速度.     

蜂窝细分

给出了一类新颖的基于六边形网络的细分方法，该方法拓广了细分曲面的种类，被形象地称为蜂窝细分法，通过引入中心控制点的概念，使蜂窝细分具有参数选取灵活，形状控制容易，网格复杂性增长缓慢，适用范围广等优点，分析了蜂窝细分方法的极限性质以及参数选取规则，可保证细分曲面处处达到切平面连续，并在适当条件下具有插值能力，该方法适用于动画造型和工业造型设计。     

Interpolatory,solid subdivision of unstructured hexahedral meshes

This paper presents a new, volumetric subdivision scheme for interpolation of arbitrary hexahedral meshes. To date, nearly every existing volumetric subdivision scheme is approximating, i.e., with each application of the subdivision algorithm, the geometry shrinks away from its control mesh. Often, an approximating algorithm is undesirable and inappropriate, producing unsatisfactory results for certain applications in solid modeling and engineering design (e.g., finite element meshing). We address this lack of smooth, interpolatory subdivision algorithms by devising a new scheme founded upon the concept of tri-cubic Lagrange interpolating polynomials. We show that our algorithm is a natural generalization of the butterfly subdivision surface scheme to a tri-variate, volumetric setting.     

一种新的六角形网格的砍边细分方法

提出了一种新的六角形网格的砍边细分算法。该算法通过面收缩和砍边两个过程,使细分网格的数目以4为倍数增长,并选择适当的几何定位使细分曲面保持C1连续性。该算法只适用于顶点的价为3的半正则网格,而对于任意的初始控制网格,算法可以通过预处理使初始网格半正则化。     

Detecting and reconstructing subdivision connectivity

inverse subdivision algorithms , with linear time and space complexity, to detect and reconstruct uniform Loop, Catmull–Clark, and Doo–Sabin subdivision structure in irregular triangular, quadrilateral, and polygonal meshes. We consider two main applications for these algorithms. The first one is to enable interactive modeling systems that support uniform subdivision surfaces to use popular interchange file formats which do not preserve the subdivision structure, such as VRML, without loss of information. The second application is to improve the compression efficiency of existing lossless connectivity compression schemes, by optimally compressing meshes with Loop subdivision connectivity. Our Loop inverse subdivision algorithm is based on global connectivity properties of the covering mesh, a concept motivated by the covering surface from Algebraic Topology. Although the same approach can be used for other subdivision schemes, such as Catmull–Clark, we present a Catmull–Clark inverse subdivision algorithm based on a much simpler graph-coloring algorithm and a Doo–Sabin inverse subdivision algorithm based on properties of the dual mesh. Straightforward extensions of these approaches to other popular uniform subdivision schemes are also discussed. Published online: 3 July 2002     

Multiresolution analysis on irregular surface meshes

Wavelet-based methods have proven their efficiency for visualization at different levels of detail, progressive transmission, and compression of large data sets. The required core of all wavelet-based methods is a hierarchy of meshes that satisfies subdivision-connectivity. This hierarchy has to be the result of a subdivision process starting from a base mesh. Examples include quadtree uniform 2D meshes, octree uniform 3D meshes, or 4-to-1 split triangular meshes. In particular, the necessity of subdivision-connectivity prevents the application of wavelet-based methods on irregular triangular meshes. In this paper, a “wavelet-like” decomposition is introduced that works on piecewise constant data sets over irregular triangular surface meshes. The decomposition/reconstruction algorithms are based on an extension of wavelet-theory allowing hierarchical meshes without property. Among others, this approach has the following features: it allows exact reconstruction of the data set, even for nonregular triangulations, and it extends previous results on Haar-wavelets over 4-to-1 split triangulations     

A Shrink Wrapping Approach to Remeshing Polygonal Surfaces

Due to their simplicity and flexibility, polygonal meshes are about to become the standard representation for surface geometry in computer graphics applications. Some algorithms in the context of multiresolution representation and modeling can be performed much more efficiently and robustly if the underlying surface tesselations have the special subdivision connectivity. In this paper, we propose a new algorithm for converting a given unstructured triangle mesh into one having subdivision connectivity. The basic idea is to simulate the shrink wrapping process by adapting the deformable surface technique known from image processing. The resulting algorithm generates subdivision connectivity meshes whose base meshes only have a very small number of triangles. The iterative optimization process that distributes the mesh vertices over the given surface geometry guarantees low local distortion of the triangular faces. We show several examples and applications including the progressive transmission of subdivision surfaces.     

n-Dimensional multiresolution representation of subdivision meshes with arbitrary topology

We present a new model for the representation of n-dimensional multiresolution meshes. It provides a robust topological representation of arbitrary meshes that are combined in closely interlinked levels of resolution. The proposed combinatorial model is formalized through the mathematical model of combinatorial maps allowing us to give a general formulation, in any dimensions, of the topological subdivision process that is a key issue to robustly and soundly define mesh hierarchies. It fully supports multiresolution edition what allows the implementation of most mesh processing algorithms – like filtering or compression – for n-dimensional meshes with arbitrary topologies.We illustrate this model, in dimension 3, with an new truly multiresolution representation of subdivision volumes. It allows us to extend classical subdivision schemes to arbitrary polyhedrons and to handle adaptive subdivision with an elegant solution to compliance issues. We propose an implementation of this model as an effective and relatively inexpensive data structure.     

RGB Subdivision

We introduce the RGB subdivision: an adaptive subdivision scheme for triangle meshes, which is based on the iterative application of local refinement and coarsening operators, and generates the same limit surface of the Loop subdivision, independently on the order of application of local operators. Our scheme supports dynamic selective refinement, as in Continuous Level Of Detail models, and it generates conforming meshes at all intermediate steps. The RGB subdivision is encoded in a standard topological data structure, extended with few attributes, which can be used directly for further processing. We present an interactive tool that permits to start from a base mesh and use RGB subdivision to dynamically adjust its level of detail.     

Biorthogonal Wavelets Based on Interpolatory Subdivision

This article presents an efficient construction of biorthogonal wavelets built upon an interpolatory         subdivision for quadrilateral meshes. The interpolatory subdivision scheme is first turned into a scheme for reversible primitive wavelet synthesis. Some desired properties are then incorporated in the primitive wavelet using the lifting scheme. The analysis and synthesis algorithms of the resulting new wavelet are finally obtained as local and in-place lifting operations. The wavelet inherits the advantage of         refinement with added levels of resolution. Numerical experiments show that the lifted wavelet built upon interpolatory         subdivision has sufficient stability and better performance in dealing with closed or open semi-regular quadrilateral meshes compared with other existing wavelets for quadrilateral manifold meshes.     

基于加权渐进插值的Loop 细分曲面等距逼近

等距曲面在CAD/CAM 领域有着重要的作用,由于细分曲面没有整体解 析表达式,使得计算细分曲面等距比参数曲面更加困难。针对目前已有的两种等距面逼近算 法进行了改进,利用加权渐进插值技术避免了传统细分等距逼近算法产生网格偏移的问题。 此外,提出了针对边界等距处理方案,使得等距后的细分曲面在内部和边界都均匀等距。该 方法无需求解线性方程组,具有全局和局部特性,能够处理闭网格和开网格,为Loop 细分 曲面数控加工奠定了良好的基础算法。最后给出的实例验证了算法的有效性。