Quadrilateral Mesh Generation Research Articles

A quadrilateral mesh generating method using mean value interpolation

Although commonly used for meshing, sub-mapping method is frequently bothered by its unstable region segmentation process. Although region segmentation can be avoided with the help of recognized models, the existing algorithms of obtaining recognized models are still flawed. In order to obtain accurate recognized models and high meshing quality, a quadrilateral mesh generation method is proposed on basis of mean value interpolation. Firstly, computational coordinates of inner loop vertices are determined by mean value interpolation according to regularization result of outer loop. Secondly, under the barycenter superposition principle, surface’s recognized model is obtained by use of regularization result of inner loops. Finally, facial mesh is generated via solving equations. Experiments are carried out to testify feasibility, advantage and stability of the proposed method. The results manifest that the proposed method is able to guarantee meshing quality and is applicable for quadrilateral mesh generation of multi-loop surfaces.

An automated approach to quadrilateral mesh generation with complex geometric feature constraints

An automated approach to quadrilateral mesh generation with complex internal geometric feature constraints is presented in this paper. It can deal with all kinds of feature constraints such as internal holes, constraint lines, constraint points, density lines and density points, etc., and satisfy special requirements of mesh generation for numerical analysis. The quadrilateral mesh is generated based on the looping algorithm. As the core of the algorithm, the new splitting criteria are put forward to improve the quality and efficiency of mesh generation. The method of dealing with feature constraints is proposed by considering constraint lines and points, density lines and density points as internal holes with zero area. The method for generating boundary elements is also introduced to improve the element quality around the boundary and feature constraints. For the situation in which feature constraints subdivide the domain into sub-domains, an automatic determination method of sub-domain boundaries is presented. An improved looping algorithm is presented for 3D surface meshing with feature constraints. The determination of proper splitting plane and the handling of feature constraints are put forward. The program of quadrilateral mesh generation has been developed based on the method presented in this paper and successfully applied to mesh generation in several engineering fields.

Quadrilateral Mesh Generation with Deferred Constraint Insertion

In this paper, we present a new method for quadrilateral mesh generation in complex 2D domains, based on deferred constraint insertion. Our method is especially designed to handle complex geological cross-sections and multi-fractured media. We first introduce a new algorithm for triangular mesh generation: starting with a initial mesh, in general simple and regular, we adaptively modify it in order to accommodate each constraint, despite its complexity. We then propose a set of heuristics to convert the achieved triangular mesh into a quadrilateral one, pursuing the alignment of elements along constraints. As a result, we achieve a very stable, efficient, good-quality, and automated mesh generator. We demonstrate the robustness of our proposal by showing resulting triangular and quadrilateral meshes for a set of geological domains with complex line constraints.

QMCF: QMorph Cross Field-driven Quad-dominant Meshing Algorithm

We propose a new method for generation of quadrilateral meshes. Our algorithm takes a triangle mesh generated on a computer-aided design surface together with a size field as input. A novel cross field, defined on vertices of the triangle mesh, is derived from both curvature directions and constraints on the boundary. Our algorithm uses a modified QMorph algorithm for quad dominant meshing, to follow size field and to align edges with the cross field previously computed.

Multi-Constrained Quadrilateral Mesh Generation for Ship Assembly

The assembly of ship blocks is achieved through welding. To get a high level of closure accuracy, finite element analysis (FEA) is always needed to predict the welding deformation. However, the fast automatic mesh generation technique during the finite element method (FEM) for the ship assembly is not mature enough yet. Due to the complex ship architecture, during FEA, the model must be built up manually in most cases. This process is complicated and the errors are easy to occur. Consequently, the efficiency of FEA during the ship assembly is highly affected. Automatic mesh generation is a key factor restricting the development of FEM, since the quality and speed of the mesh generation directly influence the accuracy of calculation and the efficiency of analysis. In the field of marine engineering and aerospace engineering, the mesh elements are required to be quadrilateral. However, the technique of the quadrilateral mesh generation is still more difficult and less mature than that of the triangular mesh generation. This work proposed a hybrid mesh generation algorithm, borrowing the advantages from both the quad-morphing algorithm and the paving algorithm as well as considering the factor of multi-constraints. An example case is also given to illustrate the result of this proposed algorithm.

Preserving isotropic element size functions in adaptivity, quadrilateral and hexahedral mesh generation

It is well known that the variations of the element size have to be controlled in order to generate a high-quality mesh. However, it is not enough to limit the gradient of the size function to generate a mesh that correctly preserves the prescribed element size. To address this issue, in this work we define a criterion to assess when an element reproduces a size field. Then, using this criterion, we develop a novel technique to modify the initial size function by solving a non-linear equation. The new size function ensures that the elements will preserve the original size function. Moreover, an approximated method is developed to improve the computational cost of solving the non-linear equation. We use these techniques in two applications. First, we show that we can reduce the number of iterations to converge an adaptive process. Second, we show that quadrilateral and hexahedral meshing algorithms benefit from the new size function since it is not needed to perform a refining process to capture the initial size function.

An Improved Paving Method of Automatic Quadrilateral Mesh Generation

This article describes an improved paving method of automatic quadrilateral mesh generation. Paving, which was first proposed by Blacker and Stephenson [1], is a kind of direct method for generating a quadrilateral mesh and has been widely used since it was presented. This article aims to improve some weaknesses of the traditional paving method by generating high-quality quadrilateral grids without employment of a background mesh. Through efficient intersection resolution and other optimization measures, the improved paving method can generate well-aligned rows of quadrilateral elements almost parallel to the boundary of the domain, automatically and quickly.

Quad‐Mesh Generation and Processing: A Survey

AbstractTriangle 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.

Lloyd’s energy minimization in the L p norm for quadrilateral surface mesh generation

Indirect methods recombine the elements of triangular meshes to produce quadrilaterals. The resulting quadrilaterals are usually randomly oriented, which is not desirable. However, by aligning the vertices of the initial triangular mesh, precisely oriented quads can be produced. Levy’s algorithm is a non-linear optimization procedure that can align points according to a locally defined orientation matrix. It minimizes an energy functional based on the L p distance. The triangulation of a set of vertices smoothed with Levy’s algorithm is mainly composed of right-angled triangles, which is ideal for quad recombination. An implementation of Levy’s algorithm based on numerical integration is presented. The implementation has the advantage of not modifying the edge meshes. It also features automatic calculation of the orientation angle. When used in combination with an indirect recombination algorithm, it can create quads of varying size and orientation. It has been tested on two-dimensional surfaces as well as globally parametrized three-dimensional surfaces. The results demonstrate an increase in the number of nodes having four neighbors and an improvement of the quads quality. The development took place in the framework of the Gmsh free software.

A boundary focused quadrilateral mesh generation algorithm for multi-material structures

This paper describes a new boundary focused mesh generation algorithm. The algorithm produces quadrilateral meshes from images of multi-material structures. The challenge of meshing such images is to create high quality elements which are aligned with complex material boundaries. The approach proposed in this paper uses the following steps: (1) extract boundaries according to pixel colours; (2) smooth the jagged boundaries; (3) generate geodesic isolines aligned with smoothed boundaries; (4) generate a mesh from the boundaries and isolines; (5) optimize the mesh using the “Pisces” pattern (which is introduced in this paper). Application examples are presented to contrast the reliability and effectiveness of the new algorithm with existing approaches.

NURBS based scheme for automatic quadrilateral mesh generation for FE and BEM analysis

In this paper, a Non Uniform Rational B-Spline (NURBS) based approach is proposed to generate structured quadrilateral meshes over three dimensional surfaces. The surfaces to be meshed are defined by NURBS. The surfaces can also have a hole of arbitrary shape. Initially an adaptive subdivision scheme applied to split the surface in parametric domain to match the boundary nodes, and then mesh generation process reduces to the formation of nodes and elements in parametric domain. In order to do that, special care is taken to maintain the continuity of the splitted surfaces. The primary objective of this paper is to recognize the neighbouring surfaces and split automatically to match the boundary points. None of the presently available CAD software has this type of feature. The proposed scheme is applied initially with simply connected surface, and then it is applied for more complicated structures. Finally the proposed method is applied to a part of a ship shaped body consisting with planar and curved surfaces to demonstrate the effectiveness of the proposed algorithm.

Template-based quadrilateral mesh generation from imaging data

This paper describes a novel template-based meshing approach for generating good quality quadrilateral meshes from 2D digital images. This approach builds upon an existing image-based mesh generation technique called Imeshp, which enables us to create a segmented triangle mesh from an image without the need for an image segmentation step. Our approach generates a quadrilateral mesh using an indirect scheme, which converts the segmented triangle mesh created by the initial steps of the Imesh technique into a quadrilateral one. The triangle-to-quadrilateral conversion makes use of template meshes of triangles. To ensure good element quality, the conversion step is followed by a smoothing step, which is based on a new optimization-based procedure. We show several examples of meshes generated by our approach, and present a thorough experimental evaluation of the quality of the meshes given as examples.

Quadrilateral meshes with provable angle bounds

In this paper, we present an algorithm that utilizes a quadtree data structure to construct a quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than $${{18.43}}^{\circ} ({=}\hbox{arctan}(\frac{1}{3}))$$ or greater than $${{171.86}}^{\circ} ({=}{{135}}^{\circ} + 2\hbox{arctan}(\frac{1}{3}))$$ . This is the first known result, to the best of our knowledge, on a direct quadrilateral mesh generation algorithm with a provable guarantee on the angles.

An indirect approach for automatic generation of quadrilateral meshes with arbitrary line constraints

AbstractA new approach to the automatic generation of a quadrilateral mesh with arbitrary line constraints is proposed in this paper. It is an indirect all‐quad mesh generation and presented in the following steps: (1) discretizing the constrained lines within the domain; (2) converting the above domain to a triangular mesh together with the line constraints; (3) transforming the generated triangular mesh with line constraints to an all‐quad mesh through performing an advancing front algorithm from the line constraints, which enables the construction of quadrilaterals layer by layer, and roughly keeps the feature of the initial triangular mesh; (4) optimizing the topology of the quadrilateral mesh to reduce the number of irregular nodes; (5) smoothing the generated mesh toward high‐quality all‐quad mesh generation. Finally, a few application examples are given to demonstrate the reliability and usefulness of the proposed algorithm. Copyright © 2011 John Wiley & Sons, Ltd.

Automated quadrilateral mesh generation for digital image structures

With the development of advanced imaging technology, digital images are widely used. This paper proposes an automatic quadrilateral mesh generation algorithm for multi-colour imaged structures. It takes an original arbitrary digital image as an input for automatic quadrilateral mesh generation, this includes removing the noise, extracting and smoothing the boundary geometries between different colours, and automatic all-quad mesh generation with the above boundaries as constraints. An application example is provided to demonstrate the usefulness and effectiveness of the proposed approach.

Adaptive meshing and analysis using transitional quadrilateral and hexahedral elements

In adaptive finite element analysis, h-type refinement can be achieved basically in two ways: (i) small elements are connected directly to large elements with full compatibility at element interfaces and (ii) transitional elements are employed to link up elements of different sizes. While there is no difficulty in generating gradation triangular and tetrahedral meshes, generation of quadrilateral and hexahedral meshes of varying element sizes without severe element distortion proved to be a formidable task. The use of transitional elements allows meshes to be refined without element distortion, and the price that we have to pay is to develop general and efficient transitional elements in two and three dimensions. Transition elements, which satisfy the patch test, can be formulated by means of the enhanced assumed strain (EAS) method, which are in general more efficient than the incompatible elements. Alternatively, in this paper, we try to develop a series of versatile transition elements based on the hybrid stress approach. Direct designing stress fields for transition elements is just too complicated and especially impractical for 3D transition hexahedral elements. However, we found that the same stress field could be used for transition elements with variable number of nodes. By means of elimination and through numerical studies on some benchmark problems, 7- and 24-mode stress fields are adopted, respectively for 2D quadrilateral and 3D hexahedral hybrid stress transition elements. Strategy for generating refinement transition element meshes will be discussed, and the size of elements generated by the 1-irregular mesh restriction is compared with the predicted element size. The comparison shows that the meshing strategy employed in this study can effectively lead to an optimal mesh whose solution error is smaller than the prescribed one.

A divide-and-conquer approach for automatic polycube map construction

Polycube map is a global cross-surface parameterization technique, where the polycube shape can roughly approximate the geometry of modeled objects while retaining the same topology. The large variation of shape geometry and its complex topological type in real-world applications make it difficult to effectively construct a high-quality polycube that can serve as a good global parametric domain for a given object. In practice, existing polycube map construction algorithms typically require a large amount of user interaction for either pre-constructing the polycubes with great care or interactively specifying the geometric constraints to arrive at the user-satisfied maps. Hence, it is tedious and labor intensive to construct polycube maps for surfaces of complicated geometry and topology. This paper aims to develop an effective method to construct polycube maps for surfaces with complicated topology and geometry. Using our method, users can simply specify how close the target polycube mimics a given shape in a quantitative way. Our algorithm can both construct a similar polycube of high geometric fidelity and compute a high-quality polycube map in an automatic fashion. In addition, our method is theoretically guaranteed to output a one-to-one map. To demonstrate the efficacy of our method, we apply the automatically-constructed polycube maps in a number of computer graphics applications, such as seamless texture tiling, T-spline construction, and quadrilateral mesh generation.

Generation of Quadrilateral Mesh from Discretized Models

Because of the inevitable tedious model repair by using CAD model as the source for mesh generation, an algorithm of generating all-quadrilateral element mesh from discretized models is proposed. By this method, discretized models, such as scattered points or STL file format model, are used as the source for mesh generation, and the original mesh generation paving method is modified to handle discretized models. Several key technologies are presented, the first one is the control of mesh size by using the discretized model as background mesh, the second one is the adjustment of mesh density distribution by mesh refinement and coarsening operation, and the third one is automatic identification of surface features in discretized models and preservation in mesh models. A new method to search intersections between paving boundaries is proposed. The effectiveness of the algorithm and the quality of the mesh generated are demonstrated by using several complex examples.

Development of automatic surface reconstruction technique in reverse engineering

The computer-aided design model reconstruction process is generally very complex, as it requires substantial efforts in planning and editing data points, curves, and surfaces. A novel method is developed in this study for automatic surface reconstruction from a huge number of triangular meshes. The proposed method is mainly composed of the following five steps: mesh simplification, quadrilateral mesh generation, curve net construction, connectivity data preparation, and multiple surfaces fitting with G1 continuity across the boundaries. The first three steps build the boundary curves of the surfaces. The fourth step prepares the data needed for surface fitting, which includes segmented points, continuity conditions on the boundaries, and topological relationship of the data. In the final step, all regions of points are fitted into appropriate surfaces, with the accuracy and smoothness of the surfaces controlled and G1 continuity between the surfaces. A detailed discussion for each of the above algorithms is provided. Successful examples are also presented to demonstrate the feasibility of the proposed method.

Characterization of Tracer Transport in Heterogeneous Fractured Reservoir by a Streamline Approach on Unstructured Grids

This article presents a numerical analysis on anomalous transport behavior in a heterogeneous fractured porous reservoir using streamlines. The authors developed a streamline simulator with a direct quadrilateral mesh generator to investigate the correlated effects of hydrological properties. Quadrilateral grids were made by constructing boundary loops automatically. The mesh generator showed reliable shapes and did not need to construct another control volume for a conventional transport model. Solute was transported using a streamline approach on the irregular grids with various values of permeabilities between matrix and fracture. Breakthrough curve has a skewed characteristic similar at a real heterogeneous medium. The trajectories of streamline, the distribution of pressure, and the skewed breakthrough confirm the applicability of our model at both porous and fractured medium.