Surface Mesh Generation Research Articles

A lightweight interactive approach for unstructured surface mesh generation

PurposeThe paper aims to propose a generation approach for unstructured surface mesh to speed up mesh generation.Design/methodology/approachThe paper proposes a lightweight interactive generation approach for unstructured surface mesh and presents several key technologies to support this approach.FindingsThe experimental results show that the proposed approach is feasible for unstructured meshes and it can accelerate the mesh generation process.Research limitations/implicationsMore geometric defects should be covered, and more convenient and efficient interactive means need to be provided.Practical implicationsThe proposed approach and key technologies are implemented in NNW-GridStar.UG, which is the unstructured version of the mesh generation software of National Numerical Windtunnel (NNW).Originality/valueThis paper proposes a lightweight interactive approach for unstructured surface mesh generation, which can speed up mesh generation.

A nonconforming surface mesh generation method by binary tree

Computer-aided engineering (CAE) has emerged as an indispensable tool for facilitating engineering practices and driving industrial innovation. However, the insufficient quality and efficiency of discretizing complex computer-aided design (CAD) models significantly impede the advancement of CAE calculation accuracy and automation. The presence of “dirty” geometry leads to the fact that it is almost impossible to generate a traditional conforming mesh without geometry repair. In most instances, automating geometry repair proves to be even more challenging than meshing. To cope with intricate CAD model with “dirty” geometry, a novel binary tree surface subdivision method (BSSM) is proposed for automatically generated conforming and nonconforming meshes directly on CAD models. In contrast to the conventional conforming mesh, the nonconforming mesh allows for hanging nodes, thereby eliminating the limitations of the mesh conformance. This facilitates rapid transitions in mesh size for automatic mesh generation when dealing with “dirty” geometry. A series of numerical models employing BSSM are presented in this study. Results reveal that BSSM can automatically, efficiently and reliably generate high level quality mesh for arbitrary structures.

Quadrilateral surface mesh generation with improved quality by combination of triangles

AbstractQuadrilateral mesh is preferred in numerical simulation compared with triangular mesh, but high‐quality and robust quadrilateral mesh generation for complex geometries remains a challenging problem. In this study, an enhanced indirect method by the combination of triangles is proposed for the generation of high‐quality quadrilateral mesh. It takes a triangular mesh as the input, and except that the number of elements needs to be even, the triangular mesh can be generated by the commonly used AFT method or Delaunay method. To ensure the quality of the combined quads, a local‐global triangular remeshing procedure is conducted first, and size gradation and vertex valence are focused in this step. Then, the well‐known Blossom algorithm is used to find the perfect matching triangles for combination. Finally, in order to reduce the number of unnecessary singularities, a connectivity optimization procedure is introduced to replace the irregular elements in local regions with regular elements and thus improve the overall quality of the combined quads. Numerical experiments on meshes in both 2D and 3D cases are presented to demonstrate the effectiveness of the proposed method.

An efficient unstructured quadrilateral-dominated surface mesh generation method for arbitrary geometry with tiny features or crack defects in DiBFM

An efficient unstructured quadrilateral-dominated surface mesh generation algorithm is presented to generate high-quality surface elements for arbitrary geometry with tiny features or crack defects. For complex entities with proximity features, a novel type of meshing template has been proposed to solve the problem of entity boundary fitting of the outside-in grid-based method. The algorithm also works for regions with proximity features, as well as for arbitrary geometry with one or multiple cracks. The procedure incorporates aspects of well-known meshing techniques, but includes some original and efficient processes. The refinement field is constructed according to mesh size, boundary curvature, surface curvature and other geometry features. In order to effectively generate the core mesh, a fast intersection algorithm between topological elements and the solid boundary is established, which improves the efficiency of intersection calculation. The geometry-based techniques are employed for boundary matching of the core mesh. The method has been successfully employed in conjunction with the dual interpolation boundary face method (DiBFM). Several realistic geometries with cracks or proximity features are applied to demonstrate the accuracy and validity of the proposed approach.

Validation of a 3D Local-Scale Adaptive Solar Radiation Model by Using Pyranometer Measurements and a High-Resolution Digital Elevation Model.

The result of the multidisciplinary collaboration of researchers from different areas of knowledge to validate a solar radiation model is presented. The MAPsol is a 3D local-scale adaptive solar radiation model that allows us to estimate direct, diffuse, and reflected irradiance for clear sky conditions. The model includes the adaptation of the mesh to complex orography and albedo, and considers the shadows cast by the terrain and buildings. The surface mesh generation is based on surface refinement, smoothing and parameterization techniques and allows the generation of high-quality adapted meshes with a reasonable number of elements. Another key aspect of the paper is the generation of a high-resolution digital elevation model (DEM). This high-resolution DEM is constructed from LiDAR data, and its resolution is two times more accurate than the publicly available DEMs. The validation process uses direct and global solar irradiance data obtained from pyranometers at the University of Salamanca located in an urban area affected by systematic shading from nearby buildings. This work provides an efficient protocol for studying solar resources, with particular emphasis on areas of complex orography and dense buildings where shadows can potentially make solar energy production facilities less efficient.

Unstructured surface mesh generation based on conformal welding

Unstructured surface mesh generation based on conformal welding

TAVI-PREP: A Deep Learning-Based Tool for Automated Measurements Extraction in TAVI Planning.

Transcatheter aortic valve implantation (TAVI) is a less invasive alternative to open-heart surgery for treating severe aortic stenosis. Despite its benefits, the risk of procedural complications necessitates careful preoperative planning. This study proposes a fully automated deep learning-based method, TAVI-PREP, for pre-TAVI planning, focusing on measurements extracted from computed tomography (CT) scans. The algorithm was trained on the public MM-WHS dataset and a small subset of private data. It uses MeshDeformNet for 3D surface mesh generation and a 3D Residual U-Net for landmark detection. TAVI-PREP is designed to extract 22 different measurements from the aortic valvular complex. A total of 200 CT-scans were analyzed, and automatic measurements were compared to the ones made manually by an expert cardiologist. A second cardiologist analyzed 115 scans to evaluate inter-operator variability. High Pearson correlation coefficients between the expert and the algorithm were obtained for most parameters (0.90-0.97), except for left and right coronary height (0.8 and 0.72, respectively). Similarly, the mean absolute relative error was within 5% for most measurements, except for left and right coronary height (11.6% and 16.5%, respectively). A greater consensus was observed among experts than when compared to the automatic approach, with TAVI-PREP showing no discernable bias towards either the lower or higher ends of the measurement spectrum. TAVI-PREP provides reliable and time-efficient measurements of the aortic valvular complex that could aid clinicians in the preprocedural planning of TAVI procedures.

ISpliter: an intelligent and automatic surface mesh generator using neural networks and splitting lines

In this paper, we present a novel surface mesh generation approach that splits B-rep geometry models into isotropic triangular meshes based on neural networks and splitting lines. In the first stage, a recursive method is designed to generate plentiful data to train the neural network model offline. In the second stage, the implemented mesh generator, ISpliter, maps each surface patch into the parameter plane, and then the trained neural network model is applied to select the optimal splitting line to divide the patch into subdomains continuously until they are all triangles. In the third stage, ISpliter remaps the 2D mesh back to the physical space and further optimizes it. Several typical cases are evaluated to compare the mesh quality generated by ISpliter and two baselines, Gmsh and NNW-GridStar. The results show that ISpliter can generate isotropic triangular meshes with high average quality, and the generated meshes are comparable to those generated by the other two software under the same configuration.

Automatic surface mesh generation by a binary-tree method

In order to realize the automation of surface mesh generation for arbitrary complex models, this paper proposes a binary-tree method (BTM) which can generate discontinuous grids. Compared with continuous grids, the adjacency relationship between discontinuous grids generated by BTM is more flexible, so it is easier to discretize “dirty” geometry without geometry repair than continuous grids. The BTM can adaptively generate meshes by features based on the curvature of curves and surfaces, and thus it does not need to construct a sizing field. Anisotropic meshes can also be directly generated by selecting the direction of subdividing meshes. Moreover, according to the periodic characteristics of periodic surfaces, the topological structure of the initial mesh can be designed to achieve mesh generation on periodic surfaces. Successful numerical examples are used to illustrate the effectiveness and robustness of the presented methods for meshing various types of geometric surfaces and reveal the excellent performance of the BTM. In addition, the BTM has been employed by the dual interpolation boundary face method (DiBFM) to solve 3D problems.

On the Efficiency of the Advancing-Front Surface Mesh Generation Algorithm

An efficient advancing front algorithm is presented to create high-quality surface elements on CAD models. Various novel schemes are developed to improve the efficiency of the algorithm while not sacrificing its robustness and the resulting mesh quality. New features include a fast projection scheme that can perform robustly in case of badly defined surfaces, a procedure that computes the ideal point by an approach that can preserve the advantageous features of both the mapping and direct methods, and an octree data structure that can speed up the local search of all existing front nodes about the ideal point. To our knowledge, the proposed algorithm is one of the fastest algorithms for surface mesh generation. On an AMD Ryzen 5 3600 machine, the sequential version of the proposed algorithm can create a quality mesh at a speed of up to 100,000 elements per second. This speed is more than 3 times higher than a state-of-the-art code can achieve. Another advantage of the proposed algorithm is its ability to maintain its high efficiency when millions or more elements are created on one single surface. In this circumstance, the efficiency of some state-of-the-arts codes slows down by one or two orders. After parallelized based on the taskflow approach, the proposed algorithm can create more than 1.6 million elements on real-world configurations in 7 s by using 6 computer cores. This speed is higher than a state-of-the-art commercial code can achieve by one order. • An efficient surface mesh generator for large-scale triangular mesh generation of industrial CAD models, which is far faster than existing schemes. • The nonlinear calculation such as orthogonal projection and ideal point calculation is comprehensively improved. • Traditional surface mesh generation methods such as direct method and mapping method are combined. • The design of spatial index data structure (octree and AD tree) makes the algorithm have strong scalability.

Optimization of mesh generation for geometric accuracy, robustness, and efficiency of biomechanical-model-based deformable image registration.

Successful generation of biomechanical-model-based deformable image registration (BM-DIR) relies on user-defined parameters that dictate surface mesh quality. The trial-and-error process to determine the optimal parameters can be labor-intensive and hinder DIR efficiency and clinical workflow. To identify optimal parameters in surface mesh generation as boundary conditions for a BM-DIR in longitudinal liver and lung CT images to facilitate streamlined image registration processes. Contrast-enhanced CT images of 29 colorectal liver cancer patients and end-exhale four-dimensional CT images of 26 locally advanced non-small cell lung cancer patients were collected. Different combinations of parameters that determine the triangle mesh quality (voxel side length and triangle edge length) were investigated. The quality of DIRs generated using these parameters was evaluated with metrics for geometric accuracy, robustness, and efficiency. Metrics for geometric accuracy included target registration error (TRE) of internal vessel bifurcations, dice similar coefficient (DSC), mean distance to agreement (MDA), Hausdorff distance (HD) for organ contours, and number of vertices in the triangle mesh. American Association of Physicists in Medicine Task Group 132 was used to ensure parameters met TRE, DSC, MDA recommendations before the comparison among the parameters. Robustness was evaluated as the success rate of DIR generation, and efficiency was evaluated as the total time to generate boundary conditions and compute finite element analysis. Voxel side length of 0.2cm and triangle edge length of 3 were found to be the optimal parameters for both liver and lung, with success rate of 1.00 and 0.98 and average DIR computation time of 100 and 143s, respectively. For this combination, the average TRE, DSC, MDA, and HD were 0.38-0.40, 0.96-0.97, 0.09-0.12, and 0.87-1.17mm, respectively. The optimal parameters were found for the analyzed patients. The decision-making process described in this study serves as a recommendation for BM-DIR algorithms to be used for liver and lung. These parameters can facilitate consistence in the evaluation of published studies and more widespread utilization of BM-DIR in clinical practice.

Implicit Tetrahedral and Surface Mesh Generation for 3D Reservoir Structural Modeling

Implicit Tetrahedral and Surface Mesh Generation for 3D Reservoir Structural Modeling

Multivariate morphometry statistics reveal the morphological change pattern of hippocampus during normal aging.

There have been numerous studies focusing on normal aging in previous decades which is accompanied by the structural and functional decline in the hippocampus, while the pattern of hippocampal alteration with age remains unclear. Figuring out the mechanism of hippocampal changes precisely is beneficial for a better understanding of the aging process. In this study, we included a total of 451 T1 MRI scans of subjects of age 50-90 who were labeled as normal in the Alzheimer's Disease Neuroimaging Initiative. Taking 10 years of age as an age band, we divided the subjects into four groups (denoted as HC1, HC2, HC3, and HC4, respectively), with the youngest being 50-60 and the oldest 81-90. Then the Multivariate Morphometry Statistics (MMS) of the hippocampus segmented from the four groups were extracted by surface reconstruction, mesh generation, and surface registration. Finally, the significant differences between the youngest group and the other three were statistically analyzed. Results showed that the earliest deformation region of the left hippocampus located in the frontal subiculum and the dorsal CA1 of the tail part and gradually expanded with aging, while the right hippocampal deformation mainly concentrated in the dorsal CA1 and spread to the posterior CA2-3, which occurred later than that of the left. All the results illustrated that the hippocampus is truly a vulnerable structure in the course of aging, and the MMS are sensitive metrics for detecting the changes in the subcortical convex structure.

Adaptive stochastic morphology simulation and mesh generation of high-quality 3D particulate composite microstructures with complex surface texture

Particulate composite materials have a broad range of potential applications in engineering and other disciplines. Accurate modeling of their microstructures and fast generation of the finite element meshes play a vital role in investigating many micromechanical phenomena and improving understanding of the underlying failure mechanisms. Due to the exceedingly intricate multiscale internal structures that they possess, the modeling and meshing of their microstructures still remain difficult in general. In this work, we present a computational framework and methodology for the representation, simulation, and mesh generation of 3D stochastic microstructures of particulate composites. Towards this goal, we propose a multi-level multiscale scheme that allows for capturing the multiscale structures of particulate composite materials at both the coarse and fine scales. A briging scale approach based on heat kernel smoothing is also presented to seamlessly link the coarse and fine scales. In addition to the microstructural modeling of particulate composite materials, we also develop an adaptive curvature-based surface and volume mesh generation algorithm for particulate composite microstructures with complex surface texture. Following the implementation of the morphology and mesh generation algorithm, a series of numerical examples are presented to demonstrate the capability and potential of the proposed method.

An algorithm for rapid ground surface mesh generation used in complex terrain wind field simulation

In the study of wind engineering problems, it is of considerable importance to obtain accurate surface wind field characteristics. Surface features have significant impacts on the characteristics of small- and micro-scale wind field, so the fine reconstruction of terrain features is the basis of small- and micro-scale wind field simulations. However, since the GIS data obtained by satellite scanning cannot be directly used for CFD numerical simulation, the geographic information data is usually of considerable amount and contains a large number of waste points, thus difficult to be completed by manual modeling. To solve this problem, an automatic waste point repair algorithm and a grid aggregation method based on greedy algorithm are proposed, which can quickly and efficiently reconstruct the surface and generate the grid. Relying on the national numerical wind tunnel project and integrating the above core algorithms with the pre-processing and post-processing modules, a general and efficient surface mesh generation software ESM (Earth Surface Mesh) has been developed. Compared with the surface modeling and grid generation modules provided by other software, ESM has more comprehensive functions, and surface grid rapid generation technologies such as waste point data processing, grid adaptive refinement based on elevation change, high fidelity interpolation technology and partition splicing generation. It supports more interfaces and can generate structured and unstructured grids. The preliminary example shows that the surface grid generated by ESM meets the needs of wind engineering simulation.

Surface reconstruction with spherical harmonics and its application for single particle crushing simulations

Particle morphology has great influence on mechanical behaviour and hydro/thermal/electrical conductivities of granular materials. Surface reconstruction and mesh generation are critical to consider realistic particle shapes in various computational simulations. This study adopts the combined finite- discrete element method (FDEM) to investigate single particle crushing behaviour. Particle shapes were reconstructed with spherical harmonic (SH) in both spherical and Cartesian coordinate systems. Furthermore, the reconstructed surface mesh qualities in two coordinate systems are investigated and compared. Although the efficiency of the two SH systems in reconstructing star-like shapes is nearly identical, SH in Cartesian coordinate system can reconstruct non-star-like shapes with the help of surface parameterisation. Meanwhile, a higher triangular mesh quality is generated with spherical coordinate. In single particle crushing tests, the low mesh quality produces more fluctuations on load–displacement curves. The particles with more surficial mesh elements tend to have a lower contact stiffness due to more contact stress concentrations induced by complexity of morphology features and more volumetric tetrahedral elements. The fracture patterns are also influenced by mesh quality and density, e.g. a particle with fewer mesh elements has a simpler fragmentation pattern. This study serves as an essential step towards modelling particle breakage using FDEM with surface mesh directly from SH reconstruction.

Automatic sizing functions for unstructured mesh generation revisited

PurposeSizing functions are crucial inputs for unstructured mesh generation since they determine the element distributions of resulting meshes to a large extent. Meanwhile, automating the procedure of creating a sizing function is a prerequisite to set up a fully automatic mesh generation pipeline. In this paper, an automatic algorithm is proposed to create a high-quality sizing function for an unstructured surface and volume mesh generation by using a triangular mesh as the background mesh.Design/methodology/approachA practically efficient and effective solution is developed by using local operators carefully to re-mesh the tessellation of the input Computer Aided Design (CAD) models. A nonlinear programming (NLP) problem has been formulated to limit the gradient of the sizing function, while in this study, the object function of this NLP is replaced by an analytical equation that predicts the number of elements. For the query of the sizing value, an improved algorithm is developed by using the axis-aligned bounding box (AABB) tree structure.FindingsThe local operations of re-meshing could effectively and efficiently resolve the banding issue caused by using the default tessellation of the model to define a sizing function. Experiments show that the solution of the revised NLP, in most cases, could provide a better solution at the lower cost of computational time. With the help of the AABB tree, the sizing function defined at a surface background mesh can be also used as the input of volume mesh generation.Originality/valueTheoretical analysis reveals that the construction of the initial sizing function could be reduced to the solution of an optimization problem. The definitions of the banding elements and surface proximity are also given. Under the guidance of this theoretical analysis, re-meshing and ray-casting technologies are well-designed to initial the sizing function. Smoothing with the revised NLP and querying by the AABB tree, the paper provides an automatic method to get a high-quality sizing function for both surface and volume mesh generation.

Polygonal surface processing and mesh generation tools for the numerical simulation of the cardiac function.

In order to simulate the cardiac function for a patient‐specific geometry, the generation of the computational mesh is crucially important. In practice, the input is typically a set of unprocessed polygonal surfaces coming either from a template geometry or from medical images. These surfaces need ad‐hoc processing to be suitable for a volumetric mesh generation. In this work we propose a set of new algorithms and tools aiming to facilitate the mesh generation process. In particular, we focus on different aspects of a cardiac mesh generation pipeline: (1) specific polygonal surface processing for cardiac geometries, like connection of different heart chambers or segmentation outputs; (2) generation of accurate boundary tags; (3) definition of mesh‐size functions dependent on relevant geometric quantities; (4) processing and connecting together several volumetric meshes. The new algorithms—implemented in the open‐source software vmtk—can be combined with each other allowing the creation of personalized pipelines, that can be optimized for each cardiac geometry or for each aspect of the cardiac function to be modeled. Thanks to these features, the proposed tools can significantly speed‐up the mesh generation process for a large range of cardiac applications, from single‐chamber single‐physics simulations to multi‐chambers multi‐physics simulations. We detail all the proposed algorithms motivating them in the cardiac context and we highlight their flexibility by showing different examples of cardiac mesh generation pipelines.

Anisotropic sources for surface and volume boundary layer mesh generation

A new approach to model and compute the metric tensor corresponding to a-priori prescribed surface and volume boundary layers is presented. This is achieved by the use of sources that model the combined anisotropic metric. Algorithms are presented to both evaluate the resulting metric value at any point in space and the efficient approximation of the minimum and maximum metric over an axis-aligned box which enables fast evaluation of the anisotropic metric independent of the approach used for mesh generation.The ability to model and evaluate the anisotropic sizing independently ensure that mesh generation algorithms that use it can produce meshes that correctly and predictably capture the sizing fields induced by the user prescribed boundary layer attributes. The method is unique in producing globally smooth representations of the final anisotropic metric including the influence of implicit anisotropy due to boundary curvature and any prescribed isotropic sizes. As a result, it addresses robustness and size smoothness issues in legacy approaches that decouple the surface and volume mesh generation stages.The value of the new method is demonstrated by several examples that include both surface and volume boundary layers prescribed on geometries with curved boundaries.

Valence optimization and angle improvement for molecular surface remeshing

Molecular surface mesh generation plays a vital role in molecular modeling and visualization. However, meshes extracted directly from Protein Data Bank files have several issues such as small and large triangles, redundant elements, self-intersections, and irregular vertices. The state-of-the-art mesh improvement methods often fail to deal with these issues. In this paper, we present a novel method for valence optimization and angle improvement. For valence optimization, we remove the bad valence vertices with its neighbor triangle making regular holes in the mesh. The holes are filled in a careful manner to improve their valences as well as angle quality. We also use a segmentation-based surface remeshing which segments the mesh into random segments and then each segment is independently remeshed. In addition, a point insertion scheme is applied to minimize the ratio of obtuse triangles. Experimental results show that our method not only improves the maximal and minimal angles to an angle bound of $$[30^{\circ }\;120^{\circ }]$$ but also improves the vertices’ regularity, reduces the ratio of obtuse triangles, preserves the area and volume, and always succeeds with downstream applications.