位移蝶形细分面片的渐进传输

随着三维激光扫描和建模技术的不断进步，三维网格模型的数据量越来越大．与此同时，无处不在的智能计算要求数据必须能够在网络上进行快速的传输，现有的三维网格渐进传输技术无论是基于任意拓扑结构网格的渐进网格技术，还是基于参数化细分面片的渐进传输技术，都存在着传输数据量大、渐进显示效果差的问题，针对这些缺点，提出了首先利用位移蝶形细分面片重建原来的网格模型，然后对于重建后的位移蝶形细分面片设计了一种新的数据简化方法，进而构造了一种渐进传输算法，该算法在减少传输数据总量的同时，提高了渐进传输的视觉效果。     

四边形网格的去边细分方法

提出一种四边形网格细分算法：每细分一次四边形网格，其数目增加为原来的两倍，细分二次结果相当于一次二分细分和一个旋转．该算法采用三次B样条张量积的形式，其生成曲面在规则点具有C^2连续性，在非规则点具有C^1连续性．由于该细分算法对网格几何操作简单，所得网格数据量增长相对缓慢，适合于3D图像重构及网络传输等应用领域。     

自适应细分技术研究进展

对自适应细分及其需要解决的关键技术作了详细的探讨，对已有的自适应细分技术进行了比较归类，并基于对具体算法的实现列举了各种各样的实例．最后指出自适应细分技术存在的问题及其可能的解决途径，以及未来的发展方向．     

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。     

Catmull-Clark细分网格数据点拾取

针对将OpenGL选择拾取机制直接作用于Catmull-Clark细分网格数据点的拾取,可能会因细分网格数据量过大而导致名字堆栈溢出的问题,借鉴细分曲面求交的思想,提出一种新的细分网格数据点拾取方法.该方法通过提取拾取对象的邻域网格并进行局部细分,将对细分任意层次上网格数据点的拾取转化为对初始控制网格以及在达到细分层次要求以前每一次局部细分网格点、边、面的拾取和对最后一次局部细分网格数据点的拾取.采用多个拾取算例进行对比分析实验,当细分网格顶点数量较多时,所给拾取方法的拾取命名对象总量和拾取时间都远小于传统OpenGL选择拾取方法.实验结果表明,所给拾取方法能快速准确实现细分网格数据点的拾取,尤其适用于数据量较大的复杂细分模型,可有效避免因拾取名字堆栈溢出而导致的拾取错误.     

基于Catmull-Clark细分的新细分算法的研究

提出一种四边形网格细分算法：每细分一次四边形网格,其数目增加为原来的两倍,细分二次结果相当于一次二分细分,采用边数缓慢增长的策略,使生成的曲面光滑连续。该算法生成曲面在规则点具有C2连续性,在非规则点具有C1连续性。该算法对网格几何操作简单,所得网格数据量增长相对缓慢,适合3D图像重构及网络传输等应用领域。由于文中细分算法对初始网格的拓扑变更,因此第一次细分会产生扭曲现象,但后面的细分会逐步光滑。     

大数据聚类算法综述

随着数据量的迅速增加,如何对大规模数据进行有效的聚类成为挑战性的研究课题。面向大数据的聚类算法对传统金融行业的股票投资分析、互联网金融行业中的客户细分等金融应用领域具有重要价值。对已有的大数据聚类算法进行了详细划分,并比较了每种聚类算法的优缺点,进一步总结了已有研究存在的问题,最后对未来的研究方向进行了展望。     

细分蒙皮曲面

对细分曲面在曲面造型中的应用进行了研究，并着重于蒙皮曲面造型技术．所提方法在传统的蒙皮曲面构造过程中引入细分方法，有效地避免了因截面曲线的相容性处理而产生的数据量激增的问题；最后生成的蒙皮曲面能够精确插值预先设计的截面曲线，并且可以在指定的截面曲线处产生折痕效果．     

一种带噪声的密集三角网格细分曲面拟合算法

实现了一个从带噪声的密集三角形拟合出带尖锐特征的细分曲面拟合系统.该系统包括了一种改进的基于图像双边滤波器的网格噪声去除方法,模型的尖锐特征提取以及保持尖锐特征的网格简化和拓扑优化.为了处理局部细节特征和模型数据量问题,提出了自适应细分方法,并将根据给定精度估计最少细分深度引入到细分曲面拟合系统中,使得拟合得到的细分曲面模型具有良好的细节特征和数据量小等特点.大量3D模型实验结果和实际工程应用结果表明了该细分曲面拟合系统的有效性.     

基于细分曲面的三维服装柔性实体模拟

提出一种基于细分曲面的三维服装柔性实体模拟算法，该算法将整个模拟过程分为两个阶段：首先利用四点细分曲面造型方法生成三维服装刚性曲面，然后在刚性曲面基础上通过引入织物的物理模型来模拟三维服装柔性曲面，通过物理和几何模拟方法有机结合，算法有效解决了复杂衣片间的缝合问题，较大地提高了模拟的计算效率，同时，也提出了一种基于细分曲面层次数据结构的碰撞检测算法，有效提高了模拟速度，提出的算法已全部在所开发的三维虚拟服装试衣系统中得以实现，实验结果表明：该算法具有模拟效率高、交互性强和易于计算机实现等优点。     

General triangular midpoint subdivision

In this paper, we introduce triangular subdivision operators which are composed of a refinement operator and several averaging operators, where the refinement operator splits each triangle uniformly into four congruent triangles and in each averaging operation, every vertex will be replaced by a convex combination of itself and its neighboring vertices. These operators form an infinite class of triangular subdivision schemes including Loop's algorithm with a restricted parameter range and the midpoint schemes for triangular meshes. We analyze the smoothness of the resulting subdivision surfaces at their regular and extraordinary points by generalizing an established technique for analyzing midpoint subdivision on quadrilateral meshes. General triangular midpoint subdivision surfaces are smooth at all regular points and they are also smooth at extraordinary points under certain conditions. We show some general triangular subdivision surfaces and compare them with Loop subdivision surfaces.     

A Unified Subdivision Scheme for Polygonal Modeling

Subdivision rules have traditionally been designed to generate smooth surfaces from polygonal meshes. In this paper we propose to employ subdivision rules as a polygonal modeling tool, specifically to add additional level of detail to meshes. However, existing subdivision schemes have several undesirable properties making them ill suited for polygonal modeling. In this paper we propose a general set of subdivision rules which provides users with more control over the subdivision process. Most existing subdivision schemes are special cases. In particular, we provide subdivision rules which blend approximating spline based schemes with interpolatory ones. Also, we generalize subdivision to allow any number of refinements to be performed in a single step.     

细分曲面拟合的局部渐进插值方法

逼近型细分方法生成的细分曲面其品质要优于插值型细分方法生成的细分曲面.然而,逼近型细分方法生成的细分曲面不能插值于初始控制网格顶点.为使逼近型细分曲面具有插值能力,一般通过求解全局线性方程组,使其插值于网格顶点.当网格顶点较多时,求解线性方程组的计算量很大,因此,难以处理稠密网格.与此不同,在不直接求解线性方程组的情况下,渐进插值方法通过迭代调整控制网格顶点,最终达到插值的效果.渐进插值方法可以处理稠密的任意拓扑网格,生成插值于初始网格顶点的光滑细分曲面.并且经证明,逼近型细分曲面渐进插值具有局部性质,也就是迭代调整初始网格的若干控制顶点,且保持剩余顶点不变,最终生成的极限细分曲面仍插值于初始网格中被调整的那些顶点.这种局部渐进插值性质给形状控制带来了更多的灵活性,并且使得自适应拟合成为可能.实验结果验证了局部渐进插值的形状控制以及自适应拟合能力.     

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。     

Adaptive and Feature-Preserving Subdivision for High-Quality Tetrahedral Meshes

We present an adaptive subdivision scheme for unstructured tetrahedral meshes inspired by the       -subdivision scheme for triangular meshes. Existing tetrahedral subdivision schemes do not support adaptive refinement and have traditionally been driven by the need to generate smooth three-dimensional deformations of solids. These schemes use edge bisections to subdivide tetrahedra, which generates octahedra in addition to tetrahedra. To split octahedra into tetrahedra one routinely chooses a direction for the diagonals for the subdivision step. We propose a new topology-based refinement operator that generates only tetrahedra and supports adaptive refinement. Our tetrahedral subdivision algorithm is motivated by the need to have one representation for the modeling, the simulation and the visualization and so to bridge the gap between CAD and CAE. Our subdivision algorithm design emphasizes on geometric quality of the tetrahedral meshes, local and adaptive refinement operations, and preservation of sharp geometric features on the boundary and in the interior of the physical domain.     

A Method for Constructing Interpolatory Subdivision Schemes and Blending Subdivisions

This paper presents a universal method for constructing interpolatory subdivision schemes from known approximatory subdivisions. The method establishes geometric rules of the associated interpolatory subdivision through addition of further weighted averaging operations to the approximatory subdivision. The paper thus provides a novel approach for designing new interpolatory subdivision schemes. In addition, a family of subdivision surfaces varying from the given approximatory scheme to its associated interpolatory scheme, namely the blending subdivisions, can also be established. Based on the proposed method, variants of several known interpolatory subdivision schemes are constructed. A new interpolatory subdivision scheme is also developed using the same technique. Brief analysis of a family of blending subdivisions associated with the Loop subdivision scheme demonstrates that this particular family of subdivisions are globally C¹ continuous while maintaining bounded curvature for regular meshes. As a further extension of the blending subdivisions, a volume‐preserving subdivision strategy is also proposed in the paper.     

Subdivision Surface Tesselation on the Fly using a versatile Mesh Data Structure

Subdivision surfaces have become a standard technique for freeform shape modeling. They are intuitive to use and permit designers to flexibly add detail. But with larger control meshes, efficient adaptive rendering techniques are indispensable for interactive visualization and shape modeling. In this paper, we present a realization of tesselation-on-the-fly for Loop subdivision surfaces as part of a framework for interactive visualization.     

Extension of half-edges for the representation of multiresolution subdivision surfaces

We address in this paper the problem of the data structures used for the representation and the manipulation of multiresolution subdivision surfaces. The classically used data structures are based on quadtrees, straightforwardly derived from the nested hierarchy of faces generated by the subdivision schemes. Nevertheless, these structures have some drawbacks: specificity to the kind of mesh (triangle or quad); the time complexity of neighborhood queries is not optimal; topological cracks are created in the mesh in the adaptive subdivision case. We present in this paper a new topological model for encoding multiresolution subdivision surfaces. This model is an extension to the well-known half-edge data structure. It allows instant and efficient navigation at any resolution level of the mesh. Its generality allows the support of many subdivision schemes including primal and dual schemes. Moreover, subdividing the mesh adaptively does not create topological cracks in the mesh. The extension proposed here is formalized in the combinatorial maps framework. This allows us to give a very general formulation of our extension.     

Quad/Triangle Subdivision

In this paper we introduce a new subdivision operator that unifies triangular and quadrilateral subdivision schemes. Designers often want the added flexibility of having both quads and triangles in their models. It is also well known that triangle meshes generate poor limit surfaces when using a quad scheme, while quad‐only meshes behave poorly with triangular schemes. Our new scheme is a generalization of the well known Catmull‐Clark and Loop subdivision algorithms. We show that our surfaces are C ¹ everywhere and provide a proof that it is impossible to construct such a C ² scheme at the quad/triangle boundary. However, we provide rules that produce surfaces with bounded curvature at the regular quad/triangle boundary and provide optimal masks that minimize the curvature divergence elsewhere. We demonstrate the visual quality of our surfaces with several examples. ACM CSS: I.3.5 Computer Graphics—Curve, surface, solid, and object representations     

Quad/triangle subdivision,nonhomogeneous refinement equation and polynomial reproduction

The quad/triangular subdivision, whose control net and refined meshes consist of both quads and triangles, provides better visual quality of subdivision surfaces. While some theoretical results such as polynomial reproduction and smoothness analysis of quad/triangle schemes have been obtained in the literature, some issues such as the basis functions at quad/triangle vertices and design of interpolatory quad/triangle schemes need further study. In our study of quad/triangle schemes, we observe that a quad/triangle subdivision scheme can be derived from a nonhomogeneous refinement equation. Hence, the basis functions at quad/triangle vertices are shifts of the refinable function associated with a nonhomogeneous refinement equation. In this paper a quad/triangle subdivision surface is expressed analytically as the linear combination of these basis functions and the polynomial reproduction of matrix-valued quad/triangle schemes is studied. The result on polynomial reproduction achieved here is critical for the smoothness analysis and construction of matrix-valued quad/triangle schemes. Several new schemes are also constructed.