Mesh Simplification Research Articles

Analysing Key Steps of the Photogrammetric Pipeline for Museum Artefacts 3D Digitisation

In recent years, massive digitisation of cultural heritage (CH) assets has become a focus of European programmes and initiatives. Among CH settings, attention is reserved to the immense and precious museum collections, whose digital 3D reproduction can support broader non-invasive analyses and stimulate the realisation of more attractive and interactive exhibitions. The reconstruction pipeline typically includes numerous processing steps when passive techniques are selected to deal with object digitisation. This article presents some insights on critical operations, which, based on our experience, can rule the quality of the final models and the reconstruction times for delivering 3D heritage results, while boosting the sustainability of digital cultural contents. The depth of field (DoF) problem is explored in the acquisition phase when surveying medium and small-sized objects. Techniques for deblurring images and masking object backgrounds are examined relative to the pre-processing stage. Some point cloud denoising and mesh simplification procedures are analysed in data post-processing. Hints on physically-based rendering (PBR) materials are also presented as closing operations of the reconstruction pipeline. This paper explores these processes mainly through experiments, providing a practical guide, tricks, and suggestions when tackling museum digitisation projects.

Digital Body Preservation

Detailed anatomical models can be produced with three‐dimensional (3D) scanning techniques and as such be digitally preserved, archived and subsequently rendered through various media. Here, a novel methodology is presented for combining and matching scan geometry with radiographic imaging. The technique encompasses joining layers of 3D surface scans in an anatomical correct spatial relationship. To do so, a computed tomography (CT) volume is used as template to join and merge different surface scan geometries by means of non‐rigid registration into a single environment. This results in a digital model that can be used in multiple digital learning environments. Finally, as computational expense is usually the main bottleneck in extended 3D applications, the influence of mesh simplification in combination with texture mapping on the quality of 3D models was investigated. The fidelity of the simplified meshes was evaluated in relation to their resolution and with respect to key anatomical features. Large‐ and medium‐scale features were well preserved despite extensive 3D mesh simplification. Subtle fine‐scale features, particular in curved areas demonstrated the major limitation to extensive mesh size reduction. Depending on the local topography, workable mesh sizes ranging from 10% to 3% of the original size could be obtained, making them usable in various learning applications and environments.

An Improved Mechanical Sensorless Maximum Power Point Tracking Method for Permanent-Magnet Synchronous Generator-Based Small Wind Turbines Systems

This article proposes an improved maximum power point tracking (MPPT) method without mechanical and voltage sensors for small wind turbines (SWT) systems. The technique is suitable for SWT systems that employ a permanent-magnet synchronous generator (PMSG), a three-phase diode bridge rectifier, and a dc–dc converter, which is one of the most popular configuration for this kind of system. The proposed MPPT extracts the maximum available power from the PMSG operating with variable speed, and it is based on the output power characteristic in relation to the output current of the rectifier. The article proves that a constant output current in the rectifier ensures extracting the maximum electrical power available in the SWT system, independent of the rotational speed. Additionally, this constant current value depends solely on the PMSG characteristics. Therefore, the proposed MPPT control strategy is a simple current mesh with a constant reference that is implemented in a dc–dc converter connected in series to the rectifier, which is responsible to guarantee a constant current in the rectifier output. The proposed MPPT method was corroborated through simulation and experimental results in a 1.5-kW SWT. The tracking efficiency of the proposed MPPT was close to 97.64%.

Constrained Remeshing Using Evolutionary Vertex Optimization

AbstractWe propose a simple yet effective method to perform surface remeshing with hard constraints, such as bounding approximation errors and ensuring Delaunay conditions. The remeshing is formulated as a constrained optimization problem, where the variables contain the mesh connectivity and the mesh geometry. To solve it effectively, we adopt traditional local operations, including edge split, edge collapse, edge flip, and vertex relocation, to update the variables. Central to our method is an evolutionary vertex optimization algorithm, which is derivative‐free and robust. The feasibility and practicability of our method are demonstrated in two applications, including error‐bounded Delaunay mesh simplification and error‐bounded angle improvement with a given number of vertices, over many models. Compared to state‐of‐the‐art methods, our method achieves higher remeshing quality.

High order approximation of Hodge Laplace problems with local coderivatives on cubical meshes

In mixed finite element approximations of Hodge Laplace problems associated with the de Rham complex, the exterior derivative operators are computed exactly, so the spatial locality is preserved. However, the numerical approximations of the associated coderivatives are nonlocal and can be regarded as an undesired effect of standard mixed methods. For numerical methods with local coderivatives, a perturbation of low order mixed methods in the sense of variational crimes has been developed for simplicial and cubical meshes. In this paper we extend the low order method to all high orders on cubical meshes using a new family of finite element differential forms on cubical meshes. The key theoretical contribution is a generalization of the linear degree, in the construction of the serendipity family of differential forms, and this generalization is essential in the unisolvency proof of the new family of finite element differential forms.

3D simulation of complex fractures with a simple mesh

AbstractRock masses are 3D in nature. The contained complex fracture networks pose great difficulty to its computer‐aided design (CAD) modeling and bring meshing burdens to classic finite element analysis (FEA). Considering the efficiency of digital images capturing complex geometries, as an extension of the previous 2D work, the 3D implementation of the image‐based simulation is carried out in this work. Continuous‐discontinuous deformations of complex rock masses are simulated in 3D with a simple structured mesh based on the numerical manifold method (NMM). Characteristics of the developed voxel crack model and its differences with discrete and smeared crack models are summarized. Based on this voxel crack model, the generating algorithm of 3D physical patches to construct the continuous‐discontinuous trial function is introduced in detail. In the developed method, the three spatial resolutions, respectively of the image model, integration voxels, and mathematical elements, are independent. These resolutions can be chosen freely by trading off the accuracy need and the computational expenses. Numerical examples investigate the accuracy and convergence of this method. Its 3D simulation capability of complex rock masses is demonstrated by calculating the continuous‐discontinuous deformation of El Capitan rock located in the Yosemite National Park with assumed complex fracture networks.

Systematic implementation of higher order Whitney forms in methods based on discrete exterior calculus

We present a systematic way to implement higher order Whitney forms in numerical methods based on discrete exterior calculus. Given a simplicial mesh, we first refine the mesh into smaller simplices which can be used to define higher order Whitney forms. Cochains on this refined mesh can then be interpolated using higher order Whitney forms. Hence, when the refined mesh is used with methods based on discrete exterior calculus, the solution can be expressed as a higher order Whitney form. We present algorithms for the three required steps: refining the mesh, solving the coefficients of the interpolant, and evaluating the interpolant at a given point. With our algorithms, the order of the Whitney forms one wishes to use can be given as a parameter so that the same code covers all orders, which is a significant improvement on previous implementations. Our algorithms are applicable with all methods in which the degrees of freedom are integrals over mesh simplices — that is, when the solution is a cochain on a simplicial mesh. They can also be used when one simply wishes to approximate differential forms in finite-dimensional spaces. Numerical examples validate the generality of our algorithms.

Angle-bounded 2D mesh simplification

We describe a method to simplify a 2D triangle mesh through decimation while preserving its quality by means of maintaining a strict lower bound on inner angles. Conformance to boundaries, interfaces, and feature constraints is preserved as well. Multiple options and strategies for the choice of local decimation operators and for the settling of geometric degrees of freedom are proposed and explored. A systematic evaluation leads to a final recommendation for the most beneficial approach. The resulting method enables the efficient generation of more parsimonious meshes than those obtained from existing methods, while exhibiting the same quality in terms of worst element shape, as is relevant, for instance, in finite element analysis and numerical simulation.

Reconstruction method of equilibrated flux for a posteriori error estimate of elliptic problems

In this paper, a method which reconstructs an H(div)-conforming local equilibrated flux is presented for equilibrated flux-based a posteriori error estimate for the finite element method of the second-order elliptic problem. The flux is reconstructed in the lowest-order Raviart–Thomas spaces for finite element approximation. For a simplicial mesh, the reconstruction which performed on every element rather than on the patch of the elements of the mesh or on the dual mesh is achieved by solving a third (or fourth)-order linear equations on every element and a second-order linear equations on every edge or face. So, the amount of computational work is small. Numerical examples demonstratex the effectiveness and improvements of our method.

Analyzing effects of temperature gradient and scan rate on metal additive manufacturing microstructure by using phase field-finite element method

Predicting the evolutionary behavior of microstructures with the help of numerical simulation techniques has become an essential tool for studying the solidification process of metal additive manufacturing. As a mesoscopic model based on the diffusion interface theory, phase field method (PFM) can be used to predict the evolution of solidification microstructure. The open-source PFM framework PRISMS-PF can not only efficiently solve systems of equations with billions of degrees of freedom, but also provide a simple adaptive mesh control module. In this paper, based on the open-source PFM framework PRISMS-PF, a phase field-finite element method (PFM-FEM) simulation flow for the solidification process of A356 aluminum alloy additive manufacturing in the two-dimensional case was established. The effects of temperature gradient, scan rate and initial solid-phase morphology on solute concentration, dendrite spacing and dendrite morphology were analyzed and compared with experimental results for verification. Analyzing the results for different temperature gradients and scan rates cases, it was found that the increase of temperature gradient or scan rate made the primary dendrite arm space decrease; as the ratio of temperature gradient to scan rate decreased, the solidification morphology gradually changed from flat crystal to cellular crystal, columnar crystal, and even dendritic structure. Analyzing the results for different initial solid-phase morphology cases, it was found that the influence of initial solid-phase morphology on dendrite growth increased as the ratio of temperature gradient to scan rate decreased. The above influence rules were mainly related to the composition overcooling zone under different conditions. This paper is expected to provide a theoretical support for the effective regulation of solidification microstructure in metal additive manufacturing.

Feature-preserving mesh simplification through anisotropic Nyquist-based adaptive sampling of points inside the segmented regions

Feature-preserving mesh simplification through anisotropic Nyquist-based adaptive sampling of points inside the segmented regions

Predictions of the Spray Characteristics of Model Gasoline, Ethanol and Ethanol-in Gasoline Fuel Blends

This paper presents predictions of spray characteristics of model gasoline, ethanol gasoline-ethanol fuel blends. Fuel breakup models and correlations between flow patterns and droplet characteristics were adopted and implemented in OpenFOAM Computational Fluid Dynamics (CFD) modeling suite l for direct gasoline injector using a simple cylindrical mesh structure at constant volume. The Rosin Rammler distribution model was used to generate the number of spray particles injected into the cylinder. The spray modeling and atomization employed the use of blob sheet model and KH-RT model while the numerical technique for simulating atomization process by CFD included the use of governing equations such as Eulerian for gas phase, Lagrangian for disperse phase and turbulence modeling. Spray evolution at various energizing times particle density and The Sauter Mean Diameter (SMD) relationships and particle size distribution were studied in simulation mode. The results showed that with longer injection time frame and wider injection angle, the penetration width was wider and the penetration length deeper (longer) resulting in better atomization. Concerning particle density and its distribution, as number of particle increased, the density of clusters became smaller.

SIMULATION STUDY OF BREAKUP AND ATOMIZATION CHARACTERISTICS OF GASOLINE-ETHANOL (GASHOLS) FUEL BLENDS

To meet the increasingly stringent constraints on mobile and point emissions in the wake of the dwindling fortunes of fossil fuels, evaluation of hybrid fuels for application in combustion engines has become an imperative, especially in the third world countries. This paper presents, modeling of atomization characteristics of gasoline-ethanol fuel blends. Fuel breakup models and correlations between flow patterns and droplet characteristics were adopted and implemented in OpenFOAM Computational Fluid Dynamics (CFD) modeling suite for direct gasoline injector using a simple cylindrical mesh structure at constant volume. The Rosin Rammler distribution model was used to generate the number of spray particles injected into the cylinder. The spray modeling and atomization employed the use of blob sheet model and Kelvin-Helmholtz-Rayleigh-Taylor (KH-RT) model while the numerical technique for simulating atomization process by CFD included the use of governing equations such as Eulerian for gas phase, Lagrangian for disperse phase and turbulence modeling. The effects of fuel blends, injection pressure, ambient gas pressure and spray cone angle were evaluated on the axial spray tip penetration, spray width, and overall Sauter Mean Diameter (SMD). The SMD was seen to be affected by varying the degree of injection cone angle. The spray tip penetration lengths were larger for higher injection cone angles while higher penetration lengths were obtained at higher injection pressures. One salient conclusion drawn from the modeling is that as the number of particle increased, the density of clusters became smaller.

Delaunay Mesh Construction and Simplification with Feature Preserving Based on Minimal Volume Destruction

Triangular meshes play critical roles in many applications, such as numerical simulation and additive manufacturing. However, the triangular meshes transformed from computer-aided design models using common algorithms may have many undesirable narrow triangles, which tends to affect the downstream applications. In this paper, we proposed two algorithms for Delaunay mesh construction and simplification to improve the quality of the triangular meshes. Two improved mesh operations of inserting vertices and collapsing vertices based on the principle of minimum volume destruction were designed. The improved vertex inserting operation is able to modify the local mesh so that it will conform to the local Delaunay property. The improved vertex collapsing operation can realize the simplification of the original mesh while maintaining the local Delaunay property. The results of visualized rendering and thermal diffusion simulations verified the improvement of the proposed algorithms in the aspects of the quantity and quality of the meshes.

メッシュ制約型離散点法を用いた移動境界流れの数値解法の検討

Meshfree particle methods are known as a powerful tool for complex numerical continuum analyses, including migration or large deformation of boundaries. However, the methods commonly tend to need higher computational costs for stable stencil calculation than mesh-based methods because the computational points, called particles, are heterogeneously distributed in a domain. To overcome this issue, we developed the mesh-constrained discrete point (MCD) approach. The MCD method can perform the stencil calculation efficiently because of constraining the arrangement of discrete points (DPs) using simple background mesh systems such as the Cartesian grids. In this study, we further develop the MCD method to address moving boundary problems. In the developed formulation, the arrangements of DP positions and related calculation masks are updated every time that follows the moving boundary. The validity of the proposed method is investigated in a simple numerical example for a moving body in two-circular channels. The calculation masks for the DPs are adequately updated even when the moving boundary crosses the background mesh.

Shaping of comminuted maxilla fractures with titanium mesh

Multiply comminuted fragmented fracturesof the maxillofacial area are difficult to fix with titanium plates because of the small size of fragments, complex 3D anatomy, thin bone which is unable to hold screws and multidirectional pull of muscles.This study intend to present a case series of extremely comminuted maxilla fractures involving orbital floor both of which rereconstructed with Titanium mesh, cut to shape and used to mold the small fragmented segments in to the shape of the facial bones. Severe fragmentation of maxillary wall leads to facial hollowing, tissue prolapse and asymmetry even after major facial buttresses are reconstructed. Simple Titanium mesh can be used to reconstruct these severe fragmentations of thin bones of the maxillary wall as shown in the series and avoid late and unsightly complications.

Three-Dimensional Reconstruction Algorithm for CT Pulmonary Angiography in Patients with Pulmonary Embolism Combined with Syncope

This paper aimed to study the clinical characteristics of patients with pulmonary embolism (PE) with syncope (PE + S) based on the three-dimensional (3D) reconstruction algorithm in computed tomography (CT) pulmonary angiography (CTPA). In this study, 857 patients with acute PE (APE) who were treated in hospital were selected as the research objects and divided into syncope group (group S) and nonsyncope group (group NS). The 3D reconstruction marching cubes (3DR-MC) algorithm was compared with the traditional MC (T-MC) algorithm and the mesh simplification MC (MMS-MC) algorithm, and the results proved that the running time of the 3DR-MC algorithm on the platform was shorter than that of the other two algorithms. The incidence of syncope in group S in women was higher than that in group NS (51.7% vs. 38.2%). The incidence of syncope classified as high risk in group S was higher than that in group NS, and the mortality rate of pulmonary embolism patients with syncope was higher, and the difference was statistically significant (χ2 = 113.332, P < 0.05 ). The incidence of syncope in group S was higher than that in group NS (χ2 = 4.074, P < 0.05 ). In short, hypertension was an independent risk factor for syncope. PE + S patients could be diagnosed and treated as early as possible based on the clinical characteristics, so as to reduce the adverse consequences of misdiagnosis.

Efficient simulation of heterogeneous materials with the finite cell method

AbstractThe finite cell method (FCM) represents a combination of high‐order finite elements with the fictitious domain approach. Due to it's simple mesh generation the FCM reduces the pre‐processing effort. For heterogeneous problems of solid mechanics however, discontinuities occur at the material interfaces, which cannot be captured by the smooth shape functions of the FCM anymore, whereby the convergence deteriorates. Thus, to recover the optimal convergence rate, we extend the FCM ansatz by specially designed shape functions, which are able to capture discontinuities at the material interfaces. To get more insight into the problem, we study the performance of the proposed method by means of a two‐dimensional example.

Effects of Different Parameter Settings for 3D Data Smoothing and Mesh Simplification on Near Real-Time 3D Reconstruction of High Resolution Bioceramic Bone Void Filling Medical Images.

Three-dimensional reconstruction plays a vital role in assisting doctors and surgeons in diagnosing the healing progress of bone defects. Common three-dimensional reconstruction methods include surface and volume rendering. As the focus is on the shape of the bone, this study omits the volume rendering methods. Many improvements have been made to surface rendering methods like Marching Cubes and Marching Tetrahedra, but not many on working towards real-time or near real-time surface rendering for large medical images and studying the effects of different parameter settings for the improvements. Hence, this study attempts near real-time surface rendering for large medical images. Different parameter values are experimented on to study their effect on reconstruction accuracy, reconstruction and rendering time, and the number of vertices and faces. The proposed improvement involving three-dimensional data smoothing with convolution kernel Gaussian size 5 and mesh simplification reduction factor of 0.1 is the best parameter value combination for achieving a good balance between high reconstruction accuracy, low total execution time, and a low number of vertices and faces. It has successfully increased reconstruction accuracy by 0.0235%, decreased the total execution time by 69.81%, and decreased the number of vertices and faces by 86.57% and 86.61%, respectively.

A low-order divergence-free H(div)-conforming finite element method for Stokes flows

Abstract In this paper, we propose a ${\textbf{P}_{1}^{c}}\oplus{RT0}-P0$ discretization of the Stokes equations on general simplicial meshes in two/three dimensions, which yields an exactly divergence-free and pressure-independent velocity approximation with optimal order. Our method has the following features. First, the global number of the degrees of freedom (DOFs) of our method is the same as the low-order Bernardi and Raugel ($B$-$R$) finite element method (Bernardi & Raugel, 1985, Analysis of some finite elements for the Stokes problem. Math. Comp., 44, 71–79), while the number of the nonzero entries of the former is about half of the latter in the velocity–velocity region of the coefficient matrix. Secondly, the ${\textbf{P}_{1}^{c}}$ component of the velocity, the $RT0$ component of the velocity and the pressure seem to solve a popular ${\textbf{P}_{1}^{c}}-{RT0}-P0$ discretization of a poroelastic-type system formally. Finally, our method can be easily transformed into a pressure-robust and stabilized ${\textbf{P}_{1}^{c}}-P0$ discretization for the Stokes problem via the static condensation of the $RT0$ component, which has a much smaller number of global DOFs. Numerical experiments illustrating the robustness of our method are also provided.