基于流线的重新网格化及多分辨率表示

提出基于场的重新三角网格化和多分辨率表示生成算法.首先,在原三角网格模型上建立拉普拉斯标量场,据此生成两组夹角为60(的流线.然后,从这两组流线构造以菱形面为主的网格并三角化得到三角基网格.最后,在基网格的基础上,再次使用流线技术对原始数据进行向上重采样,得到模型的多分辨率表示.一般地,基网格的三角形接近等边三角形,实验也表明该方法能够得到较高质量的结果.     

一种基于多区域并行的网格模型简化的两步法

针对三角形网格模型简化中保持细节特征的要求，引入了图像的区域分割原理，提出了一种基于区域生长的网格模型区域分割方法．在此基础之上，提出了一种基于多区域并行的自适应三角网格模型简化的两步法，对于不同的区域采取按照比例进行简化的并行机制．此方法的特点是保持模型细节的基础上，大大地加快了模型的简化速度．另外，还提出了一种基于多区域并行的累进网格模型的实现方法，有效地实现了保持细节特征的多分辨率模型，并实现了具有细节特征的多分辨模型间的层次过渡．经实验证明，该方法能够快速有效地对三角形网格模型进行简化，并具有保持模型的三角形网格密度分布的特点．     

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．     

基于三角形折叠的网格简化算法

在计算机图形学中，物体常常用三角形网格模型来描述。本文提出了一种新的基于三角形折叠的网格简化算法。该网格简化算法不仅能减少模型中的三角形数目而且能保持模型拓扑结构。算法给出了一种基于点到平面距离的有效的误差控制方法，并能在用户指定的误差范围内通过使原始网格中的三角形折叠达到大量简化的目的。该算法实现简单并且速度快。另外为了有效地支持多分辨率模型的表示以及相邻层次模型间的连续过渡，本文还给出了一种基     

虚拟环境中多细节层次模型自动生成算法

虚拟环境是限时计算和限时图形绘制技术的典型应用．本文对用于限时图形绘制的多细节层次模型表示进行研究，提出了基于三角形网格简化的多细节层次模型自动生成算法．该算法多次遍历现有三角形网格模型的每一个顶点，使用局部几何和拓扑特征移去满足简化标准的顶点，对移去顶点后产生的多边形区域进行局部三角化．多次执行上述过程，结果形成不同细节层次的三角形网格模型．文中给出的实例说明了该算法的有效性．     

带 2细分结构的四边形化

在Morse函数理论的基础上,提出一种新的从三角网格中建立四边形网格多分辨率表示的方法．先由人工指定或从拉普拉斯矩阵的特征函数中提取临界点,计算带约束的拉普拉斯方程得到光滑的Morse函数．函数的临界点（极大、极小和鞍点）有规律地分布在模型表面,在三角网格表面梯度场的引导下, 生成临界点间流线,得到临界点间的拓扑关系．通过临界点交换规则,同样是采用流线的方法,得到更精细的四边形网格。 最终可实现无需参数化而仅用流线方法来建立不同多分辨率表示的四边形网格。     

带2~(1/2)细分结构的四边形化

在Morse函数理论的基础上,提出一种新的从三角网格中建立四边形网格多分辨率表示的方法.先由人工指定或从拉普拉斯矩阵的特征函数中提取临界点,计算带约束的拉普拉斯方程得到光滑的Morse函数.函数的临界点(极大、极小和鞍点)有规律地分布在模型表面,在三角网格表面梯度场的引导下,生成临界点间流线,得到临界点间的拓扑关系.通过临界点交换规则,同样是采用流线的方法,得到更精细的四边形网格。最终可实现无需参数化而仅用流线方法来建立不同多分辨率表示的四边形网格。     

三维复杂模型的实时连续多分辨率绘制

本文给出了一种能实时产生由三角网格表示的三维复杂模型的连续多分辨率近似模型并加以绘制的新算法。该算法分为预处理和实时显示两个阶段，在预处理中，对模型上的每个观点按照它们的重要程度进行排序，同时也规定了每个顶点在实时简化过程中的合并操作，实质上也就是确定了模型中的三角形的删除顺序，这使得在实时显示中可以立即得到近似模型。该算法具有两个优点：首先，它建立了视点参数与被选择的分辨率的直接关系；其次，它提     

可减少模型简化误差的边折叠简化算法及应用

基于三角形网格边折叠简化思想，提出一种基于边顶点重要度简化算法，简化算法能有效保持模型局部特征，减小简化模型和原始模型之间的误差；采用一种改进的三角形网格数据结构，利用二叉树对顶点重要度进行快速排序并记录三角形合并关系，得到所需分辨率下的近似网格模型。数据结构具有层次清楚、操作简单、可扩充性等特点，能有效支持多分辨率简化与快速可视化。     

基于可变模版的三角网格拓扑压缩

针对三角网格模型的拓扑信息。提出了一种高效压缩方法.不同于以往的单纯利用算术编码或霍夫曼鳊码对遍历三角网格生成的拓扑流进行编码压缩,根据三角网格模型(特别是规则三角网格模型)的特点,自适应地提高编码过程中对当前编码字符发生的预测准确率,实现对三角网格模型的拓扑信息的高效压缩.算法首先遍历三角网格模型,得到操作符序列;然后对得到的操作符序列的每个操作符作模版可变的自适应算术编码.在编码过程中,根据当前编码字符的前一个操作符、三角网格模型的特点以及网格遍历方法为当前编码操作符计算一个模版,在这个模版中,预测准确率高的操作符用较短的二进制串表示.根据当前编码操作符的可变模版,可以得到该操作符的二进制表示,并对这个二进制表示的每个比特作自适应算术编码.该方法是针对流形三角网格模型的拓扑信息作单分辨率的基于面的无损压缩,可以得到很好的三角网格拓扑信息的压缩结果,其压缩比甚至比拓扑压缩领域压缩比方面最好的TG算法的压缩比还要好.     

Efficient implementation of real-time view-dependent multiresolution meshing

In this paper, we present an efficient (topology preserving) multiresolution meshing framework for interactive level-of-detail (LOD) generation and rendering of large triangle meshes. More specifically, the presented approach, called FastMesh, provides view-dependent LOD generation and real-time mesh simplification that minimizes visual artifacts. Multiresolution triangle mesh representations are an important tool for reducing triangle mesh complexity in interactive rendering environments. Ideally, for interactive visualization, a triangle mesh is simplified to the maximal tolerated visible error and, thus, mesh simplification is view-dependent. This paper introduces an efficient hierarchical multiresolution triangulation framework based on a half-edge triangle mesh data structure and presents optimized implementations of several view-dependent or visual mesh simplification heuristics within that framework. Despite being optimized for performance, these error heuristics provide conservative error bounds. The presented framework is highly efficient both in space and time cost and needs only a fraction of the time required for rendering to perform the error calculations and dynamic mesh updates.     

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.     

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.     

体积保持的多分辨率多边形网格的光顺造型

给出了一个高效的多边形网格的多分辨率光顺造型算法。该算法首先通过引入体积保持约束,快速地实现稠密多边形网格的多分辨率表示,然后结合一个有效的无收缩光顺算法,对网格执行高效的多分辨率光顺编辑,与传统编辑方法不同,该方法利用体积保持约束及优化技术,来自动恢复编辑区域中相应的细节,而无需引入非常损耗资源的局部标架。实验结果表明,该算法计算稳定、高效,能产生复杂的模型。     

大型网格模型多分辨率的外存构建与交互绘制

结合多分辨率、网格排布和基于视点的绘制技术,提出一种外存多分辨率构建和绘制算法.采用适应性八叉树对模型的包围盒进行划分,自顶向下构建模型的多分辨率层次结构,较好地保持了原模型的细节分布;并对多分辨率结构中每个节点所包含的三角形片段进行网格排布优化,降低了缓存的平均失效率;在实时绘制时,采用基于视点的细节层次选择策略进行模型的细化;最后通过引入数据预取机制来隐藏磁盘I/O延时,进一步提高绘制性能.实验结果表明,该算法在绘制速度与细节保留上均优于同类MRMM算法.     

Multiresolution Shape Deformations for Meshes with Dynamic Vertex Connectivity

Multiresolution shape representation is a very effective way to decompose surface geometry into several levels of detail. Geometric modeling with such representations enables flexible modifications of the global shape while preserving the detail information. Many schemes for modeling with multiresolution decompositions based on splines, polygonal meshes and subdivision surfaces have been proposed recently. In this paper we modify the classical concept of multiresolution representation by no longer requiring a global hierarchical structure that links the different levels of detail. Instead we represent the detail information implicitly by the geometric difference between independent meshes. The detail function is evaluated by shooting rays in normal direction from one surface to the other without assuming a consistent tesselation. In the context of multiresolution shape deformation, we propose a dynamic mesh representation which adapts the connectivity during the modification in order to maintain a prescribed mesh quality. Combining the two techniques leads to an efficient mechanism which enables extreme deformations of the global shape while preventing the mesh from degenerating. During the deformation, the detail is reconstructed in a natural and robust way. The key to the intuitive detail preservation is a transformation map which associates points on the original and the modified geometry with minimum distortion. We show several examples which demonstrate the effectiveness and robustness of our approach including the editing of multiresolution models and models with texture.     

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.     

Constrained Fairing for Meshes

In this paper, we present a novel fairing algorithm for the removal of noise from uniform triangular meshes without shrinkage and serious distortion. The key feature of this algorithm is to keep all triangle centers invariant at each smoothing step by including some constraints in the energy minimization functional. The constrained functional is then minimized efficiently using an iterative method. Further, we apply this smoothing technique to a multiresolution representation to remove arbitrary levels of detail. A volume-preserving decimation algorithm is presented to generate the multiresolution representation. The experimental results demonstrate the combined algorithm's stability and efficiency.     

Triangle Strip Compression

In this paper we introduce a simple and efficient scheme for encoding the connectivity and the stripification of a triangle mesh. Since generating a good set of triangle strips is a hard problem, it is desirable to do this just once and store the computed strips with the triangle mesh. However, no previously reported mesh encoding scheme is designed to include triangle strip information into the compressed representation. Our algorithm encodes the stripification and the connectivity in an interwoven fashion, that exploits the correlation existing between the two.