Mesh Simplification Research Articles

3D RECONSTRUCTION AND MESH OPTIMIZATION OF UNDERWATER SPACES FOR VIRTUAL REALITY

Abstract. In this contribution, we propose a versatile image-based methodology for 3D reconstructing underwater scenes of high fidelity and integrating them into a virtual reality environment. Typically, underwater images suffer from colour degradation (blueish images) due to the propagation of light through water, which is a more absorbing medium than air, as well as the scattering of light on suspended particles. Other factors, such as artificial lights, also, diminish the quality of images and, thus, the quality of the image-based 3D reconstruction. Moreover, degraded images have a direct impact on the user perception of the virtual environment, due to geometric and visual degenerations. Here, it is argued that these can be mitigated by image pre-processing algorithms and specialized filters. The impact of different filtering techniques on images is evaluated, in order to eliminate colour degradation and mismatches in the image sequences. The methodology in this work consists of five sequential pre-processes; saturation enhancement, haze reduction, and Rayleigh distribution adaptation, to de-haze the images, global histogram matching to minimize differences among images of the dataset, and image sharpening to strengthen the edges of the scene. The 3D reconstruction of the models is based on open-source structure-from-motion software. The models are optimized for virtual reality through mesh simplification, physically based rendering texture maps baking, and level-of-details. The results of the proposed methodology are qualitatively evaluated on image datasets captured in the seabed of Santorini island in Greece, using a ROV platform.

How many sample points are sufficient for 3D model surface representation and accurate mesh simplification?

Growing of 3D model products and its applications in mobile devices and multimedia tools increases demands to establish an effective approach for representing and compressing of these models. In this paper, we propose an algorithm to simplify a complex 3D mesh and reduce the number of vertices by re-sampling the mesh based on the Nyquist theorem in order to find the sufficient number of samples that is necessary to save the quality of the reconstructed mesh, precisely. To achieve the optimum number of samples in the simplified mesh, both maximum curvature (Cmax) and minimum curvature (Cmin) in the original mesh are employed for adaptive sampling in different directions. Since the samples are adaptively taken regarding the curvature variations in both directions of maximum and minimum curvatures, the least number of vertices is obtained to represent the model. Hence, the method not only simplifies the complex mesh, but also preserves fine scale features in the mesh. The proposed method is applied to different complex mesh surfaces. The experimental results demonstrate that our proposed framework can represent a mesh surface with the least number of samples besides preserving important features in the surface.

Adaptive BEM for elliptic PDE systems, part I: abstract framework, for weakly-singular integral equations

In the present work, we consider weakly-singular integral equations arising from linear second-order elliptic PDE systems with constant coefficients, including, e.g. linear elasticity. We introduce a general framework for optimal convergence of adaptive Galerkin BEM. We identify certain abstract conditions for the underlying meshes, the corresponding mesh-refinement strategy, and the ansatz spaces that guarantee that the weighted-residual error estimator is reliable and converges at optimal algebraic rate if used within an adaptive algorithm. These conditions are satisfied, e.g. for discontinuous piecewise polynomials on simplicial meshes as well as certain ansatz spaces used for isogeometric analysis. Technical contributions include the localization of (non-local) fractional Sobolev norms and local inverse estimates for the (non-local) boundary integral operators associated to the PDE system.

Mesh Simplification by Curvature-Enhanced Quadratic Error Metrics

Polygonal meshes have a significant role in computer graphics, design and manufacturing technology for surface representation and it is often required to reduce their complexity to save memory. An efficient algorithm for detail retaining mesh simplification is proposed; in particular, the method presented is an iterative edge contraction algorithm based on the work of Garland and Heckberts. The original algorithm is improved by enhancing the quadratic error metrics with a penalizing factor based on discrete Gaussian curvature, which is estimated efficiently through the Gauss-Bonnet theorem, to account for the presence of fine details during the edge decimation process. Experimental results show that this new algorithm helps preserve the visually salient features of the model without compromising performance.

A transient three-dimensional model for thermo-fluid simulation of cryogenic plate-fin heat exchangers

This work proposes a novel, three-dimensional model for transient simulation of cryogenic plate-fin heat exchangers (PFHE). This model is based on the combination of computational fluid dynamics with well-established correlations for calculating heat transfer and pressure drop occurring during fluid flow through various fin types. This reduces the complex geometry of a PFHE to a geometrically simple mesh, allowing for efficient simulation of large-scale industrial PFHE. Successful validation of the model is carried out using both data available in the literature and results calculated using commercial software. The necessity for a three-dimensional model is further demonstrated using a transient case study in which the design of inlet distributors is shown to cause unfavorable distribution of fluid flow and hence severe temperature maldistribution in the PFHE. These results show that the proposed model can be useful in both detailed engineering and lifetime investigations of flexible PFHE.

EMBEDDED MULTILEVEL MONTE CARLO FOR UNCERTAINTY QUANTIFICATION IN RANDOM DOMAINS

The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for uncertainty quantification (UQ) in partial differential equation (PDE) models. It combines approximations at different levels of accuracy using a hierarchy of meshes whose generation is only possible for simple geometries. On top of that, MLMC and Monte Carlo (MC) for random domains involve the generation of a mesh for every sample. Here we consider the use of embedded methods which make use of simple background meshes of an artificial domain (a bounding-box) for which it is easy to define a mesh hierarchy. We use the recent aggregated finite element method (AgFEM) method, which permits to avoid ill-conditioning due to small cuts, to design an embedded MLMC (EMLMC) framework for (geometrically and topologically) random domains implicitly defined through a random level-set function. Predictions from existing theory are verified in numerical experiments and the use of AgFEM is statistically demonstrated to be crucial for complex and uncertain geometries in terms of robustness and computational cost.

A Simple Immersed Boundary Method for Modeling Forced Convection Heat Transfer

Abstract As nonbody-conforming numerical methods using simple Cartesian mesh, immersed boundary methods have become increasingly popular in modeling fluid–solid interaction. They usually do this by adding a body force term in the momentum equation. The magnitude and direction of this body force ensure that the boundary condition on the solid–fluid interface are satisfied without invoking complicated body-conforming numerical methods to impose the boundary condition. A similar path has been followed to model forced convection heat transfer by adding a source term in the energy equation. The added source term will ensure that thermal boundary conditions on the solid–fluid interface are imposed without invoking a boundary conforming mesh. These approaches were developed to handle the Dirichlet boundary condition (constant wall temperature). Few of them deal with the Neumann boundary condition (constant wall heat flux). This paper presents a simple new immersed boundary method. It can deal with the Dirichlet boundary condition, Neumann boundary condition, and conjugated heat transfer by adding an energy source or sink term in the energy conservation equation. The presented approach is validated against the analytical solutions and a very good match is achieved.

Numerical Analysis of a Stable Finite Volume Scheme for a Generalized Thermistor Model

Abstract A generalized thermistor model is discretized thanks to a fully implicit vertex-centered finite volume scheme on simplicial meshes. An assumption on the stiffness coefficients is mandatory to prove a discrete maximum principle on the electric potential. This property is fundamental to handle the stability issues related to the Joule heating term. Then the convergence to a weak solution is established. Finally, numerical results are presented to show the efficiency of the methodology and to illustrate the behavior of the temperature together with the electric potential within the medium.

New boundary conditions for simulating the filling stage of the injection molding process

PurposeThe purpose of this paper is to develop new boundary conditions for simulating the injection molding process of polymer melts.Design/methodology/approachThe boundary conditions are derived and implemented to simulate real-life air vents (used to allow the air escape from the mold). The simulations are performed in the computational library OpenFOAM® by considering two different fluid models, namely, Newtonian and generalized Newtonian (Bird–Carreau model).FindingsA detailed study on the accuracy of the solver interFoam for simulating the filling stage is presented, by considering simple geometries and adaptive mesh refinement. The verified code is then used to study the three-dimensional filling of a more complex geometry.Originality/valueThe results obtained showed that the numerical method is stable and allows one to model the filling process, simulating the real injection molding process.

Mesh Simplification Algorithms for Rendering Performance

Mesh Simplification Algorithms for Rendering Performance

A two dimensional VCFEM formulated with plastic, creep and thermal strain for simulate fatigue of porous material

In this paper, a two-dimensional Voronoi cell finite element model is developed for analyzing homogeneous materials containing dispersed voids in the matrix. The complementary energy functional, formulated with plastic, creep and thermal strain, is applied for the numerical simulation of fatigue behavior of porous materials under different conditions. The paper starts with a description of 2D porous material. To complete the computation of nonlinear strain, the constitutive relation of material in the complementary energy functional is changed. In order to verify the validity and accuracy of the model, the result of simulations is compared with the counterpart of the normal displacement finite element program ABAQUS. The comparison results suggest that the VCFEM, with the same accuracy, have the advantages of simple meshing, faster computation. In the numerical simulation, the model is applied for simulating low-cycle fatigue, variable temperature low cycle fatigue and thermo-mechanical fatigue, at the same time, the influence of porosity is also discussed.

Enveloping CAD models for visualization and interaction in XR applications

3D visualization of and interaction with CAD models are fundamental tasks in web and mobile XR applications. Meshes of CAD model surfaces, however, have too many triangles to be interactively rendered in these environments. Despite all development in mesh simplification literature, currently, there is no algorithm capable of producing a low-poly representation of the CAD model’s outer shape with only thousands of triangles. In this work, we propose a new automatic method to obtain a radically simplified representation of a CAD model by computing an adaptive envelope that wraps it. This envelope is represented by a 2-manifold triangular mesh that iteratively approximates the outer surface of the CAD model to capture its details. The envelope’s topology allows the surface to be further decimated using classical algorithms to reach the desired resolution. Furthermore, the representation proposed here can also be easily parameterized to obtain texture coordinates and then apply a texture baking technique. We also present an evaluation of the geometric and visual error of our method using real models.

A Simple Method for Network Visualization

In this article, we present a simple method for network visualization. The proposed method is based on distmesh [P.O. Persson and G. Strang, A simple mesh generator in MATLAB, SIAM Review 46 (2004) pp. 329–345], which is a simple unstructured triangular mesh generator for geometries represented by a signed distance function. We demonstrate a good performance of the proposed algorithm through several network visualization examples.

Kinetic Shape Reconstruction

Converting point clouds into concise polygonal meshes in an automated manner is an enduring problem in computer graphics. Prior works, which typically operate by assembling planar shapes detected from input points, largely overlooked the scalability issue of processing a large number of shapes. As a result, they tend to produce overly simplified meshes with assembling approaches that can hardly digest more than 100 shapes in practice. We propose a shape assembling mechanism that is at least one order of magnitude more efficient, both in time and in number of processed shapes. Our key idea relies upon the design of a kinetic data structure for partitioning the space into convex polyhedra. Instead of slicing all the planar shapes exhaustively as prior methods, we create a partition where shapes grow at constant speed until colliding and forming polyhedra. This simple idea produces a lighter yet meaningful partition with a lower algorithmic complexity than an exhaustive partition. A watertight polygonal mesh is then extracted from the partition with a min-cut formulation. We demonstrate the robustness and efficacy of our algorithm on a variety of objects and scenes in terms of complexity, size, and acquisition characteristics. In particular, we show the method can both faithfully represent piecewise planar structures and approximate freeform objects while offering high resilience to occlusions and missing data.

LEoPart: A particle library for FEniCS

This paper introduces LEoPart, an add-on for the open-source finite element software library FEniCS to seamlessly integrate Lagrangian particle functionality with (Eulerian) mesh-based finite element (FE) approaches. LEoPart- which is so much as to say: ‘Lagrangian–Eulerian on Particles’ - contains tools for efficient, accurate and scalable advection of Lagrangian particles on simplicial meshes. In addition, LEoPart comes with several projection operators for exchanging information between the scattered particles and the mesh and vice versa. These projection operators are based on a variational framework, which allows extension to high-order accuracy. In particular, by implementing a dedicated PDE-constrained particle–mesh projection operator, LEoPart provides all the tools for diffusion-free advection, while simultaneously achieving optimal convergence and ensuring conservation of the projected particle quantities on the underlying mesh. A range of numerical examples that are prototypical to passive and active tracer methods highlight the properties and the parallel performance of the different tools in LEoPart. Lastly, future developments are identified. The source code for LEoPart is actively maintained and available under an open-source license at https://bitbucket.org/jakob_maljaars/leopart.

Variational shape approximation of point set surfaces

In this work, we present a translation of the complete pipeline for variational shape approximation (VSA) to the setting of point sets. First, we describe an explicit example for the theoretically known non-convergence of the currently available VSA approaches. The example motivates us to introduce an alternate version of VSA based on a switch operation for which we prove convergence. Second, we discuss how two operations—split and merge—can be included in a fully automatic pipeline that is in turn independent of the placement and number of initial seeds. Third and finally, we present two approaches how to obtain a simplified mesh from the output of the VSA procedure. This simplification is either based on simple plane intersection or based on a variational optimization problem. Several qualitative and quantitative results prove the relevance of our approach.

Spectral Mesh Simplification

AbstractThe spectrum of the Laplace‐Beltrami operator is instrumental for a number of geometric modeling applications, from processing to analysis. Recently, multiple methods were developed to retrieve an approximation of a shape that preserves its eigenvectors as much as possible, but these techniques output a subset of input points with no connectivity, which limits their potential applications. Furthermore, the obtained Laplacian results from an optimization procedure, implying its storage alongside the selected points. Focusing on keeping a mesh instead of an operator would allow to retrieve the latter using the standard cotangent formulation, enabling easier processing afterwards. Instead, we propose to simplify the input mesh using a spectrum‐preserving mesh decimation scheme, so that the Laplacian computed on the simplified mesh is spectrally close to the one of the input mesh. We illustrate the benefit of our approach for quickly approximating spectral distances and functional maps on low resolution proxies of potentially high resolution input meshes.

A framework to perform high‐order deconvolution for finite‐volume method on simplicial meshes

SummaryIn this article, a new framework to design high‐order approximations in the context of node‐centered finite volumes on simplicial meshes is proposed. The major novelty of this method is that it relies on very simple and compact differential operators, which is a critical point to achieve good performances in the High‐performance computing context. This method is based on deconvolution between nodal and volume‐average values, which can be conducted to any order. The interest of the new method is illustrated through three different applications: mesh‐to‐mesh interpolation, levelset curvature computation, and numerical scheme for convection. Higher order can also be achieved within the present framework by introducing high‐rank tensors. Although these tensors feature much symmetries, their manipulation can quickly become an overwhelming task. For this reason and without loss of generality, the present articles are limited to third‐order expansion. This method, although tightly connected to the k‐exact schemes theory, does not rely on successive corrections: the high‐order property is obtained in a single operation, which makes them more attractive in terms of performances.

A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model

In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any elastic properties. The mathematical model is a simplified case of the seven-equation Baer–Nunziato model of compressible multi-phase flows. The resulting governing PDE system is a nonlinear system of hyperbolic conservation laws with non-conservative products. The geometry of the solid bodies is simply specified via a scalar field that represents the volume fraction of the fluid present in each control volume. This allows the discretization of arbitrarily complex geometries on simple uniform or adaptive Cartesian meshes. Inside the solid bodies, the fluid volume fraction is zero, while it is unitary inside the fluid phase. Due to the diffuse interface nature of the model, the volume fraction function can assume any value between zero and one in mixed cells that are occupied by both, fluid and solid.We also prove that at the material interface, i.e. where the volume fraction jumps from unity to zero, the normal component of the fluid velocity assumes the value of the normal component of the solid velocity. This result can be directly derived from the governing equations, either via Riemann invariants or from the generalized Rankine Hugoniot conditions according to the theory of Dal Maso et al. (1995)[89], which justifies the use of a path-conservative approach for treating the non-conservative products.The governing partial differential equations of our new model are solved on simple uniform Cartesian grids via a high order path-conservative ADER discontinuous Galerkin (DG) finite element method with a posteriori sub-cell finite volume (FV) limiter. Since the numerical method is of the shock capturing type, the fluid-solid boundary is never explicitly tracked by the numerical method, neither via interface reconstruction, nor via mesh motion.The effectiveness of the proposed approach is tested on a set of different numerical test problems, including 1D Riemann problems as well as supersonic flows over fixed and moving rigid bodies.

Evaluation of efficacy of self-gripping mesh in open and laparoscopic inguinal hernia repair

1.1 Background: Inguinal hernioplasty is one of the most common surgeries perfomed. With the extensive use of prosthetic mesh implants in open and laparoscopic inguinal hernia repair, recurrence rates have decreased substantially. Therefore, the focus has been shifted from the clinical outcomes, such as recurrence, towards patient-experienced endpoints, such as chronic pain. Use of self adhesive mesh eliminates the complication risk, increased operation time, and expense that come with the mechanical fixation of mesh. Hence this study, to prove the efficacy of self-gripping mesh in open and laparoscopic hernia repair in terms of post-op complications, recurrence rate and cost effectiveness. 1.2 Methods: A study was conducted between June 2017 and April 2019. Patients aged between 18 to 60 years with primary inguinal hernia were operated either open or laparoscopically using self-gripping mesh. The patients were followed up for 6 months to look for post-operative complications and recurrence. 1.3 Results: In total, 60 patients, 30 in open group and 30 in laparoscopic group underwent operation. Postoperative pain was low in both groups in comparison to previous studies on use of simple polypropylene mesh fixed with suture or tacker. Self-gripping mesh was found to be more cost effective as compared to polypropylene mesh with added cost of suture or tacker. 1.4 Conclusions: In conclusion use of self-gripping mesh in inguinal hernia repair either in open or laparoscopic method is more efficacious than simple polypropylene mesh.