3D Mesh Generation Research Articles

Maximal Disjoint Ball Decompositions for shape modeling and analysis

A large number of geometric representations have been proposed to address the needs of specific engineering applications. This, in turn, exacerbates the inherent challenges associated with system interoperability for downstream engineering applications.In this paper, we define the Maximal Disjoint Ball Decomposition (MDBD) as the location of the largest d-dimensional closed balls recursively placed in the interior of a d-dimensional domain and show that the proposed decomposition can be used to provide an underlying common analysis framework for geometric models using different representation schemes. Importantly, our decomposition only relies on the ability of an existing geometric representation to compute distances, which must be supported by any valid geometric representation scheme, and does not require an explicit representation conversion. Moreover, MDBD is unique for a given domain up to rigid body transformation, reflection, as well as uniform scaling, and its formulation suggests appealing stability and robustness properties against small boundary modifications.Furthermore, we show that MDBD can be used as a universal shape descriptor to perform shape similarity of models coming from various geometric representation schemes. A salient attribute of this decomposition is that it provides adequate support for key downstream applications for models coming from disparate geometric representations. For example, MDBD can be naturally used to carry out meshless solutions to boundary value problems; efficient collision detection; and 3D mesh generation of models that use any valid geometric representation scheme. Finally, our hierarchical formulation of the proposed Maximal Disjoint Ball Decomposition allows for a choice of model complexity at run-time to match the available computational resources.

Stability analysis of leaning historic masonry structures

This paper introduces an automatic, powerful and easy to use procedure for undertaking stability analyses of leaning historic masonry structures, based on an upper bound finite element limit analysis (FELA) approach. The procedure proposed here consists of a comprehensive workflow which involves the automatic point cloud manipulation, the 3D mesh generation of the actual geometry for structural purposes (e.g. FE mesh), and a two-step FELA that reduces drastically optimization variables assuming only active few elements inside a restricted processing zone. To generalize the Heyman's intuition to complex real geometries, the use of a 3D upper bound FELA with a recursive kernel of variables reduction becomes necessary for a precise evaluation of the limit inclination that makes the structure collapse under gravity loads. This outcome permits to estimate the structural health condition of a historic structure by comparing the critical inclination angle against the actual one. To demonstrate the effectiveness of the automated procedure, the southwest leaning tower of the Caerphilly castle (Wales, UK) is investigated and failure mechanisms with collapse inclination angles are evaluated through FELA. The proposed procedure presents a high degree of automation at each operational level and, hence, could be effectively used to assess the stability of historic structures at a national scale and provide useful information to asset owners to classify the structural health condition of leaning historic masonry structures in their care.

A spring system method for a mesh generation problem

A new direct method for the 2d-mesh generation for a simply-connected domain using a spring system is observed. The method can be used with other methods to modify a mesh for growing solid problems. Advantages and disadvantages of the method are shown. Different types of boundary conditions are explored. The results of modelling for different target domains are given. Some applications for composite materials are studied.

Discretization of Maxwell’s Equations for Non-inertial Observers Using Space-Time Algebra

We employ classical Maxwell’s equations formulated in space-time algebra to perform discretization of moving geometries directly in space-time. All the derivations are carried out without any non-relativistic assumptions, thus the application area of the scheme is not restricted to low velocities. The 4D mesh construction is based on a 3D mesh stemming from a conventional 3D mesh generator. The movement of the system is encoded in the 4D mesh geometry, enabling an easy extension of well-known 3D approaches to the space-time setting. As a research example, we study a manifestation of Sagnac’s effect in a rotating ring resonator. In case of constant rotation, the space-time approach enhances the efficiency of the scheme, as the material matrices are constant for every time step, without abandoning the relativistic framework.

MATLAB 2D higher-order triangle mesh generator with finite element applications using subparametric transformations

This paper presents a novel automated higher-order (HO) unstructured triangular mesh generation of the two-dimensional domain. The proposed HO scheme uses the nodal relations obtained from subparametric transformations with parabolic arcs, especially for curved geometry. This approach is shown to drastically simplify the computational complexities involved in the HO finite element (HOFE) formulation of any partial differential equation (PDE). The prospective generalised MATLAB 2D mesh generation codes, HOmesh2d for the regular domain and CurvedHOmesh2d for a circular domain are based on the MATLAB mesh generator distmesh of Persson and Strang. As an input, the code takes a signed distance function of the domain geometry and the desired order for the triangular elements and as outputs, the code generates an HO triangular mesh with element connectivity, node coordinates, and boundary data (edges and nodes). The working principle of HOFE scheme, using subparametric transformations with the proposed HO automated mesh generator is explained. The simplicity, efficiency, and accuracy of the HOFE method, with the proposed HO automated mesh generator up to 28-noded triangular elements, are illustrated with elliptic PDE. The proposed techniques are applied to some electromagnetic problems. The use of higher order elements from the proposed mesh generator is shown to increase the accuracy and efficiency of the numerical results. Also, with the proposed HOFE scheme it is verified that HO elements significantly decrease the numbers of degrees of freedom, and elements required to achieve a specific level of accuracy compared to lower order elements. Numerical results show that the HO elements outperform the lower order elements in terms of efficiency and accuracy of the numerical results.

High-quality 2D mesh generation without obtuse and small angles

In this paper, we present an efficient method to eliminate the obtuse triangles for high quality 2D mesh generation. Given an initialization (e.g., from Centroidal Voronoi Tessellation—CVT), a limited number of point insertions and removals are performed to eliminate obtuse or small angle triangles. A mesh smoothing and optimization step is then applied. These steps are repeated till a desired good quality mesh is reached. We tested our algorithm on various 2D polygonal domains and verified that our algorithm always converges after inserting a few number of new points, and generates high quality triangulation with no obtuse triangles.

Engineering applications of 2D and 3D finite element mesh generation in hydrogeology and water resources

This paper develops an automatic density-controlled 2-D and 3-D finite element mesh generation system to solve practical engineering applications in geology, hydraulics, hydrology, water resources, etc. The Delaunay triangulation method is adopted to create triangular meshes based on the required density specified by users. A triangle-to-quadrilateral conversion method is used to generate quadrilateral meshes adaptively. Density control algorithms of adaptive 2-D mesh generation are presented to satisfy the various requirements of the overland and subsurface hydrogeology and water resources in the actual target area. According to the alignment of boundary edges and distribution of surface nodes, this paper proposes the main algorithm and basic criteria to generate supplementary triangle and quadrilateral meshes for filling the water regions of river reaches and junctions with storage. A stretch mode is proposed to generate triangular prism and hexahedral meshes by stretching the 2-D mesh into 3-D space based on the materials of geometric regions. The 1-D/2-D/3-D correspondence between the finite element mesh and the river reaches, junctions with and without storage, ponds, lakes, control structures and fractures is established. Finally, practical 2-D and 3-D meshing applications are provided to demonstrate the accuracy and effectiveness of the finite element mesh generator developed in this paper.

3D Metric-aligned and orthogonal solution adaptive mesh generation

A new 3D metric-orthogonal method for metric-based anisotropic tetrahedral mesh generation is presented. The approach uses an advancing-point type point placement that aligns the elements with the underlying metric field and creates quasi-structured local topology. It is based on well-proven methodology and adds novel point-placement strategies that produce solution-adapted anisotropic meshes that are optimal in size and alignment with the solution gradients upon which the metric field is based. The overall methodology is extended to 3D from a previously developed 2D process. Results for several analytical and actual CFD simulation examples are presented that demonstrate that aligned high-quality anisotropic tetrahedral meshes which are optimal for the solution process can be reliably generated.

Image-based object reconstruction using run-length representation

This paper presents an image-based object reconstruction with a low memory footprint using run-length representation. While conventional volume-based approaches, which utilize voxels as primitives, are intuitive and easy to manipulate 3D data, they require a large amount of memory and computation during the reconstruction process. To overcome these burdens, this paper uses 3D runs to represent a 3D object and reconstructs each 3D run from multi-view silhouettes with a small amount of memory. The proposed geometry reconstruction is also computationally inexpensive, as it processes multiple voxels simultaneously. And for the compatibility with the conventional data formats, generation of polygonal 3D meshes from the reconstructed 3D runs is proposed as well. Lastly, texture mapping is proposed to additionally reduce the amount of memory for object reconstruction. The proposed reconstruction scheme has been simulated using various types of multi-view datasets. The results show that the proposed method performs object reconstruction with a smaller amount of memory and computation than voxel-based approaches.

Degenerate tetrahedra removal

Standard 3D mesh generation algorithms may produce a low quality tetrahedral mesh, i.e., a mesh where the tetrahedra have very small dihedral angles. In this paper, we propose a series of operations to recover these badly-shaped tetrahedra.In particular, we will focus on the shape of these undesired mesh elements by proposing a novel method to distinguish and classify them. For each of these configurations, we apply a suitable sequence of operations to get a higher mesh quality. Finally, we employ a random algorithm to avoid locks and loops in the procedure.The reliability of the proposed mesh optimization algorithm is numerically proved with several examples.

Advanced finite element modeling of excavation and advancement processes in mechanized tunneling

Mechanized tunneling is characterized by complex interactions between the shield machine and the surrounding ground during the TBM advancement process. In this paper, a new computational framework is developed to enable an efficient and realistic three-dimensional modeling of the tunneling process for arbitrary alignments using the finite element method. A new steering algorithm for the advancement of the Tunnel Boring Machine (TBM) for arbitrary alignments during shield tunneling is incorporated in the proposed model. This algorithm simulates the shield behavior and accordingly provides the numerical model with the required information to keep the TBM on track during the simulation. However, the utilization of this algorithm is only possible using a finite element discretization which adapts to the actual motion path of the shield machine. For this purpose, a re-meshing technique is proposed in order to automate the process of mesh generation in the vicinity of the tunnel face, denoted as the region of interest, within the advancing process. The combination of a computational steering algorithm and a 3D automatic adaptive mesh generation procedure form a novel framework for process oriented finite element simulations of the mechanized tunnel construction process. The applicability of the proposed modeling technique for predicting the shield behavior and the soil-tunnel interactions during tunneling along curved alignments is demonstrated by means of selected examples.

A SYSTEMATIC COMPARISON OF DIRECT AND IMAGE-BASED GEOREFERENCING IN CHALLENGING URBAN AREAS

Abstract. Image-based mobile mapping systems enable an efficient acquisition of georeferenced image sequences, which can be used for geo-data capture in subsequent steps. In order to provide accurate measurements in a given reference frame while e.g. aiming at high fidelity 3D urban models, high quality georeferencing of the captured multi-view image sequences is required. Moreover, sub-pixel accurate orientations of these highly redundant image sequences are needed in order to optimally perform steps like dense multi-image matching as a prerequisite for 3D point cloud and mesh generation. While direct georeferencing of image-based mobile mapping data performs well in open areas, poor GNSS coverage in urban canyons aggravates fulfilling these high accuracy requirements, even with high-grade inertial navigation equipment. Hence, we conducted comprehensive investigations aiming at assessing the quality of directly georeferenced sensor orientations as well as the expected improvement by image-based georeferencing in a challenging urban environment. Our study repeatedly delivered mean trajectory deviations of up to 80 cm. By performing image-based georeferencing using bundle adjustment for a limited set of cameras and a limited number of ground control points, mean check point residuals could be lowered from approx. 40 cm to 4 cm. Furthermore, we showed that largely automated image-based georeferencing is capable of detecting and compensating discontinuities in directly georeferenced trajectories.

A SYSTEMATIC COMPARISON OF DIRECT AND IMAGE-BASED GEOREFERENCING IN CHALLENGING URBAN AREAS

Image-based mobile mapping systems enable an efficient acquisition of georeferenced image sequences, which can be used for geo-data capture in subsequent steps. In order to provide accurate measurements in a given reference frame while e.g. aiming at high fidelity 3D urban models, high quality georeferencing of the captured multi-view image sequences is required. Moreover, sub-pixel accurate orientations of these highly redundant image sequences are needed in order to optimally perform steps like dense multi-image matching as a prerequisite for 3D point cloud and mesh generation. While direct georeferencing of image-based mobile mapping data performs well in open areas, poor GNSS coverage in urban canyons aggravates fulfilling these high accuracy requirements, even with high-grade inertial navigation equipment. Hence, we conducted comprehensive investigations aiming at assessing the quality of directly georeferenced sensor orientations as well as the expected improvement by image-based georeferencing in a challenging urban environment. Our study repeatedly delivered mean trajectory deviations of up to 80 cm. By performing image-based georeferencing using bundle adjustment for a limited set of cameras and a limited number of ground control points, mean check point residuals could be lowered from approx. 40 cm to 4 cm. Furthermore, we showed that largely automated image-based georeferencing is capable of detecting and compensating discontinuities in directly georeferenced trajectories.

Integration of experimental and computational methods for identifying geometric, thermal and diffusive properties of biomaterials

Abstract Knowledge of physical properties of biomaterials is important in understanding and designing agri-food and wood processing industries. In the study presented in this paper computational methods were developed and combined with experiments to enhance identification of agri-food and forest product properties, and to predict heat and water transport in such products. They were based on the finite element model of heat and water transport and supplemented with experimental data. Algorithms were proposed for image processing, geometry meshing, and inverse/direct finite element modelling. The resulting software system was composed of integrated subsystems for 3D geometry data acquisition and mesh generation, for 3D geometry modelling and visualization, and for inverse/direct problem computations for the heat and water transport processes. Auxiliary packages were developed to assess performance, accuracy and unification of data access. The software was validated by identifying selected properties and using the estimated values to predict the examined processes, and then comparing predictions to experimental data. The geometry, thermal conductivity, specific heat, coefficient of water diffusion, equilibrium water content and convective heat and water transfer coefficients in the boundary layer were analysed. The estimated values, used as an input for simulation of the examined processes, enabled reduction in the uncertainty associated with predictions.

라인 레이저 기반 3차원 스캐너에서 투영을 이용한 고속 3D 메쉬 생성

ABSTRACT This paper presents a fast 3D mesh generation method using projection for line laser-based 3D scanners. The well-known method for 3D mesh generation utilizes convex hulls for 4D vertices that is converted from the input 3D vertices. This 3D mesh generation for a large set of vertices requires a lot of time. To overcome this problem, the proposed method takes (θ-y) 2D depth map into account. The 2D depth map is a projection version of 3D data with a form of (θ, y, z) which are intermediately acquired by line laser-based 3D scanners. Thus, our 2D-based method is a very fast 3D mesh generation method. To evaluate our method, we conduct experiments with intermediate 3D vertex data from line-laser scanners. Experimental results show that the proposed method is superior to the existing method in terms of mesh generation speed. 키워드 : 2D 깊이지도, 3D 스캐너, 라인레이저 스캐너, 메쉬 생성법 Key word : 2D depth map, 3D scanner, Line laser scanner, Mesh generation Received 23 December 2015, Revised 13 January 2016,

OS0606 自己交差を含む三次元メッシュの形状維持修正法

3D mesh data obtained by 3D scanner has self-intersection surface because of 3D scanner error and mesh generation error. These mesh data that include self-intersection can't be used for 3D printing and FEM, etc. Therefore, self-intersection need to be removed. In this paper, a new self-intersection removing Algorithm is presented. The proposed algorithm has four processes. First, detect self-intersection surfaces. Second, divide to detect surfaces. Third, judge divide surface is inner or outer. Fourth, delete inner and burying surface. This proposed algorithm could remove self-intersection surface in 3D mesh data without changing original shape. So this method is more accurate than the conventional method with regard to outer shape.

Optimized Aerodynamic Design of Axial Turbines for Waste Energy Recovery

Industrial processes experience waste of energy when throttling valves are used for flow control. In such cases, the overall process efficiency can be improved by means of inline installations of well suited turbines in place of throttling valves, in order to recover useful power from the pressure drops, which otherwise result in a waste of energy. Energy recovery turbines may require an “ad hoc” design when their operating ranges are unsuitable for traditional design methods. For this purpose, a general methodology is proposed, which can be helpful in the aerodynamic design of these non-conventional turbines. The design procedure is iterative and begins with a one dimension (1-D) study for the definition of the main geometric parameters, once appropriate loss coefficients are considered. Then, the blade profiles are designed by means of panel method with “viscous/inviscid interaction”. Finally, the actual values of the loss coefficients are evaluated by means of fully 3-D CFD simulations, and used for updating the loss coefficients used in 1-D calculations. The iterative design procedure has been automatized by means of a Matlab script for the 1-D study, a ModeFrontier project for the blade design optimization and a log file for the automated 3D mesh generation. In order to validate the proposed methodology and show its generality, the design of a first stage of a steam turbine whose reference data were available in the literature, is presented.

Application of FEM Mesh Generation Algorithm for Digital Processing of Handmade Sketches

Handmade sketches of different shapes roof structures, often with openings, are outlined on plain sheet of paper. Then, they are transformed by a 2D mesh generation and applied to FEM calculations. Algorithm where only main coordinates of nodes are used as user input data is studied by the Authors. Shape of the surface, its curvature and openings are detected through the procedures developed in the C++ programming language. A particular emphasis is put to the automation of the process. At a present version the method is used for rectangular shapes, which are quite common in civil engineering structures e.g. building elevations. Detection and processing algorithms are implemented with a usage of a library based on a open code called OpenCV. The computer software is described in this paper and some examples are given

Methods and applications for cardiovascular 3D-printing

Background: Three-dimensional printing is rapidly growing field that enables the exact replication of anatomical structures in a physical model. 3D printing may be used for cardiothoracic procedural planning, education and a variety of research purposes. Multiple 3D printer designs exist and the technological requirements may be complex for clinician scientists. Methods: Using high quality imaging data from multiple modalities we have 3d-printed a range of cardiovascular structures using different printing techniques in order to assess their suitability for cardiovascular applications. We isolated and generated 3D meshes of a whole heart (gated cardiac CT), aortic coarctation (cardiac MRI), mitral valve (3D echocardiography) and left atrium (cardiac CT). We used fusedfilament fabrication (FFF), polymer jet, laser stereolithographic (SLA) and powder bed 3D printers to print selected structures. The advantages and limitation of each printing method was assessed. Results: 3D printing is highly contingent on the quality of the underlying imaging data and image post-processing is required. 3D mesh generation can be difficult and care needs to be taken to preserve accuracy during data manipulation. Printing techniques vary widely with regards to minimal resolution, colour reproduction, speed, cost and geometric limitations. Conclusion: 3D printing is a useful and feasible technique for displaying three-dimensional cardiac imaging. The printing technique used should be tailored to the application. Current technology allows 3D printing to be widely implemented.

Stress Analysis of Air Compressor Crankshaft Based on ANSYS

The paper uses the preprocessor of ANSYS to generate the model of 3D entity and mesh generation on WW0.8/10 air compressor crankshaft. Mesh generators are transferred into data that will be used in finite element analysis. Passing by dealing with force and commitment, it calculates the forces of pressure working conditions of crankshaft. They are used in stress analysis. The stress data is calculated from the calculator of ANSYS. The static load safe coefficient and the fatigue safe coefficient of the crankshaft are tested from known stress. The result provides a high reference value for the optimization improvement of the crankshaft.