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     

一种随机采样的特征保持的网格简化算法

提出了一种局部几何特征驱动的随机采样的网格简化算法。该算法首先计算模型中每个三角形的局部几何特征值,根据定义的概率分布函数随机确定每个三角形被选择的概率。然后对选择出的三角形进行三角形折叠,根据折叠前后网格体积变化最小这一准则来确定新生成的顶点的位置。实验证明该算法不仅能使简化前后的模型的体积变化较小,还能有效地保持模型的细节特征。     

Controlled topology simplification

We present a simple, robust, and practical method for object simplification for applications where gradual elimination of high frequency details is desired. This is accomplished by converting an object into multi resolution volume rasters using a controlled filtering and sampling technique. A multiresolution triangle mesh hierarchy can then be generated by applying the Marching Cubes algorithm. We further propose an adaptive surface generation algorithm to reduce the number of triangles generated by the standard Marching Cubes. Our method simplifies the topology of objects in a controlled fashion. In addition, at each level of detail, multilayered meshes can be used for an efficient antialiased rendering     

基于STL文件的Laplacian网格优化算法

针对三角网格模型优化算法对模型几何细节描述不够精确的问题,提出一种基于Laplacian坐标的网格模型全局优化算法。模型几何细节描述方面,采用网格顶点Laplacian坐标。网拓扑结构不变的前提下,可精确描述网格曲面局部几何特性。顶点重新定位方面,采用在最小二乘意义下求解由权重控制的包含顶点位置,以及Laplacian坐标双重约束的线性系统最优解的方法。实验结果表明,该算法在优化提高模型三角面片质量的同时,可较好地保留原始模型的几何细节。     

Block-balanced meshes in iterative uniform refinement

In this paper we study and delimit a property of known four triangle subdivisions that is useful in tri to quad mesh conversion methods. We provide both theoretical results and empirical evidence showing that iterative application of the four triangles longest-edge subdivision and the four triangles similar subdivision produces block-balanced meshes, meshes in which triangle pairs sharing a common longest edge tend to cover the area of the entire mesh. Some other properties of such triangle subdivisions regarding mesh quality and adjacency relationships are also discussed.     

Fitting polynomial surfaces to triangular meshes with Voronoi squared distance minimization

This paper introduces Voronoi squared distance minimization (VSDM), an algorithm that fits a surface to an input mesh. VSDM minimizes an objective function that corresponds to a Voronoi-based approximation of the overall squared distance function between the surface and the input mesh (SDM). This objective function is a generalization of the one minimized by centroidal Voronoi tessellation, and can be minimized by a quasi-Newton solver. VSDM naturally adapts the orientation of the mesh elements to best approximate the input, without estimating any differential quantities. Therefore, it can be applied to triangle soups or surfaces with degenerate triangles, topological noise and sharp features. Applications of fitting quad meshes and polynomial surfaces to input triangular meshes are demonstrated.     

Multiresolution Isosurface Extraction with Adaptive Skeleton Climbing

An isosurface extraction algorithm which can directly generate multiresolution isosurfaces from volume data is introduced. It generates low resolution isosurfaces, with 4 to 25 times fewer triangles than that generated by marching cubes algorithm, in comparable running times. By climbing from vertices (0-skeleton) to edges (1-skeleton) to faces (2-skeleton), the algorithm constructs boxes which adapt to the geometry of the true isosurface. Unlike previous adaptive marching cubes algorithms, the algorithm does not suffer from the gap-filling problem. Although the triangles in the meshes may not be optimally reduced, it is much faster than postprocessing triangle reduction algorithms. Hence the coarse meshes it produces can be used as the initial starts for the mesh optimization, if mesh optimality is the main concern.     

Obtuse triangle suppression in anisotropic meshes

Anisotropic triangle meshes are used for efficient approximation of surfaces and flow data in finite element analysis, and in these applications it is desirable to have as few obtuse triangles as possible to reduce the discretization error. We present a variational approach to suppressing obtuse triangles in anisotropic meshes. Specifically, we introduce a hexagonal Minkowski metric, which is sensitive to triangle orientation, to give a new formulation of the centroidal Voronoi tessellation (CVT) method. Furthermore, we prove several relevant properties of the CVT method with the newly introduced metric. Experiments show that our algorithm produces anisotropic meshes with much fewer obtuse triangles than using existing methods while maintaining mesh anisotropy.     

Edgebreaker: connectivity compression for triangle meshes

Edgebreaker is a simple scheme for compressing the triangle/vertex incidence graphs (sometimes called connectivity or topology) of three-dimensional triangle meshes. Edgebreaker improves upon the storage required by previously reported schemes, most of which can guarantee only an O(t log(t)) storage cost for the incidence graph of a mesh of t triangles. Edgebreaker requires at most 2t bits for any mesh homeomorphic to a sphere and supports fully general meshes by using additional storage per handle and hole. For large meshes, entropy coding yields less than 1.5 bits per triangle. Edgebreaker's compression and decompression processes perform identical traversals of the mesh from one triangle to an adjacent one. At each stage, compression produces an op-code describing the topological relation between the current triangle and the boundary of the remaining part of the mesh. Decompression uses these op-codes to reconstruct the entire incidence graph. Because Edgebreaker's compression and decompression are independent of the vertex locations, they may be combined with a variety of vertex-compressing techniques that exploit topological information about the mesh to better estimate vertex locations. Edgebreaker may be used to compress the connectivity of an entire mesh bounding a 3D polyhedron or the connectivity of a triangulated surface patch whose boundary need not be encoded. The paper also offers a comparative survey of the rapidly growing field of geometric compression     

一种基于视觉特性的三角网格简化算法

在计算机图形学和几何造型中,实体模型经常采用多边形网格描述,由于绘制时间和存储量与网格的数量成正比,因此复杂的网格模型通常并不实用,从而必须进行模型简化。因为任意多边形可以很方便地被剖分为三角形,由此该文提出一种新的基于视觉特性的三角形网格简化算法。该算法基于人类的视觉特性对三角形网格进行重要性分析,模型细节的选择取决于整个模型对视觉效果的贡献程度,在用户指定的尺度范围内,通过采用收缩三角形以达到迅速简化的目的,以较小的图形生成代价获取丰富的图形视觉效果。实验结果表明,该算法具有实现简单,速度快的特点,能有效地支持细节层次模型的表示。     

Efficiently using connectivity information between triangles in a mesh for real-time rendering

Triangle meshes are the most popular standard model used to represent polygonal surfaces. Drawing these meshes as a set of independent triangles involves sending a vast amount of information to the graphics system. Taking advantage of the connectivity information between the triangles in a mesh dramatically diminishes the amount of information the graphics system must handle. Multiresolution Triangle Strips (MTS) represent a triangle mesh as a collection of multiresolution triangles strips. These strips are the basis of both the storage and the rendering stage. The coherence between the extraction of two levels of detail is used in the model in order to decrease the visualisation time.     

任意三角网格模型体积的快速精确计算方法

三角网格是使用最为广泛的网格模型。提出了一种仅根据三角网格模型的三角面片集合计算模型体积的方法。该方法通过指定投影平面,计算每个三角面片及其在投影平面上的投影所围成的凸五面体的带符号体积（必要时对三角面片进行细分）,整个模型的体积为所有凸五面体带符号体积的代数和。所提出的三角网格模型体积计算方法能实现模型体积的快速准确计算。在大型水电工程施工模拟中施工单元的方量计算测试和不同规模的三角网格模型体积计算测试都证实了该方法的有效性。     

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.     

基于逆3 细分的渐进网格生成算法研究

提出一种基于逆3 细分的渐进网格生成算法,用于解决图形的快速传输和显示问 题。算法的基本思路是：将细密网格通过边折叠操作得到简化网格,以细分极限点逼近原始网 格为准则进行网格调整,采用3 细分得到高密度网格,调整后进行逆3 细分,即逐层次删除 部分顶点,生成用于重构渐进网格模型的基网格,并记录每层删除顶点在采用本层表示时相对 于细分计算位置的几何调整量。3 细分过程中三角片数量增长速度较慢,采用逆3 细分利于 生成多层次的渐进网格,经实例验证,逆3 细分生成渐进网格的效果能满足快速、多分辨率显 示要求。     

Dynamically refining animated triangle meshes for rendering

We present a method to dynamically apply local refinements to an irregular triangle mesh as it deforms in real time. The method increases surface smoothness in regions of high deformation by splitting triangles in a fashion similar to one or two steps of Loop subdivision. The refinement is computed for an arbitrary triangle mesh, and the subdivided triangles are simply passed to the rendering engine, leaving the mesh itself unchanged. The algorithm can thus be easily plugged into existing systems to enhance the visual appearance of animated meshes. The refinement step has very low computational overhead and is easy to implement. We demonstrate the use of the algorithm in a physics-based facial animation system.     

A reliable triangular mesh intersection algorithm and its application in geological modelling

We introduce a reliable intersection algorithm for manifold surface meshes. The proposed algorithm builds conforming surface meshes from a set of intersecting triangulated surfaces. This algorithm effectively handles all degenerate triangle–triangle intersection cases. The key idea of the algorithm is based on an extensive set of triangle–edge intersection cases, combined with an intersection curve tracking method. The intersection operations do not rely on global spatial search operations and no remeshing steps are needed. The intersection curves are introduced into each surface mesh using a unique curve imprinting algorithm. The imprinting algorithm naturally handles degenerate intersection cases of many surfaces at an edge or at a point. The algorithm produces a consistent mesh data structure for subsequent mesh optimization operations. The mesh intersection algorithm is used within a general framework for modelling and meshing of geological formations, which are essential for reliable mathematical modelling of oil reservoirs.     

A parallelized surface extraction algorithm for large binary image data sets based on an adaptive 3D delaunay subdivision strategy

In this paper we describe a novel 3D subdivision strategy to extract the surface of binary image data. This iterative approach generates a series of surface meshes that capture different levels of detail of the underlying structure. At the highest level of detail, the resulting surface mesh generated by our approach uses only about 10% of the triangles in comparison to the marching cube algorithm (MC) even in settings were almost no image noise is present. Our approach also eliminates the so-called "staircase effect" which voxel based algorithms like the MC are likely to show, particularly if non-uniformly sampled images are processed. Finally, we show how the presented algorithm can be parallelized by subdividing 3D image space into rectilinear blocks of subimages. As the algorithm scales very well with an increasing number of processors in a multi-threaded setting, this approach is suited to process large image data sets of several gigabytes. Although the presented work is still computationally more expensive than simple voxel-based algorithms, it produces fewer surface triangles while capturing the same level of detail, is more robust towards image noise and eliminates the above-mentioned "staircase" effect in anisotropic settings. These properties make it particularly useful for biomedical applications, where these conditions are often encountered.     

Efficient Coding of Nontriangular Mesh Connectivity

We describe an efficient algorithm for coding the connectivity information of general polygon meshes. In contrast to most existing algorithms which are suitable only for triangular meshes, and pay a penalty for treatment of nontriangular faces, this algorithm codes the connectivity information in a direct manner. Our treatment of the special case of triangular meshes is shown to be equivalent to the Edgebreaker algorithm. Using our methods, any triangle mesh may be coded in no more than 2 bits/triangle (approximately 4 bits/vertex), a quadrilateral mesh in no more than 3.5 bits/quad (approximately 3.5 bits/vertex), and the most common case of a quad mesh with few triangles in no more than 4 bits/polygon.     

Uniform remeshing with an adaptive domain: a new scheme for view-dependent level-of-detail rendering of meshes

We present a new algorithm for view-dependent level-of-detail rendering of meshes. Not only can it effectively resolve complex geometry features similar to edge collapse-based schemes, but it also produces meshes that modern graphics hardware can render efficiently. This is accomplished through a novel hybrid approach: for each frame, we view-dependently refine the progressive mesh (PM) representation of the original mesh and use the output as the base domain of uniform regular refinements. The algorithm exploits frame-to-frame coherence and only updates portions of the output mesh corresponding to modified domain triangles. The PM representation is built using a custom volume preservation-based error function. A simple k-d tree enhanced jump-and-walk scheme is used to quickly map from the dynamic base domain to the original mesh during regular refinements. In practice, the PM refinement provides a view-optimized base domain for later regular refinements. The regular refinements ensure almost-everywhere regularity of output meshes, allowing optimization for vertex cache coherence and caching of geometry data in high-performance graphics memory. Combined, they also have the effect of allowing our algorithm to operate on uniform clusters of triangles instead of individual ones, reducing CPU workload.