All-quadrilateral Mesh Research Articles

Feature-preserving quadrilateral mesh Boolean operation with cross-field guided layout blending

Compared to triangular meshes, high-quality quadrilateral meshes offer significant advantages in the field of simulation. However, generating high-quality quadrilateral meshes has always been a challenging task. By synthesizing high-quality quadrilateral meshes based on existing ones through Boolean operations such as mesh intersection, union, and difference, the automation level of quadrilateral mesh modeling can be improved. This significantly reduces modeling time. We propose a feature-preserving quadrilateral mesh Boolean operation method that can generate high-quality all-quadrilateral meshes through Boolean operations while preserving the geometric features and shape of the original mesh. Our method, guided by cross-field techniques, aligns mesh faces with geometric features of the model and maximally preserves the original mesh's geometric shape and layout. Compared to traditional quadrilateral mesh generation methods, our approach demonstrates higher efficiency, offering a substantial improvement to the pipeline of mesh-based modeling tools.

An algorithm for decomposition of sub-domains and quadrilateral mesh generation with line constraints

The technique for quadrilateral mesh generation on arbitrary 2-D domain has been quite mature; however, the existing methods and software can not directly deal with mesh generation with internal line constraints. In flood analysis and other analysis, the analysis models often contain a large number of constraint lines. In mesh generation, the sides of elements besides constraint lines must be attached to constraint lines, so that boundary conditions can be defined on these constraint lines. In this paper, a general method for automatic quadrilateral mesh generation with internal line constraints is presented. The mesh generation process is mainly divided into two stages, i.e. the automatic decomposition of sub-domains and quadrilateral mesh generation in each sub-domain. The sub-domains enclosed by constraint lines and boundaries are determined automatically with the proposal algorithm in this paper. Then nodes are generated on each edge of sub-domains based on mesh size requirements. By solving an integer linear programming problem, the number of nodes on each edge is adjusted automatically, so that the total number of boundary nodes in each sub-domain is even, satisfying the necessary condition for generating all-quadrilateral mesh. For free constraint lines in each sub-domain, the method of regarding constraint lines as holes with zero area is proposed, so that constraint lines can be treated as internal boundaries. The merging method of constraint lines and outer boundary is given, which can deal with all possible distribution of constraint lines and has generality. The examples of mesh generation with a large number of constraint lines are given to demonstrate the reliability of proposed method.

A new quadtree-based approach for automatic quadrilateral mesh generation

In this paper, we present a new method for adaptive all-quadrilateral mesh generation for two-dimensional domains, including domains modeled by constraints with complex geometry or with varying scales. The method subdivides the domain's bounding box using a new extended quadtree scheme. In this subdivision process, the quadtree node corners are moved onto the geometrical constraints using local deformation criteria during the tree refinement steps. We define new subdivision patterns as part of our extended quadtree to add flexibility in the adaptation and guarantee that geometrical constraints are entirely modeled by tree edges. During the process, we ensure grid alignment with constraint accuracy and element quality at every scale. Our proposal converts the tree structure into a mesh with only quadrilateral elements. Results showed that our method generates elements of reasonable quality even for complex geometries and varying scales. The small number of parameters controlling the process is intuitive and makes our method efficient and user friendly.

QEx

The most popular and actively researched class of quad remeshing techniques is the family of parametrization based quad meshing methods . They all strive to generate an integer-grid map , i.e. a parametrization of the input surface into R 2 such that the canonical grid of integer iso-lines forms a quad mesh when mapped back onto the surface in R 3 . An essential, albeit broadly neglected aspect of these methods is the quad extraction step, i.e. the materialization of an actual quad mesh from the mere "quad texture". Quad (mesh) extraction is often believed to be a trivial matter but quite the opposite is true: numerous special cases, ambiguities induced by numerical inaccuracies and limited solver precision, as well as imperfections in the maps produced by most methods (unless costly countermeasures are taken) pose significant challenges to the quad extractor. We present a method to sanitize a provided parametrization such that it becomes numerically consistent even in a limited precision floating point representation. Based on this we are able to provide a comprehensive and sound description of how to perform quad extraction robustly and without the need for any complex tolerance thresholds or disambiguation rules. On top of that we develop a novel strategy to cope with common local fold-overs in the parametrization. This allows our method, dubbed QEx , to generate all-quadrilateral meshes where otherwise holes, non-quad polygons or no output at all would have been produced. We thus enable the practical use of an entire class of maps that was previously considered defective. Since state of the art quad meshing methods spend a significant share of their run time solely to prevent local fold-overs, using our method it is now possible to obtain quad meshes significantly quicker than before. We also provide libQEx, an open source C++ reference implementation of our method and thus significantly lower the bar to enter the field of quad meshing.

Matching interior and exterior all-quadrilateral meshes with guaranteed angle bounds

This paper presents an extension of our earlier work on quadtree-based all-quadrilateral mesh generation, which generates guaranteed-quality meshes for the interior or exterior domain of any given planar curve. In this paper, we develop an algorithm to match the generated interior and exterior meshes with conformal boundary, preserving the guaranteed angle bounds. In addition, we introduce another automatic and robust approach to preserve sharp features. All the elements in the final mesh are within $$[45^{\circ} - \varepsilon, 135^{\circ} + \varepsilon] (\varepsilon \leq 5^{\circ}),$$ except small sharp angles present in the input geometry. Here, $$\varepsilon$$ is an input parameter. The smaller $$\varepsilon$$ is, the better angle bounds we can get. Finally, we group all the elements into six types, and most elements only need a few flops to construct the element stiffness matrix. This will significantly reduce the computational time during the finite element analysis.

Hexagon-based all-quadrilateral mesh generation with guaranteed angle bounds

In this paper, we present a novel hexagon-based mesh generation method which creates all-quadrilateral (all-quad) meshes with guaranteed angle bounds and feature preservation for arbitrary planar domains. Given any planar curves, an adaptive hexagon-tree structure is constructed by using the curvature of the boundaries and narrow regions. Then a buffer zone and a hexagonal core mesh are created by removing elements outside or around the boundary. To guarantee the mesh quality, boundary edges of the core mesh are adjusted to improve their formed angles facing the boundary, and two layers of quad elements are inserted in the buffer zone. For any curve with sharp features, a corresponding smooth curve is firstly constructed and meshed, and then another layer of elements is inserted to match the smooth curve with the original one. It is proved that for any planar smooth curve all the element angles are within [60° − ε, 120° + ε] ( ε ⩽ 5°). We also prove that the scaled Jacobians defined by two edge vectors are in the range of [ sin (60° − ε), sin 90°], or [0.82, 1.0]. The same angle range can be guaranteed for curves with sharp features, with the exception of small angles in the input curve. Furthermore, an approach is introduced to match the generated interior and exterior meshes with a relaxed angle range, [30°, 150°]. We have applied our algorithm to a set of complicated geometries, including the China map, the Lake Superior map, and a three-component air foil with sharp features. In addition, all the elements in the final mesh are grouped into five types, and most elements only need a few flops to construct the stiffness matrix for finite element analysis. This will significantly reduce the computational time and the required memory during the stiffness matrix construction.

Guaranteed-quality all-quadrilateral mesh generation with feature preservation

In this paper, a quadtree-based mesh generation method is described to create guaranteed-quality, geometry-adapted all-quadrilateral (all-quad) meshes with feature preservation for arbitrary planar domains. Given point cloud, our method generates all-quad meshes with these points as vertices and all the angles are within [45°, 135°]. For given planar curves, quadtree-based spatial decomposition is governed by the curvature of the boundaries and narrow regions. 2-refinement templates are chosen for local mesh refinement without creating any hanging nodes. A buffer zone is created by removing elements around the boundary. To guarantee the mesh quality, the angles facing the boundary are improved via template implementation, and two buffer layers are inserted in the buffer zone. It is proved that all the elements of the final mesh are quads with angles between 45° ± ε and 135° ± ε ( ε ≤ 5°) with the exception of badly shaped elements that may be required by the sharp angles in the input geometry. We also prove that the scaled Jacobians defined by two edge vectors are in the range of [ sin(45° − ε), sin90°], or [0.64, 1.0]. Furthermore, sharp features and narrow regions are detected and preserved automatically. Boundary layer meshes are generated by splitting elements of the second buffer layer. We have applied our algorithm to a set of complicated geometries, including the Lake Superior map and the air foil with multiple components.

All‐hexahedral element meshing: automatic elimination of self‐intersecting dual lines

AbstractThere has been some degree of success in all‐hexahedral meshing. Standard methods start with the object geometry defined by means of an all‐quadrilateral mesh, followed by the use of the combinatorial dual to the mesh in order to define the internal connectivities among elements. For all of the known methods using the dual concept, it is necessary to first prevent or eliminate self‐intersecting (SI) dual lines of the given quadrilateral mesh. The relevant features of SI lines are studied, giving a method to remove them, which avoids deforming the original geometry. Some examples of resulting meshes are shown where the current meshing method has been successfully applied. Copyright © 2002 John Wiley & Sons, Ltd.

All-hexahedral element meshing: Generation of the dual mesh by recurrent subdivision

The domain geometry is defined by means of a closed all-quadrilateral mesh. The outer mesh imposes very strong restrictions on the possible connectivities between the inner hexahedral elements. Following the guidelines of the outer topology, the inner one is almost entirely defined. Several ways may be decided for certain configurations, some of them requiring special considerations in order to achieve a valid FEM mesh. The process is entirely performed by constructing the (graph theoretical) dual of the hexahedral mesh, this means no metric information is handled until the final (positioning and smoothing) steps. The essential steps of this scheme are described by means of examples.

Q-Morph: an indirect approach to advancing front quad meshing

Q-Morph is a new algorithm for generating all-quadrilateral meshes on bounded three-dimensional surfaces. After first triangulating the surface, the triangles are systematically transformed to create an all-quadrilateral mesh. An advancing front algorithm determines the sequence of triangle transformations. Quadrilaterals are formed by using existing edges in the triangulation, by inserting additional nodes, or by performing local transformations to the triangles. A method typically used for recovering the boundary of a Delaunay mesh is used on interior triangles to recover quadrilateral edges. Any number of triangles may be merged to form a single quadrilateral. Topological clean-up and smoothing are used to improve final element quality. Q-Morph generates well-aligned rows of quadrilaterals parallel to the boundary of the domain while maintaining a limited number of irregular internal nodes. The proposed method also offers the advantage of avoiding expensive intersection calculations commonly associated with advancing front procedures. A series of examples of Q-Morph meshes are also presented to demonstrate the versatility of the proposed method. Copyright © 1999 John Wiley & Sons, Ltd.

Analysis automation with paving: A new quadrilateral meshing technique

This paper describes the impact of paving, a new automatic mesh generation algorithm, on the analysis portion of the design process. Paving generates an all-quadrilateral mesh in arbitrary 2D geometries. The paving technique significantly impacts the analysis process by drastically reducing the time and expertise requirements of traditional mesh generation. Paving produces a high quality mesh based on geometric boundary definitions and user specified element sizing constraints. In this paper we describe the paving algorithm, discuss varying aspects of the impact of the technique on design automation, and elaborate on current research into 3D all-hexahedral mesh generation.