基于圆形参数域和重要性采样的三维模型网格重建

给出了一个基于参数化和重要性采样的网格重建算法.算法搜索一条切线将三维模型表面切分成一片碟形表面,并将其参数化到二维单位圆中.根据模型的曲率信息和参数化的扭曲度生成一张控制图.利用蓝噪声采样算法对用控制图调制后的采样密度采样得到离散采样点.通过对采样点进行平面三角化并将其映射回三维空间实现了三维网格重建.实验证明,该方法有效地改善了参数化的扭曲度,并能得到具有自适应性的高度规则网格.     

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.     

Isotropic Surface Remeshing Using Constrained Centroidal Delaunay Mesh

We develop a novel isotropic remeshing method based on constrained centroidal Delaunay mesh (CCDM), a generalization of centroidal patch triangulation from 2D to mesh surface. Our method starts with resampling an input mesh with a vertex distribution according to a user‐defined density function. The initial remeshing result is then progressively optimized by alternatively recovering the Delaunay mesh and moving each vertex to the centroid of its 1‐ring neighborhood. The key to making such simple iterations work is an efficient optimization framework that combines both local and global optimization methods. Our method is parameterization‐free, thus avoiding the metric distortion introduced by parameterization, and generating more well‐shaped triangles. Our method guarantees that the topology of surface is preserved without requiring geodesic information. We conduct various experiments to demonstrate the simplicity, efficacy, and robustness of the presented method.     

Surface remeshing in arbitrary codimensions

We present a method for remeshing surfaces that is both general and efficient. Existing efficient methods are restrictive in the type of remeshings they produce, while methods that are able to produce general types of remeshings are generally based on iteration, which prevents them from producing remeshes at interactive rates. In our method, the input surface is directly mapped to an arbitrary (possibly high-dimensional) range space, and uniformly remeshed in this space. Because the mesh is uniform in the range space, all the quantities encoded in the mapping are bounded, resulting in a mesh that is simultaneously adapted to all criteria encoded in the map, and thus we can obtain remeshings of arbitrary characteristics. Because the core operation is a uniform remeshing of a surface embedded in range space, and this operation is direct and local, this remeshing is efficient and can run at interactive rates.     

Vertex location optimisation for improved remeshing

Remeshing aims to produce a more regular mesh from a given input mesh, while representing the original geometry as accurately as possible. Many existing remeshing methods focus on where to place new mesh vertices; these samples are placed exactly on the input mesh. However, considering the output mesh as a piecewise linear approximation of some geometry, this simple scheme leads to significant systematic error in non-planar regions. Here, we use parameterised meshes and the recent mathematical development of orthogonal approximation using Sobolev-type inner products to develop a novel sampling scheme which allows vertices to lie in space near the input surface, rather than exactly on it. The algorithm requires little extra computational effort and can be readily incorporated into many remeshing approaches. Experimental results show that on average, approximation error can be reduced by 40% with the same number of vertices.     

Direct (Re)Meshing for Efficient Surface Processing

We propose a novel surface remeshing algorithm. While many remeshing algorithms are based on global parametrization or local mesh optimization, our algorithm is closely related to surface reconstruction techniques and it requires no explicit parameterization. Our approach is based on the advancing‐front paradigm, and it can be used to both incrementally remesh the complete surface, or simply to remesh a portion of it with a high‐quality mesh. It is accurate, fast, robust, and suitable for use with interactive mesh processing applications that require local remeshing. We show a number of applications, including matching the resolution of meshes when doing Boolean operations such as unions and intersections. We also show how to adapt the algorithm to blend and merge mixed‐mode objects — for example, to compute the union of a point‐set surface and a triangle mesh.     

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.     

Geodesic Polar Coordinates on Polygonal Meshes

Geodesic Polar Coordinates (GPCs) on a smooth surface S are local surface coordinates that relates a surface point to a planar parameter point by the length and direction of a corresponding geodesic curve onS . They are intrinsic to the surface and represent a natural local parameterization with useful properties. We present a simple and efficient algorithm to approximate GPCs on both triangle and general polygonal meshes. Our approach, named DGPC, is based on extending an existing algorithm for computing geodesic distance. We compare our approach with previous methods, both with respect to efficiency, accuracy and visual qualities when used for local mesh texturing. As a further application we show how the resulting coordinates can be used for vector space methods like local remeshing at interactive frame‐rates even for large meshes.     

Polygonal surface remeshing with Delaunay refinement

Polygonal meshes are used to model smooth surfaces in many applications. Often these meshes need to be remeshed for improving the quality, density or gradedness. We apply the Delaunay refinement paradigm to design a provable algorithm for isotropic remeshing of a polygonal mesh that approximates a smooth surface. The proofs provide new insights and our experimental results corroborate the theory.     

Optimal parametrizations for surface remeshing

We present different linear parametrization techniques for the purpose of surface remeshing: the energy minimizing harmonic map, the convex map, and the least square conformal map. The implementation of those mappings as well as the associated boundary conditions is presented in a unified manner and the issues of triangle flipping and folding that may arise with discrete linear mappings are discussed. We explore the optimality of these parametrizations for surface remeshing by applying several classical 2D meshing algorithms in the parametric space and by comparing the quality of the generated elements. We present various examples that permit to draw guidelines that a user can follow in choosing the best parametrization scheme for a specific topology, geometry, and characteristics of the target output mesh.     

基于三角块的曲面纹理合成

根据曲面网格上的切向矢量场,采用广度优先搜索策略从样本纹理空间中为每个三角面片映射纹理面片,直至完全覆盖整个网格．在搜索和映射过程中,首先使网格上相邻三角面片的纹理有最小的匹配误差;然后对相邻的三角面片纹理使用图的分割方法拼接纹理,得到曲面上连续的合成纹理;最后压缩存储合成的三角面片纹理．该算法适用于多种类型的样本纹理和任意的三角化曲面．     

Approximating isosurfaces by guaranteed-quality triangular meshes

We describe a new method for approximating an implicit surface F by a piecewise-flat triangulated surface whose triangles are as close as possible to equilateral. The main advantage is improved mesh quality which is guaranteed for smooth surfaces. The GradNormal algorithm generates a triangular mesh that gives a piecewise-differentiable approximation of F, with angles between 35.2 and 101.5 degrees. As the mesh size approaches 0, the mesh converges to F through surfaces that are isotopic to F.     

Constructing hierarchies for triangle meshes

We present a method to produce a hierarchy of triangle meshes that can be used to blend different levels of detail in a smooth fashion. The algorithm produces a sequence of meshes M₀, M₁, M ₂..., M_n, where each mesh M_i can be transformed to mesh M_i+1 through a set of triangle-collapse operations. For each triangle, a function is generated that approximates the underlying surface in the area of the triangle, and this function serves as a basis for assigning a weight to the triangle in the ordering operation and for supplying the points to which the triangles are collapsed. The algorithm produces a limited number of intermediate meshes by selecting, at each step, a number of triangles that can be collapsed simultaneously. This technique allows us to view a triangulated surface model at varying levels of detail while insuring that the simplified mesh approximates the original surface well     

Perceptually guided polygon reduction

The properties of the human visual system are taken into account, along with the geometric aspects of an object, in a new surface remeshing algorithm and a new mesh simplification algorithm. Both algorithms have a preprocessing step and are followed by the remeshing or mesh simplification steps. The preprocessing step computes an importance map that indicates the visual masking potential of the visual patterns on the surface. The importance map is then used to guide the remeshing or mesh simplification algorithms. Two different methods are proposed for computing an importance map that indicates the masking potential of the visual patterns on the surface. The first one is based on the Sarnoff visual discrimination metric, and the second one is inspired by the visual masking tool available in the current JPEG2000 standard. Given an importance map, the surface remeshing algorithm automatically distributes few samples to surface regions with strong visual masking properties due to surface texturing, lighting variations, bump mapping, surface reflectance and inter-reflections. Similarly, the mesh simplification algorithm simplifies more aggressively where the light field of an object can hide more geometric artifacts.     

Out-of-Core remeshing of large polygonal meshes

We propose an out-of-core method for creating semi-regular surface representations from large input surface meshes. Our approach is based on a streaming implementation of the MAPS remesher of Lee et al. [18]. Our remeshing procedure consists of two stages. First, a simplification process is used to obtain the base domain. During simplification, we maintain the mapping information between the input and the simplified meshes. The second stage of remeshing uses the mapping information to produce samples of the output semi-regular mesh. The out-of-core operation of our method is enabled by the synchronous streaming of a simplified mesh and the mapping information stored at the original vertices. The synchronicity of two streaming buffers is maintained using a specially designed write strategy for each buffer. Experimental results demonstrate the remeshing performance of the proposed method, as well as other applications that use the created mapping between the simplified and the original surface representations.     

Retiling scheme: a novel approach of direct anisotropic quad-dominant remeshing

Remeshing has been an active research topic in Digital Geometry Processing. In this paper, a novel approach of direct anisotropic quad-dominant remeshing is proposed. We apply the retiling method to the particular problem of quad-dominant remeshing. Compared with other methods, this method can simply partition the surface of an original triangular mesh into connected quads with the mesh edges aligning to the principal directions. The first step in this method is to estimate and smooth the curvature tensor field of the surface at the vertices, and then the quad-dominant mesh is obtained by retiling the quad surface so that quadrilateral edges are parallel to the local principal curvature directions. In addition, to preserve the sharp feature information during remeshing processes, the feature lines can be extracted using mesh segmentation method, and the intersections between the feature lines and the orthogonal planes can be found during the process of retiling. A feature fusion process is presented to join the feature edges and feature points into the quad-dominant mesh. The experiment results show that this new remeshing method is simple and easy to implement. The resolution of the quadrilateral mesh can be controlled during the remeshing. It is applicable to arbitrary genus meshes and can generate high-quality quad-dominant mesh.     

Geodesic Remeshing Using Front Propagation

In this paper, we propose a complete framework for 3D geometry modeling and processing that uses only fast geodesic computations. The basic building block for these techniques is a novel greedy algorithm to perform a uniform or adaptive remeshing of a triangulated surface. Our other contributions include a parameterization scheme based on barycentric coordinates, an intrinsic algorithm for computing geodesic centroidal tessellations, and a fast and robust method to flatten a genus-0 surface patch. On large meshes (more than 500,000 vertices), our techniques speed up computation by over one order of magnitude in comparison to classical remeshing and parameterization methods. Our methods are easy to implement and do not need multilevel solvers to handle complex models that may contain poorly shaped triangles.     

离散曲面的近似Poisson盘采样

Poisson盘采样作为计算机图形学的一个重要课题,在重网格化、过程纹理、物体分布、光照计算等方面都有重要应用.虽然最近几年对于2维平面Poisson盘采样的研究比较密集,但是直接对于2维流形表面上的Poisson盘采样的研究却比较少.在本文中,我们提出了一种可以直接在Mesh表面生成近似Poisson盘分布的方法.此方法实现简单,同时可以通过简单修改适用于保特征的采样和自适应采样.文中引入了张量投票的方法来实现特征识别和自适应采样半径的计算,并给出了采样后的重网格化结果,作为此算法的一个后期应用.通过大量实例表明,本文方法快速、鲁棒、适用广泛.     

A robust high-resolution details preserving denoising algorithm for meshes

Poisson disk sampling has been widely used in many applications such as remeshing, procedural texturing, object distribution, illumination, etc. While 2D Poisson disk sampling is intensively studied in recent years, direct Poisson disk sampling on 2-manifold surface is rarely covered. In this paper, we present a novel framework which generates approximate Poisson disk distribution directly on mesh, a discrete representation of 2-manifold surfaces. Our framework is easy to implement and provides extra flexibility to specified sampling issues like feature-preserving sampling and adaptive sampling. We integrate the tensor voting method into feature detection and adaptive sample radius calculation. Remeshing as a special downstream application is also addressed. According to our experiment results, our framework is efficient, robust, and widely applicable.     

Field‐Aligned Isotropic Surface Remeshing

We present a novel isotropic surface remeshing algorithm that automatically aligns the mesh edges with an underlying directional field. The alignment is achieved by minimizing an energy function that combines both centroidal Voronoi tessellation (CVT) and the penalty enforced by a six‐way rotational symmetry field. The CVT term ensures uniform distribution of the vertices and high remeshing quality, and the field constraint enforces the directional alignment of the edges. Experimental results show that the proposed approach has the advantages of isotropic and field‐aligned remeshing. Our algorithm is superior to the representative state‐of‐the‐art approaches in various aspects.