水平集网格简化算法在遗址场景中的应用

将水平集方法引入到三维模型网格简化中,构造符号距离函数,函数的零集定义为初始曲面;引入一个能量泛涵,通过对其极小化诱导出一个水平集形式的二阶几何偏微分方程,从而将网格简化过程转化为隐式模型的体素扩散过程。该方法目前已经用于文化遗产数字化的大场景和文物的模型简化中。对水平集网格简化算法和现常用的基于点对收缩的网格简化算法在视觉质量和几何误差方面做了比较和分析,实验表明该方法适用于任意拓扑形状的网格模型,使得模型大规模简化后,在保持较低误差的同时,仍然能够保持相当多的重要几何特征和较好的整体视觉效果。     

Accurate Simplification of Multi‐Chart Textured Models

Scanning and acquisition methods produce highly detailed surface meshes that need multi‐chart parameterizations to reduce stretching and distortion. From these complex shape surfaces, high‐quality approximations are automatically generated by using surface simplification techniques. Multi‐chart textures hinder the quality of the simplification of these techniques for two reasons: either the chart boundaries cannot be simplified leading to a lack of geometric fidelity; or texture distortions and artefacts appear near the simplified boundaries. In this paper, we present an edge‐collapse based simplification method that provides an accurate, low‐resolution approximation from a multi‐chart textured model. For each collapse, the model is reparameterized by local bijective mappings to avoid texture distortions and chart boundary artefacts on the simplified mesh due to the geometry changes. To better apply the appearance attributes and to guarantee geometric fidelity, we drive the simplification process with the quadric error metrics weighted by a local area distortion measure.     

Wavelet-based progressive compression scheme for triangle meshes: wavemesh

We propose a new lossy to lossless progressive compression scheme for triangular meshes, based on a wavelet multiresolution theory for irregular 3D meshes. Although remeshing techniques obtain better compression ratios for geometric compression, this approach can be very effective when one wants to keep the connectivity and geometry of the processed mesh completely unchanged. The simplification is based on the solving of an inverse problem. Optimization of both the connectivity and geometry of the processed mesh improves the approximation quality and the compression ratio of the scheme at each resolution level. We show why this algorithm provides an efficient means of compression for both connectivity and geometry of 3D meshes and it is illustrated by experimental results on various sets of reference meshes, where our algorithm performs better than previously published approaches for both lossless and progressive compression.     

Reconstruction of 3D Object Meshes from Silhouette Images

In this work we propose a method for computing mesh representations of 3D objects reconstructed from a set of silhouette images. Our method is based on the polygonization of volumetric reconstructions by using a modified version of the dual contouring method. In order to apply dual contouring on volumetric reconstruction from silhouettes we devised a method that is able to determine the discrete topology of the surface in relation to the octree cells. We also developed a new scheme for computing hermitian data representing the intersections of conic volumes with the octree cells and their corresponding normals with subpixel accuracy. Due to the discrete and extremely noisy nature of the data used in the reconstruction we had to devise a different criterion for mesh simplification that applies topological consistency tests only when the geometric error measure is beyond a given tolerance. We present results of the application of the proposed method in the extraction of a mesh corresponding to the surface of objects of a real scene.     

Geometric surface mesh optimization

This paper presents a surface mesh optimization method suitable to obtain a geometric finite element mesh, given an initial arbitrary surface triangulation. The first step consists of constructing a geometric support, continuous, associated with the initial surface triangulation, which represents an adequate approximation of the underlying surface geometry. The initial triangulation is then optimized with respect to this geometry as well as to the element shape quality. A specific application of this technique to the geometric mesh simplification is then outlined, which aims at reducing the number of mesh entities while preserving the geometric approximation of the surface. Several examples of surface meshes intended for different application areas emphasize the efficiency of the proposed approach. Received: 11 September 1997 / Accepted: 19 February 1998     

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。     

Enhancing digital documents by including 3D-models

Due to their simplicity, triangle meshes are used to represent geometric objects in many applications. Since the number of triangles often goes beyond the capabilities of computer graphics hardware and the transmission time of such data is often inappropriately high, a large variety of mesh simplification algorithms has been proposed in the last years. In this paper we identify major requirements for the practical usability of general purpose mesh reduction algorithms to enable the integration of triangle meshes into digital documents. The driving idea is to understand mesh reduction algorithms as a software extension to make more complex meshes accessible with limited hardware resources (regarding both transmission and display). We show how these requirements can be efficiently satisfied and discuss implementation aspects in detail. We present a mesh decimation scheme that fulfills these design goals and which has already been evaluated by several users from different application areas. We apply this algorithm to typical mesh data sets to demonstrate its performance.     

Multilevel mesh simplification

The goal of a multilevel simplification method is to produce different levels of refinement of a mesh, reducing the resolution (total number of faces), while preserving the original topology and a good approximation to the original geometry. A new approach to simplification based on the evolution of surfaces under p-Laplacian flow is presented. Such an evolution provides a natural geometric clustering process where the spatial effect of the p-Laplacian allows for identifying suitable regions that need to be simplified. The concrete scheme is a multiresolution framework composed, at each simplification level, of a spatial clustering diffusion flow to determine the potential candidates for deletion, followed by an incremental decimation process to update the mesh vertex locations in order to decrease the overall resolution. Numerical results show the effectiveness of our strategy in multilevel simplification of different models with different complexities, in particular for models characterized by sharp features and flat parts.     

基于逆 Loop 细分的半正则网格简化算法

摘 要：三维网格简化是在保留目标物体几何形状信息的前提下尽量减小精细化三维模型 中的点数和面数的一种操作,对提高三维网格数据的存取和网络传输速度、编辑和渲染效率具 有十分重要的作用。针对大多网格简化算法在简化过程中未考虑网格拓扑结构与视觉质量的问 题,提出了一种基于逆 Loop 细分的半正则网格简化算法。首先根据邻域质心偏移量进行特征 点检测,随后随机选取种子三角形,以边扩展方式获取正则区域并执行逆 Loop 细分进行简化。 最后,以向内分割方式进行边缘拼接,获取最终的简化模型。与经典算法在公开数据集上进行 实验对比,结果表明,该算法能够在简化的同时有效地保持网格特征,尽可能保留与原始网格 一致的规则的拓扑结构,并且在视觉质量上优于边折叠以及聚类简化算法。     

Multi‐Resolution Cloth Simulation

We propose a novel, multi‐resolution method to efficiently perform large‐scale cloth simulation. Our cloth simulation method is based on a triangle‐based energy model constructed from a cloth mesh. We identify that solutions of the linear system of cloth simulation are smooth in certain regions of the cloth mesh and solve the linear system on those regions in a reduced solution space. Then we reconstruct the original solutions by performing a simple interpolation from solutions computed in the reduced space. In order to identify regions where solutions are smooth, we propose simplification metrics that consider stretching, shear, and bending forces, as well as geometric collisions. Our multi‐resolution method can be applied to many existing cloth simulation methods, since our method works on a general linear system. In order to demonstrate benefits of our method, we apply our method into four large‐scale cloth benchmarks that consist of tens or hundreds of thousands of triangles. Because of the reduced computations, we achieve a performance improvement by a factor of up to one order of magnitude, with a little loss of simulation quality.     

一种基于区域分割的几何模型简化方法

根据几何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,提出了一种利用曲度进行区域生长的网格模型区域分割方法,用A型种子或B型种子进行生长,将模型分割为一些区域;在此基础之上,提出了一种基于区域分割的几何模型简化方法,各个区域按照三角形数目的比例进行简化.该方法在保持模型细节特征的基础之上,大大地加快了模型简化的速度;另外还提出了一种累进网格模型的实现方法,实现了具有细节特征的多分辨模型间的层次过渡.实验证明本文所提出的几何模型简化方法加快了网格模型的简化速度,并具有保持模型的三角形网格密度分布的特点,是一种实用、方便和有效的简化方法.     

Simplifying Character Skins with Analytic Error Metrics

Traditionally, levels of detail (LOD) for animated characters are computed from a single pose. Later techniques refined this approach by considering a set of sample poses and evaluating a more representative error metric. A recent approach to the character animation problem, animation space, (AS) provides a framework for measuring error analytically. The work presented here uses the animation-space framework to derive two new techniques to improve the quality of LOD approximations.
First, we use an animation-space distance metric within a progressive mesh-based LOD scheme, giving results that are reasonable across a range of poses, without requiring that the pose space be sampled.
Second, we simplify individual vertices by reducing the number of bones that influence them, using a constrained least-squares optimization. This influence simplification is combined with the progressive mesh to form a single stream of simplifications. Influence simplification reduces the geometric error by up to an order of magnitude, and allows models to be simplified further than is possible with only a progressive mesh.
Quantitative (geometric error metrics) and qualititative (user perceptual) experiments confirm that these new extensions provide significant improvements in quality over traditional, naïve simplification; and while there is naturally some impact on the speed of the off-line simplification process, it is not prohibitive.     

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.     

Adaptive physics based tetrahedral mesh generation using level sets

We present a tetrahedral mesh generation algorithm designed for the Lagrangian simulation of deformable bodies. The algorithm’s input is a level set (i.e., a signed distance function on a Cartesian grid or octree). First a bounding box of the object is covered with a uniform lattice of subdivision-invariant tetrahedra. The level set is then used to guide a red green adaptive subdivision procedure that is based on both the local curvature and the proximity to the object boundary. The final topology is carefully chosen so that the connectivity is suitable for large deformation and the mesh approximates the desired shape. Finally, this candidate mesh is compressed to match the object boundary. To maintain element quality during this compression phase we relax the positions of the nodes using finite elements, masses and springs, or an optimization procedure. The resulting mesh is well suited for simulation since it is highly structured, has topology chosen specifically for large deformations, and is readily refined if required during subsequent simulation. We then use this algorithm to generate meshes for the simulation of skeletal muscle from level set representations of the anatomy. The geometric complexity of biological materials makes it very difficult to generate these models procedurally and as a result we obtain most if not all data from an actual human subject. Our current method involves using voxelized data from the Visible Male [1] to create level set representations of muscle and bone geometries. Given this representation, we use simple level set operations to rebuild and repair errors in the segmented data as well as to smooth aliasing inherent in the voxelized data.     

Coarse-to-fine surface simplification with geometric guarantees

Let PC be a 3D point cloud and ε be a positive value called tolerance. We aim at constructing a triangulated surface S based on a subset PCU of PC such that all the points in PCL = PC ∖ PCU are at distance at most ε from a facet of S . (PCU and PCL respectively stand for Point Cloud Used and Point Cloud Left .) We call this problem simplification with geometric guarantees.
This paper presents a new framework to simplify with geometric guarantees. The approach relies on two main ingredients. First an oracle providing information on the surface being reconstructed even though the triangulated surface itself has not been computed. Second, a reconstruction algorithm providing incremental updates of the reconstructed surface, as well as a fast point-to-triangles distance computation. The oracle is used to guess a subset of the point cloud from which a triangulated surface is reconstructed. It relies on an implicit surface the triangulated surface is an approximation of, and is therefore available before the triangle mesh. The point-to-triangles distance computation and the local updates are then invoked to insert new vertices until the tolerance is met.
We also present a detailed experimental study which shows the efficiency of the simplification process both in terms of simplification rate and running time.
To the best of our knowledge, this algorithm is the first one performing coarse-to-fine surface simplification with geometric guarantees.     

Shape‐adaptive 3‐D mesh simplification based on local optimality measurement

Mesh simplification is the process of reducing the number of triangles in a mesh representation of object surface. For a given level of detail or error tolerance, the conventional mesh simplification algorithms maximize the edge length globally, without explicitly considering local object shape. In this paper, we present a shape‐adaptive mesh simplification algorithm that locally maximizes edge length, depending on local shape. The proposed algorithm achieves shape‐adaptive simplification by iteratively maximizing edges between vertices, based on comparison with the ‘optimal’ edge lengths derived from local directional curvatures for a given error tolerance. Edge‐based processing facilitates the local shape adaptation and preserves sharp features. Experimental results demonstrate the efficacy of the proposed algorithm, by showing good visual quality and extremely small approximation error. Copyright © 2003 John Wiley & Sons, Ltd.     

Topology-preserving simplification of 2D nonmanifold meshes with embedded structures

Mesh simplification has received tremendous attention over the years. Most of the previous work in this area deals with a proper choice of error measures to guide the simplification. Preserving the topological characteristics of the mesh and possibly of data attached to the mesh is a more recent topic and the subject of this paper. We introduce a new topology-preserving simplification algorithm for triangular meshes, possibly nonmanifold, with embedded polylines. In this context, embedded means that the edges of the polylines are also edges of the mesh. The paper introduces a robust test to detect if the collapse of an edge in the mesh modifies either the topology of the mesh or the topology of the embedded polylines. This validity test is derived using combinatorial topology results. More precisely, we define a so-called extended complex from the input mesh and the embedded polylines. We show that if an edge collapse of the mesh preserves the topology of this extended complex, then it also preserves both the topology of the mesh and the embedded polylines. Our validity test can be used for any 2-complex mesh, including nonmanifold triangular meshes, and can be combined with any previously introduced error measure. Implementation of this validity test is described. We demonstrate the power and versatility of our method with scientific data sets from neuroscience, geology, and CAD/CAM models from mechanical engineering.     

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。     

Gradient and curvature approximation in data–dependent surface simplification

In Scientific Visualization, it is often necessary to represent surfaces with data components attached to them, e.g. cutting surfaces or isosurfaces in CFD data sets with multiple data components. They can contain a vast number of very small triangles. To make the interactive visual analysis of large data sets still feasible, surface simplification algorithms are used to reduce the number of triangles significantly. The order of triangles to be removed iteratively is determined by a priority criterion taking into account as well geometric properties of the surface as irregularities of the data components attached to it. In the present paper, different gradient and curvature approximation schemes are described and compared with respect to efficiency, robustness, and their usefulness as priority criteria in our surface simplification method. Received: 30 June 1998 / Accepted: 9 July 1999