Surface Mesh Research Articles

Interactive Invigoration: Volumetric Modeling of Trees with Strands

Generating realistic models of trees and plants is a complex problem because of the vast variety of shapes trees can form. Procedural modeling algorithms are popular for defining branching structures and steadily increasing their expressive power by considering more biological findings. Most existing methods focus on defining the branching structure of trees based on skeletal graphs, while the surface mesh of branches is most commonly defined as simple cylinders. One critical open problem is defining and controlling the complex details observed in real trees. This paper aims to advance tree modeling by proposing a strand-based volumetric representation for tree models. Strands are fixed-size volumetric pipes that define the branching structure. By leveraging strands, our approach captures the lateral development of trees. We combine the strands with a novel branch development formulation that allows us to locally inject vigor and reshape the tree model. Moreover, we define a set of editing operators for tree primary and lateral development that enables users to interactively generate complex tree models with unprecedented detail with minimal effort.

A molecular dynamics study on pore structure: Performance comparison between metal foam and artificial mesh porous surface

With the development of surface engineering, porous surfaces have emerged as a significant research subject in boiling heat transfer. The latter, in turn, plays a crucial role in various industries such as power plants, distillation plants, and microelectronic technology. In this paper, the Molecular Dynamics method is adopted to investigate the wicking dynamics and boiling dynamics of two porous surfaces: foam, which exhibits randomly distributed pores, and mesh, composed of ordered square wires with relatively uniform pore sizes. Three wettability, namely hydrophilic, neutral, and hydrophobic wetting states, are assigned to the two porous surfaces de-coupling the effect of wettability from surface structure. Results reveal that, during the wicking process, the foam surface shows better wetting ability as it absorbs liquid under both hydrophilic and neutral wettability. Comparatively, the mesh surface has the fastest wicking speed under hydrophilic wettability yet it becomes non-wetting under neutral wettability. During the boiling process, the boiling dynamics differ greatly under three wettability. More importantly, the difference in surface structure makes the foam surface possess a better heat transfer whereas the mesh surface causes gentle pressure variation. Our findings provide insights into the design of artificial porous surfaces for certain purpose and their potential application.

A Novel Computational Paradigm for Reconstructing Solid CAD Features from a Segmented Manifold Triangular Mesh

We introduce a novel computational paradigm for reconstructing solid computer-aided design (CAD) features from the surface of a segmented manifold triangular mesh. This paradigm addresses the challenge of capturing high-level design semantics for manifold triangular meshes and facilitates parametric and variational design capabilities. We categorize four prevalent features, namely extrusion, rotation, sweep, and loft, as generalized swept bodies driven by cross-sectional sketches and feature paths, providing a unified mathematical representation for various feature types. The numerical optimization-based approach conducts geometric processing on the segmented manifold triangular mesh patch, extracting cross-sectional sketch curves and feature paths from its surface, and then reconstructing appropriate features using the Open CASCADE kernel. We employ the personalized three-dimensional (3D) printed model as a case study. Parametric and variant designs of the 3D-printed models are achieved through feature reconstruction of the manifold triangular mesh obtained via 3D scanning.

Computational fluid dynamics of bladder voiding using 3D dynamic MRI.

Over the last couple of decades, image-based computational fluid dynamics (CFD) has revolutionized cardiovascular research by uncovering hidden features of wall strain, impact of vortices, and its use in treatment planning, as examples, that were simply not evident in the gold-standard catheterization studies done previously. In the work presented here, we have applied magnetic resonance imaging (MRI)-based CFD to study bladder voiding and to demonstrate the feasibility and potential of this approach. We used 3D dynamic MRI to image the bladder and urethra during voiding. A surface mesh processing tool was developed to process the bladder wall prior to executing a wall-motion driven CFD simulation of the bladder and urethra. The obtained flow rate and pressure were used to calculate urodynamic nomograms, which are currently used in the clinical setting to assess bladder voiding dysfunction. These nomograms concluded that our healthy volunteer has an unobstructed bladder and normal contractility. We calculated the work done to void the bladder and propose this as an additional quantitative metric to comprehensively assess bladder function. Further, we discuss the areas that would improve this relatively new methodology of image-based CFD in urodynamics.

Hydrogel Coated Mesh with Controlled Flux for Oil/Water Separation.

Superwetting surfaces are often applied in oil/water separation. Hydrogels have been widely prepared as superhydrophilic/underwater superoleophobic materials for oil/water separation since they are naturally hydrophilic. Hydrogels usually need to be combined with porous substrates such as stainless steel mesh (SSM) due to their poor mechanical properties. However, it is usually inevitable that the pores of the substrate are clogged during the actual preparation process, leading to a significant decrease in the flux, which limits its effective application. In this study, acrylic acid (AA), chitosan (CS) and modified silica were utilized to form a layer of dual-network PAA/CS@SiO2 hydrogel by photopolymerization on SSM, followed by a simple and novel ultrasonic-assisted pore-making method to generate numerous pores in situ on the surface of the hydrogel-coated mesh, which led to an increase in water flux from 0 to 70,000 L m-2 h-1 without decreasing the separation efficiency. After 100 separations of a mixture of n-hexane and water, the flux was still higher than 50,000 L m-2 h-1 with a separation efficiency above 99%, which is superior to most of hydrogel-coated meshes reported so far. Moreover, the prepared PAA/CS@SiO2 hydrogel-coated mesh also has good environmental stability, low swelling, and self-cleaning properties. We believe that the strategy of this study will provide a simple new perspective when hydrogels block the substrate pores, resulting in low water flux.

An efficient procedure for the blood flow computer simulation of patient-specific aortic dissections

In this work we present a novel methodology for the numerical simulation of patient-specific aortic dissections. Our proposal, which targets the seamless virtual prototyping of customized scenarios, combines an innovative two-step segmentation procedure with a CutFEM technique capable of dealing with thin-walled bodies such as the intimal flap. First, we generate the fluid mesh from the outer aortic wall disregarding the intimal flap, similarly to what would be done in a healthy aorta. Second, we create a surface mesh from the approximate midline of the intimal flap. This approach allows us to decouple the segmentation of the fluid volume from that of the intimal flap, thereby bypassing the need to create a volumetric mesh around a thin-walled body, an operation widely known to be complex and error-prone. Once the two meshes are obtained, the original configuration of the dissection into true and false lumen is recovered by embedding the surface mesh into the volumetric one and calculating a level set function that implicitly represents the intimal flap in terms of the volumetric mesh entities. We then leverage the capabilities of unfitted mesh methods, specifically relying on a CutFEM technique tailored for thin-walled bodies, to impose the wall boundary conditions over the embedded intimal flap. We tested the method by simulating the flow in four patient-specific aortic dissections, all involving intricate geometrical patterns. In all cases, the preprocess is greatly simplified with no impact on the computational times. Additionally, the obtained results are consistent with clinical evidence and previous research.

Morphological patterns and spatial probability maps of the inferior frontal sulcus in the human brain.

The inferior frontal sulcus (ifs) is a prominent sulcus on the lateral frontal cortex, separating the middle frontal gyrus from the inferior frontal gyrus. The morphology of the ifs can be difficult to distinguish from adjacent sulci, which are often misidentified as continuations of the ifs. The morphological variability of the ifs and its relationship to surrounding sulci were examined in 40 healthy human subjects (i.e., 80 hemispheres). The sulci were identified and labeled on the native cortical surface meshes of individual subjects, permitting proper intra-sulcal assessment. Two main morphological patterns of the ifs were identified across hemispheres: in Type I, the ifs was a single continuous sulcus, and in Type II, the ifs was discontinuous and appeared in two segments. The morphology of the ifs could be further subdivided into nine subtypes based on the presence of anterior and posterior sulcal extensions. The ifs was often observed to connect, either superficially or completely, with surrounding sulci, and seldom appeared as an independent sulcus. The spatial variability of the ifs and its various morphological configurations were quantified in the form of surface spatial probability maps which are made publicly available in the standard fsaverage space. These maps demonstrated that the ifs generally occupied a consistent position across hemispheres and across individuals. The normalized mean sulcal depths associated with the main morphological types were also computed. The present study provides the first detailed description of the ifs as a sulcal complex composed of segments and extensions that can be clearly differentiated from adjacent sulci. These descriptions, together with the spatial probability maps, are critical for the accurate identification of the ifs in anatomical and functional neuroimaging studies investigating the structural characteristics and functional organization of this region in the human brain.

Morphology of the scaphotrapeziotrapezoid joint: A multi-domain statistical shape modeling approach.

The scaphotrapeziotrapezoid (STT) joint is involved in load transmission between the wrist and thumb. A quantitative description of baseline STT joint morphometrics is needed to capture the variation of normal anatomy as well as to guide staging of osteoarthritis. Statistical shape modeling (SSM) techniques quantify variations in three-dimensional shapes and relative positions. The objectives of this study are to describe the morphology of the STT joint using a multi-domain SSM. We asked: (1) What are the dominant modes of variation that impact bone and articulation morphology at the STT joint, and (2) what are the morphometrics of SSM-generated STT joints? Thirty adult participants were recruited to a computed tomography study of normal wrist imaging and biomechanics. Segmentations of the carpus were converted to three-dimensional triangular surface meshes. A multi-domain, particle-based entropy system SSM was used to quantify variation in carpal bone shape and position as well as articulation morphology. Articular surface areas and interosseous proximity distributions were calculated between mesh vertex pairs on adjacent bones within distance (2.0 mm) and surface-normal angular (35°) thresholds. In the SSM, the first five modes of variation captured 76.2% of shape variation and contributed to factors such as bone scale, articular geometries, and carpal tilt. Median interosseous proximities-a proxy for joint space-were 1.39 mm (scaphotrapezium), 1.42 mm (scaphotrapezoid), and 0.61 mm (trapeziotrapezoid). This study quantifies morphological and articular variations at the STT joint, presenting a range of normative anatomy. The range of estimated interosseous proximities may guide interpretation of imaging-derived STT joint space.

An Unfitted Finite Element Poisson-Boltzmann Solver with Automatic Resolving of Curved Molecular Surface.

So far, the existing Poisson-Boltzmann (PB) solvers that accurately take into account the interface jump conditions need a pregenerated body-fitted mesh (molecular surface mesh). However, qualified biomolecular surface meshing and its implementation into numerical methods remains a challenging and laborious issue, which practically hinders the progress of further developments and applications of a bunch of numerical methods in this field. In addition, even with a molecular surface mesh, it is only a low-order approximation of the original curved surface. In this article, an interface-penalty finite element method (IPFEM), which is a typical unfitted finite element method, is proposed to solve the Poisson-Boltzmann equation (PBE) without requiring the user to generate a molecular surface mesh. The Gaussian molecular surface is used to represent the molecular surface and can be automatically resolved with a high-order approximation within our method. Theoretical convergence rates of the IPFEM for the linear PB equation have been provided and are well validated on a benchmark problem with an analytical solution (we also noticed from numerical examples that the IPFEM has similar convergence rates for the nonlinear PBE). Numerical results on a set of different-sized biomolecules demonstrate that the IPFEM is numerically stable and accurate in the calculation of biomolecular electrostatic solvation energy.

Postoperative facial prediction for mandibular defect based on surface mesh deformation

Objectives: This study aims to introduce a novel predictive model for the post-operative facial contours of patients with mandibular defect, addressing limitations in current methodologies that fail to preserve geometric features and lack interpretability.Methods: Utilizing surface mesh theory and deep learning, our model diverges from traditional point cloud approaches by employing surface triangular mesh grids. We extract latent variables using a Mesh Convolutional Restricted Boltzmann Machines (MCRBM) model to generate a three-dimensional deformation field, aiming to enhance geometric information preservation and interpretability.Results: Experimental evaluations of our model demonstrate a prediction accuracy of 91.2 %, which represents a significant improvement over traditional machine learning-based methods.Conclusions: The proposed model offers a promising new tool for pre-operative planning in oral and maxillofacial surgery. It significantly enhances the accuracy of post-operative facial contour predictions for mandibular defect reconstructions, providing substantial advancements over previous approaches.

Transient Three-Dimensional Measurement of Ice Crystal Accretion Using a Plenoptic Camera

Monitoring the three-dimensional formation of ice layers on airfoils during icing wind tunnel experiments is extremely challenging. For the first time, this paper demonstrates the use of a single plenoptic camera to perform transient, nonintrusive in situ measurements of ice crystal accretion. Experiments have been conducted in the Altitude Icing Wind Tunnel at the National Research Council of Canada under different icing conditions to assess the potential of the new technique. Using the camera in a close-up configuration, the results show the evolution of the three-dimensional shape of the accreted ice in high spatial and temporal resolution and in absolute metric units. The computed surface meshes allow for a detailed analysis in terms of ice shape, surface area, and ice volume. Posttest shapes are compared to measurements taken using a commercial laser scanner. Although not rated for ice surfaces, this device is used as a reference to compare the detailed surface structure after registering the data sets. The results of the two methods are in good agreement and show a mean relative deviation of the plenoptic camera of about 0.15 mm.

Laplacian2Mesh: Laplacian-Based Mesh Understanding.

Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation. When the input is a polygonal surface, one has to suffer from the irregular mesh structure. Motivated by the geometric spectral theory, we introduce Laplacian2Mesh, a novel and flexible convolutional neural network (CNN) framework for coping with irregular triangle meshes (vertices may have any valence). By mapping the input mesh surface to the multi-dimensional Laplacian-Beltrami space, Laplacian2Mesh enables one to perform shape analysis tasks directly using the mature CNNs, without the need to deal with the irregular connectivity of the mesh structure. We further define a mesh pooling operation such that the receptive field of the network can be expanded while retaining the original vertex set as well as the connections between them. Besides, we introduce a channel-wise self-attention block to learn the individual importance of feature ingredients. Laplacian2Mesh not only decouples the geometry from the irregular connectivity of the mesh structure but also better captures the global features that are central to shape classification and segmentation. Extensive tests on various datasets demonstrate the effectiveness and efficiency of Laplacian2Mesh, particularly in terms of the capability of being vulnerable to noise to fulfill various learning tasks.

Numerical study on the hydrodynamic performance of a high-speed taxiing fuselage: Investigation on the affecting factors in the numerical simulation

A seaplane, distinctively designed for water takeoffs and landings, differs significantly from conventional ships and airplanes in terms of hydrodynamic performance. Accurately assessing the hydrodynamic characteristics of a taxiing fuselage using traditional ship methods, particularly at high speeds, presents considerable challenges. Consequently, this study delves into an extensive investigation to explore the variables influencing numerical simulations, aiming for a comprehensive comprehension of the fuselage's hydrodynamic behavior during taxiing. The research begins by conducting numerical computations to analyze the fuselage's taxiing state across varying speed coefficients, comparing these against experimental data. Results indicate a critical threshold within a speed coefficient range of 3.5–4.5. Numerical outputs closely align with experimental observations below this range, while a noticeable deviation occurs beyond it. Concurrently, with increased speed, the fuselage wake elongates longitudinally and contracts laterally. A subsequent detailed investigation focuses on the condition where the speed coefficient equals 4, examining diverse numerical parameters. The findings emphasize the efficacy of the Realizable k−ε turbulence model during the high-speed taxiing phase of seaplanes. Additionally, it is evident that the scale of the surface mesh directly influences the computed surface liquid phase volume fractions upon model stabilization, subsequently impacting the model's orientation. Larger surface meshes can lead to significant numerical discrepancies.

Research on the performance of foamed concrete based on superhydrophobic bulk modification

Foamed concrete is a kind of lightweight insulation material formed by the uniform mixture of foam and cement slurry. The superhydrophobic bulk modification of foamed concrete can reduce its high water absorption and prolong its service life. In this paper, the compatibility of three hydrophobic agents named polydimethylsiloxane (PDMS), isoctyltriethoxysilane (ICTS) and SBT®-TIA with foams was studied, and the reasons of incompatibility were revealed. Then, the superhydrophobic bulk foamed concrete system was constructed by physical foaming method, adding polydimethylsiloxane (PDMS), calcium stearate (CS), nano-silica (NS) and covering the surface of the specimen with 200-mesh wire mesh. The results show that the maximum contact angles of the meshed surface and the internal polished surface of superhydrophobic foamed concrete were 162.7° and 153.5°, respectively. At the same time, the water absorption rate of the modified specimen was significantly reduced, and the reduction rate was up to 90 %. In addition, the deterioration degree of thermal insulation performance after soaking and the dry shrinkage rate were significantly reduced compared with ordinary foamed concrete. Scanning electron microscopy (SEM) revealed that increasing the multi-scale roughness could improve the hydrophobic properties of foamed concrete. Fourier infrared spectroscopy (FT-IR) also confirmed that low surface energy groups such as -CH2 and -CH3 in PDMS bonded to the cement hydration products, indicating the successful preparation of superhydrophobic bulk foamed concrete.

IMESH: A DSL for Mesh Processing

Mesh processing algorithms are often communicated via concise mathematical notation (e.g., summation over mesh neighborhoods). However, conversion of notation into working code remains a time-consuming and error-prone process, which requires arcane knowledge of low-level data structures and libraries—impeding rapid exploration of high-level algorithms. We address this problem by introducing a domain-specific language (DSL) for mesh processing called I MESH, which resembles notation commonly used in visual and geometric computing and automates the process of converting notation into code. The centerpiece of our language is a flexible notation for specifying and manipulating neighborhoods of a cell complex, internally represented via standard operations on sparse boundary matrices. This layered design enables natural expression of algorithms while minimizing demands on a code generation backend. In particular, by integrating I MESH with the linear algebra features of the I LA DSL and adding support for automatic differentiation, we can rapidly implement a rich variety of algorithms on point clouds, surface meshes, and volume meshes.

A Framework for Solving Parabolic Partial Differential Equations on Discrete Domains

We introduce a framework for solving a class of parabolic partial differential equations on triangle mesh surfaces, including the Hamilton-Jacobi equation and the Fokker-Planck equation. PDE in this class often have nonlinear or stiff terms that cannot be resolved with standard methods on curved triangle meshes. To address this challenge, we leverage a splitting integrator combined with a convex optimization step to solve these PDE. Our machinery can be used to compute entropic approximation of optimal transport distances on geometric domains, overcoming the numerical limitations of the state-of-the-art method. In addition, we demonstrate the versatility of our method on a number of linear and nonlinear PDE that appear in diffusion and front propagation tasks in geometry processing.

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.

Computational fluid dynamics in carbonate rock wormholes using magnetic resonance images as structural information

Computational fluid dynamics (CFD) is an essential tool with growing applications in many fields. In petrophysics, it is common to use computed tomography in those simulations, but in medicine, magnetic resonance imaging (MRI) is also being used as a basis for structural information. Wormholes are high-permeability structures created by the acidification of carbonate reservoirs and can impact reservoir production. CFD combined with MRI can benefit the study of wormholes in petrophysics, but combining both techniques is still a challenge. The objective of this study is to develop a pipeline for performing CFD in wormholes with MRI data. Using three samples of carbonate rocks acidified with 1.5% hydrochloric acid at 0.1, 1, and 10 ml/min, we acquired 300μm resolution T2-weighted images and experimental measurements of pressure data within flow rates of 5 to 50 ml/min. We applied cropping, bias field correction, non-local means denoising, and segmentation in the image processing step. For the 3D reconstruction, we used marching cubes to generate the surface mesh, the Taubin filter for surface smoothing, and boundary modeling with Blender. Finally, for the CFD, we generated volumetric meshes with cfMesh and used the OpenFOAM simpleFoam solver to simulate an incompressible, stationary, and laminar flow. We analyzed the effect of surface smoothing, estimating edge displacements, and measured the simulation pressure at the same flow rates as the experiments. Surface smoothing had a negligible impact on the overall edge position. For most flow rates, the simulation and experimental pressure measurements matched. A possible reason for the discrepancies is that we did not consider the surrounding porous media in the simulations. In summary, our work had satisfactory results, demonstrating CFD’s feasibility in studying wormholes using MRI.

A general-purpose IGA mesh generation method: NURBS Surface-to-Volume Guided Mesh Generation

AbstractThe NURBS Surface-to-Volume Guided Mesh Generation (NSVGMG) is a general-purpose mesh generation method, introduced to increase the scope of isogeometric analysis in computing complex-geometry problems. In the NSVGMG, NURBS patch surface meshes serve as guides in generating the patch volume meshes. The interior control points are determined independent of each other, with only a small subset of the surface control points playing a role in determining each interior point. In the updated version of the NSVGMG we are introducing in this article, in the process of determining the location of an interior point in a parametric direction, more weight is given to the closer guides, with the closeness measured along the guides in the other parametric directions. Tests with 2D and 3D shapes show the effectiveness of the NSVGMG in generating good quality meshes, and the robustness of the updated NSVGMG even in mesh generation for complex shapes with distorted boundaries.

Superconvergence of Differential Structure for Finite Element Methods on Perturbed Surface Meshes

Superconvergence of Differential Structure for Finite Element Methods on Perturbed Surface Meshes