全局各向异性四边形主导网格重建方法

四边形网格的结构特点要求网格单元满足全局一致性,难以取得网格质量与表达效率之间的平衡.为此,提出一种基于全局的各向异性四边形主导网格重建方法,可生成网格质量好且冗余程度低的四边形网格.重建过程以主曲率线为基本采样单元,首先计算模型表面的主曲率场并对主曲率场积分,得到密集的主曲率线采样;再根据贪心算法,利用几何形体自身的各向异性找出冗余度最高的主曲率线并予以删除;如此循环,直至达到理想的采样密度.该重建方法适用于任意拓扑网格模型,所得到的各向异性四边形主导网格在网格模型分辨率下降时,由于始终保留重要主曲率线,从而可以更好地保持模型特征.同时,在基于贪心算法的渐进式主曲率线删除过程中,可产生分辨率连续可调的四边形主导网格.     

基于曲率流的四边形主导网格的光顺方法

网格模型是计算机图形学和数字几何处理中运用最为广泛的三维几何表达方式.四边网格(以四边形为主的网格)由于其符合人们对几何形状变化的自然感知,在表示三维几何上有其独有的优势,并且可以更为直接地应用在几何造型、细分曲面、建筑设计等方面.文中针对四边形主导网格含有噪声的情况,设计了一种基于表面微分属性的光顺方法,该方法具有易实现、计算效率高的特点.基于曲率流的几何扩散可以有效地保持原网格的几何特征,同时还针对四边形主导网格的T-顶点进行了特殊处理.     

Generation of bi-monotone patches from quadrilateral mesh for reverse engineering

Thanks to recent improvements, computational methods can now be used to convert triangular meshes into quadrilateral meshes so that the quadrilateral elements capture well the principal curvature directional fields of surfaces and intrinsically have surface parametric values. In this study, a quadrilateral mesh generated using the mixed integer quadrangulation technique of Bommes et al. is used for input. We first segment a quadrilateral mesh into four-sided patches. The feature curves inside these patches are then detected and are constrained to act as the patch boundaries. Finally, the patch configuration is improved to generate large patches. The proposed method produces bi-monotone patches, which are appropriate for use in reverse engineering to capture the surface details of an object. A shape control parameter that can be adjusted by the user during the patch generation process is also provided to support the creation of patches with good bi-monotone shapes. This study mainly targets shape models of mechanical parts consisting of major smooth surfaces with feature curves between them.     

Feature aligned quad dominant remeshing using iterative local updates

In this paper we present a new algorithm which turns an unstructured triangle mesh into a quad dominant mesh with edges well aligned to the principal directions of the underlying surface. Instead of computing a globally smooth parameterization or integrating curvature lines along a tangent vector field, we simply apply an iterative relaxation scheme which incrementally aligns the mesh edges to the principal directions. We further obtain the quad dominant mesh by dropping the not-aligned diagonal edges from the triangle mesh. A post-processing stage is introduced to further improve the results. The major advantage of our algorithm is its conceptual simplicity since it is merely based on elementary mesh operations such as edge collapse, flip, and split. Various results are presented in the paper; they show a good alignment to surface features and rather uniform distribution of mesh vertices. This makes them well suited, e.g., as Catmull-Clark Subdivision control meshes.     

Surface Fairing towards Regular Principal Curvature Line Networks

Freeform surfaces whose principal curvature line network is regularly distributed, are essential to many real applications like CAD modeling, architecture design, and industrial fabrication. However, most designed surfaces do not hold this nice property because it is hard to enforce such constraints in the design process. In this paper, we present a novel method for surface fairing which takes a regular distribution of the principal curvature line network on a surface as an objective. Our method first removes the high‐frequency signals from the curvature tensor field of an input freeform surface by a novel rolling guidance tensor filter, which results in a more regular and smooth curvature tensor field, then deforms the input surface to match the smoothed field as much as possible. As an application, we solve the problem of approximating freeform surfaces with regular principal curvature line networks, discretized by quadrilateral meshes. By introducing the circular or conical conditions on the quadrilateral mesh to guarantee the existence of discrete principal curvature line networks, and minimizing the approximate error to the original surface and improving the fairness of the quad mesh, we obtain a regular discrete principal curvature line network that approximates the original surface. We evaluate the efficacy of our method on various freeform surfaces and demonstrate the superiority of the rolling guidance tensor filter over other tensor smoothing techniques. We also utilize our method to generate high‐quality circular/conical meshes for architecture design and cyclide spline surfaces for CAD modeling.     

Anisotropic Strain Limiting for Quadrilateral and Triangular Cloth Meshes

The cloth simulation systems often suffer from excessive extension on the polygonal mesh, so an additional strain‐limiting process is typically used as a remedy in the simulation pipeline. A cloth model can be discretized as either a quadrilateral mesh or a triangular mesh, and their strains are measured differently. The edge‐based strain‐limiting method for a quadrilateral mesh creates anisotropic behaviour by nature, as discretization usually aligns the edges along the warp and weft directions. We improve this anisotropic technique by replacing the traditionally used equality constraints with inequality ones in the mathematical optimization, and achieve faster convergence. For a triangular mesh, the state‐of‐the‐art technique measures and constrains the strains along the two principal (and constantly changing) directions in a triangle, resulting in an isotropic behaviour which prohibits shearing. Based on the framework of inequality‐constrained optimization, we propose a warp and weft strain‐limiting formulation. This anisotropic model is more appropriate for textile materials that do not exhibit isotropic strain behaviour.     

隐式曲面重新多边形化

首先用Bloomenthal的多边形化算法生成一个粗糙的初始网格;然后在初始网格上分布若干个新顶点,新顶点可以均匀分布,也可以按曲率分布;再把初始网格上的老顶点和新顶点连接起来,生成一个中间网格,从中间网格上删除初始网格上的老顶点,得到重新多边形化的网格;最后细分这个网格．实验结果表明：该算法可以生成近似等边的、大小由曲率指导的三角网格．     

QuadCover - Surface Parameterization using Branched Coverings

We introduce an algorithm for the automatic computation of global parameterizations on arbitrary simplicial 2-manifolds, whose parameter lines are guided by a given frame field, for example, by principal curvature frames. The parameter lines are globally continuous and allow a remeshing of the surface into quadrilaterals. The algorithm converts a given frame field into a single vector field on a branched covering of the 2-manifold and generates an integrable vector field by a Hodge decomposition on the covering space. Except for an optional smoothing and alignment of the initial frame field, the algorithm is fully automatic and generates high quality quadrilateral meshes.     

Feature Sensitive Remeshing

Remeshing artifacts are a fundamental problem when converting a given geometry into a triangle mesh. We propose a new remeshing technique that is sensitive to features. First, the resolution of the mesh is iteratively adapted by a global restructuring process which additionally optimizes the connectivity. Then a particle system approach evenly distributes the vertices across the original geometry. To exactly find the features we extend this relaxation procedure by an effective mechanism to attract the vertices to feature edges. The attracting force is imposed by means of a hierarchical curvature field and does not require any thresholding parameters to classify the features.     

Motorcycle graph enumeration from quadrilateral meshes for reverse engineering

Recently proposed quad-meshing techniques allow the generation of high-quality semi-regular quadrilateral meshes. This paper outlines the generation of quadrilateral segments using such meshes. Quadrilateral segments are advantageous in reverse engineering because they do not require surface trimming or surface parameterization. The motorcycle graph algorithm of Eppstein et al. produces the motorcycle graph of a given quadrilateral mesh consisting of quadrilateral segments. These graphs are preferable to base complexes, because the mesh can be represented with a smaller number of segments, as T-joints (where the intersection of two neighboring segments does not involve the whole edge or the vertex) are allowed in quadrilateral segmentation.The proposed approach in this study enumerates all motorcycle graphs of a given quadrilateral mesh and optimum graph for reverse engineering is then selected. Due to the high computational cost of enumerating all these graphs, the mesh is cut into several sub-meshes whose motorcycle graphs are enumerated separately. The optimum graph is then selected based on a cost function that produces low values for graphs whose edges trace a large number of highly curved regions in the model. By applying several successive enumeration steps for each sub-mesh, a motorcycle graph for the given mesh is found. We also outline a method for the extraction of feature curves (sets of highly curved edges) and their integration into the proposed algorithm. Quadrilateral segments generated using the proposed techniques are validated by B-spline surfaces.     

Centroidal Voronoi diagrams for isotropic surface remeshing

This paper proposes a new method for isotropic remeshing of triangulated surface meshes. Given a triangulated surface mesh to be resampled and a user-specified density function defined over it, we first distribute the desired number of samples by generalizing error diffusion, commonly used in image halftoning, to work directly on mesh triangles and feature edges. We then use the resulting sampling as an initial configuration for building a weighted centroidal Voronoi diagram in a conformal parameter space, where the specified density function is used for weighting. We finally create the mesh by lifting the corresponding constrained Delaunay triangulation from parameter space. A precise control over the sampling is obtained through a flexible design of the density function, the latter being possibly low-pass filtered to obtain a smoother gradation. We demonstrate the versatility of our approach through various remeshing examples.     

Quad‐Mesh Generation and Processing: A Survey

Triangle meshes have been nearly ubiquitous in computer graphics, and a large body of data structures and geometry processing algorithms based on them has been developed in the literature. At the same time, quadrilateral meshes, especially semi‐regular ones, have advantages for many applications, and significant progress was made in quadrilateral mesh generation and processing during the last several years. In this survey we discuss the advantages and problems of techniques operating on quadrilateral meshes, including surface analysis and mesh quality, simplification, adaptive refinement, alignment with features, parametrisation and remeshing.     

Improving surface meshing from discrete data by feature recognition

In this paper, we propose a method to identify, on a mesh, geometric primitives commonly used in mechanical parts (plane, sphere, cylinder, torus, cone) in order to improve the quality of the surface remeshing. We have already presented techniques to adapt an existing surface mesh based on a mesh-free technique denoted as diffuse interpolation. In this approach, a secondary local geometrical model is built from the mesh. From this model, principal curvatures are calculated and the type of surface can be determined from the computation of the curvatures. Some of the concepts presented here are original while others have been adapted from techniques used in reverse engineering. Our approach is not limited to feature recognition on meshes but has been extended to a set of points.     

车身冲压模型腔表面四边形网格的局部粗化

给定一车身冲压模型腔表面上结构化的四边形网格，通过单元合并对网格进行自动的粗化，其目的在于简化冲压仿真模型，提高仿真计算速度，首先，根据单元节点曲率半径的分布，搜寻出满足单元合并条件的初始四边形区域，接头，判断初始合交区域的边界过渡条件，最后，进行单合并，冲压成型仿真应用实例证明，文中算法既提高了仿真速度，又保持了仿真精度，该算法可以推广到任意曲面结构化四边形网格的局部粗化问题。     

An effective quad-dominant meshing method for unorganized point clouds

To perform quad meshing on raw point clouds, existing algorithms usually require a time-consuming parameterization or Voronoi space partition process. In this paper, we propose an effective method to generate quad-dominant meshes directly from unorganized point clouds. In the proposed method, we first apply Marinov’s curvature tensor optimization to the input point cloud to reduce the umbilical regions in order to obtain a smooth curvature tensor. We then propose an efficient marching scheme to extract the curvature lines with controllable density from the point cloud. Finally, we apply a specialized K-Dimension (KD) tree structure, which converts the nearest neighbor searching problem into a sorting problem, to efficiently estimate the intersections of curvature lines and recover the topology of the quad-dominant meshes. We have tested the proposed method on different point clouds. Our results show that the proposed method produces good quality meshes with high computational efficiency and low memory requirement.     

四边形网格间接生成方法

研究了基于背景三角网格的四边形网格间接生成算法,并针对三角形合并过程中容易残留三角形的缺陷提出了确定侧边的详细算法,该算法主要是依据背景三角网格中边的位置和前沿边的情形,通过背景三角网格中已存在的边、边交换或边分割确定侧边,以避免在三角形合并过程中残留三角形单元。最后给出实例验证了算法的有效性。     

Direct quad-dominant meshing of point cloud via global parameterization

In this paper, we present a new algorithm for quad-dominant meshing of unorganized point clouds based on periodic global parameterization. Our meshing method is guided by principal directions so as to preserve the intrinsic geometric properties. We use local Delaunay triangulation to smooth the initial principal directions and adapt the global parameterization to point clouds. By optimizing the fairness measure we can find the two scalar functions whose gradients best align with the guided principal directions. To handle the redundant vertices in the iso-lines due to overlapped triangles, an approach is specially designed to clean the iso-lines. Our approach is fully automatic and applicable to a surface of arbitrary genus. We also show an application of our method in curve skeleton extraction from incomplete point cloud data.     

Ridge extraction and its application to surface meshing

Geometrical feature lines, such as ${{\mathcal{C}}}^1Geometrical feature lines, such as -discontinuity lines, lines of curvature, ridges, asymptotic lines, etc., provide useful information about the surface geometry. The inclusion of these lines into a surface mesh contributes to improving the quality of the geometrical approximation, independently from the element size. In particular, if the element size is locally large with respect to the minimal radius of curvature, then the geometrical approximation of the surface will generally be poor. In this case, the presence of ridges in the mesh improves the geometrical approximation. This paper proposes a new method to extract the extremal graph whose graph nodes are the umbilics and the extremal points, and edges are extremal lines. A function is also introduced to classify the extremal lines to be able to select the ridges from a parametric surface. The resulting graph of ridges is then simplified and integrated as a constraint in a classical surface mesh generation via an indirect approach. A numerical example will illustrate the pertinence of this method.

Boris Clémen?onEmail:

     

Perceptual-saliency extremum lines for 3D shape illustration

Owing to their efficiency for conveying perceptual information of the underlying shape and their pleasing perceiving in visual aesthetics experience, line drawings are now becoming a widely used technique for illustrating 3D shapes. Using a center-surrounding bilateral filter operator on Gaussian-weighted average of local projection height between mesh vertices and their neighbors, a new perceptual-saliency measure which can depict surface salient features, is proposed in this paper. Due to the definition of perceptual-saliency measure, our perceptual-saliency extremum lines can be considered as the ridge-valley lines of perceptual-saliency measure along the principal curvature directions on triangular meshes. The experimental results demonstrate that these extremum lines effectively capture and depict 3D shape information visually, especially for archaeological artifacts.     

PowerRTF: Power Diagram based Restricted Tangent Face for Surface Remeshing

Triangular meshes of superior quality are important for geometric processing in practical applications. Existing approximative CVT-based remeshing methodology uses planar polygonal facets to fit the original surface, simplifying the computational complexity. However, they usually do not consider surface curvature. Topological errors and outliers can also occur in the close sheet surface remeshing, resulting in wrong meshes. With this regard, we present a novel method named PowerRTF, an extension of the restricted tangent face (RTF) in conjunction with the power diagram, to better approximate the original surface with curvature adaption. The idea is to introduce a weight property to each sample point and compute the power diagram on the tangent face to produce area-controlled polygonal facets. Based on this, we impose the variable-capacity constraint and centroid constraint to the PowerRTF, providing the trade-off between mesh quality and computational efficiency. Moreover, we apply a normal verification-based inverse side point culling method to address the topological errors and outliers in close sheet surface remeshing. Our method independently computes and optimizes the PowerRTF per sample point, which is efficiently implemented in parallel on the GPU. Experimental results demonstrate the effectiveness, flexibility, and efficiency of our method.