Triangular Surface Research Articles

Filling the Holes on 3D Heritage Object Surface Based on Automatic Segmentation Algorithm

ABSTRACTReconstructing and processing 3D objects are activities in the research field of computer graphics, image processing and computer vision. The 3D objects are processed based on geometric modelling (a branch of applied mathematics and computational geometry) or machine learning algorithms based on image processing. The computation of geometrical objects includes processing the curves and surfaces, subdivision, simplification, meshing, holes filling or reconstructing the 3D surface's objects on both point cloud data and triangular mesh. While the machine learning methods are developed using deep learning models. With the support of 3D laser scan devices and LiDAR techniques, the obtained dataset is close to the original shape of the real objects. Besides, photography and its application based on modern techniques in recent years help us collect data and process the 3D models more precisely. This article proposes a new method for filling holes on the 3D object's surface based on automatic segmentation. Instead of filling the hole directly as the existing methods, we now subdivide the hole before filling it. The hole is first determined and segmented automatically based on the computation of its local curvature. It is then filled on each part of the hole to match its local curvature shape. The method can work on both 3D point cloud surfaces and triangular mesh surfaces. Compared to the state‐of‐the‐art (SOTA) methods, our proposed method obtained higher accuracy of the reconstructed 3D objects.

Synchronous measurement of wind pressure and flow field in wind tunnel: device, method and application

Accurate assessment of the relationship between flow field and surface wind pressure distribution around buildings in wind tunnel tests is crucial for understanding the interaction mechanism between wind and buildings. Despite notable technological advancements in dynamic pressure measurement and flow visualization, the acquirement of synchronous data on flow and wind pressure around buildings still faces challenges in terms of accuracy, cost, and operational complexity. Given this, a frame synchronization technique has been developed to collect flow field and wind pressure data based on particle image velocimetry and Scanivalve dynamic pressure measurement. Meanwhile, this study established a more precise correction method for the distortion effect of the synchronously measured wind pressure signal. Furthermore, the paper demonstrates the feasibility of synchronously measuring the flow field and the corrected wind pressure in time through the flow around triangular prism test. Experimental results indicate that the corrected wind pressure distribution on triangular prism surface is consistent with the temporal variations in instantaneous flow velocity and vorticity change, thereby verifying the reliability of the synchronous test system.

A reverse tracing of the water flow path algorithm for slope length extraction based on triangulated irregular network

Terrain factor is an important factor affecting soil erosion, in which slope length is an important indicator of terrain factor. In this paper, we model the regional topographic relief with triangulated irregular network TIN, use the slope aspect of the TIN triangular surface to determine the flow direction, and propose an algorithm (RT-WFP) for extracting the slope length by tracing the water flow trajectory in reverse direction. The slope cutoff point rule is set in the algorithm to improve the accuracy of the slope length extraction results. We calculated the slope length of the experimental area of the small watershed of Golden Hook-shaped collapsing hill in Bailu Township, Ganxian District, and the rationality of the algorithm proposed in this paper is verified through the comparison and analysis with the traditional slope length extraction algorithm. The experimental results show that, compared with the traditional D8 algorithm, the water flow path extracted by this algorithm in the experimental area more closely matches the water flow path based on contour mapping, and the slope length extracted by this algorithm has a lower sensitivity to the resolution of the data, and the percentage of cells with a slope length value of no more than 300 m (the limit standard of the RUSLE model) at a resolution of 30 m reaches 94.19%.

Theoretical analysis of effect of MHD, couple stress and slip velocity on squeeze film lubrication of rough Triangular plates

In this study, Christensen's stochastic theory is utilized on rough surfaces' hydrodynamic lubricating effect to examine how surface roughness, couple stress fluid, slip velocity, magnetohydrodynamic (MHD), and the triangular surface interact. Modified Reynolds equation is derived analytically using combining theories of Stokes couple stresses, Lorentz forces, and Christensen's stochastic hypothesis about hydrodynamic lubrication. Pressure, load carrying capacity and squeeze film time expression is derived mathematically using Reynolds equation that accounts for surface roughness and coupling stress. For various parameters including rough parameter, slip velocity, Hartmann number, and couple stress, the lubricating characteristics are analysed graphically. Squeeze film time, load carrying capacity, and pressure are enhanced by an increase in slip velocity, couplestress and magnetic field. The lubrication characteristics decreases (increases) on squeeze film pressure, load carrying capacity and squeeze film time through increasing values of the longitudinal (transverse) roughness parameter.

CFD-DEM coupled study of erosion resistance characteristics of ribbed walls

Industrial bulk material transfer systems are exposed to high erosion risk due to prolonged scouring by particle flow. In order to improve the erosion resistance of the system components, this study proposes a wear-resistant improvement scheme by adding square and triangular ribs on the wall surface. A coupled CFD-DEM method was used to analyse the abrasion characteristics of particle flow hitting the flat and ribbed wall surfaces at different particle incidence angles, particle velocities and particle volume fractions. The results show that square ribbed plate is more targeted to reduce the erosion ratio of the groove surface and transfer the risk to the ribs, whereas triangular ribbed plate provides an optimal balance between sacrificial velocity and erosion resistance of the ribbed structure; moreover, square ribbed plate is slightly more capable of transferring the maximum wear to the ribs to reduce the risk of perforation of the wall surface. As the particle velocity increased from 5 m/s to 25 m/s, the triangular ribbed plate reduced the erosion ratio by up to 45 %; both square and triangular ribbed plate groove surfaces reduced the maximum wear rate by about 65 % and 35 %, respectively. With the increase of particle volume fraction from 0.025 % to 0.125 %, the erosion ratios of the square and triangular ribbed plates decreased rapidly by up to 16 % and 73 %, respectively; the groove surface of the square ribbed plate decreased by about 63 % of the maximum wear rate, while the groove surface of the triangular ribbed plate decreased by up to 48 % of the maximum wear rate.

Distance‐Based Smoothing of Curves on Surface Meshes

AbstractThe smoothing of surface curves is an essential tool in mesh processing, important to applications that require segmenting and cutting surfaces such as surgical planning. Surface curves are typically designed by professionals to match certain surface features. For this reason, the smoothed curves should be close to the original and easily adjustable by the user in interactive tools. Previous methods achieve this desired behavior, e.g., by utilizing energy‐minimizing splines or generalizations of Bézier splines, which require a significant number of control points and may not provide interactive frame rates or numerical stability. This paper presents a new algorithm for robust smoothing of discrete surface curves on triangular surface meshes. By using a scalar penalty potential as the fourth coordinate, the given surface mesh is embedded into the 4D Euclidean space. Our method is based on finding geodesics in this lifted surface, which are then projected back onto the original 3D surface. The benefits of this approach include guaranteed convergence and good approximation of the initial curve. We propose a family of penalty potentials with one single parameter for adjusting the trade‐off between smoothness and similarity. The implementation of our method is straightforward as we rely on existing methods for computing geodesics and penalty fields. We evaluate our implementation and confirm its robustness and efficiency.

Facile Preparation of Superhydrophobic PDMS Polymer Films with Good Mechanical Strength Based on a Wear-Resistant and Reusable Template.

In this paper, a new method involving a wear-resistant and reusable template is proposed for the preparation of high-mechanical-strength superhydrophobic polymer film based on wire electrical discharge machining (WEDM). A solid-liquid-contact-angle simulation model was established to obtain surface-texture types and sizes that may achieve superhydrophobicity. The experimental results from template preparation show that there is good agreement between the simulation and experimental results for the contact angle. The maximum contact angle on the template can reach 155.3° given the appropriate triangular surface texture and WEDM rough machining. Besides, the prepared superhydrophobic template exhibits good wear resistance and reusability. PDMS superhydrophobic polymer films were prepared by the template method, and their properties were tested. The experimental results from the preparation of superhydrophobic polymer films show that the maximum contact angle of the polymer films can be up to 154.8° and that these films have good self-cleaning and anti-icing properties, wear resistance, bending resistance, and ductility.

Quantitative analysis of the polishing performance of Wurtzite-SiC surface texture on surface quality and material removal rate

Molecular dynamics simulation is used to study Wurtzite-SiC's structural changes after polishing process. For realistic planarization conditions, various surface-textured structures are also used. Polishing speed greatly impacts dislocation distribution. Increasing velocity to 2 Å/ps reduces dislocation length from 800 to 500 Å quickly. Increasing polishing depth from 15 to 30 Å improves surface roughness by 25 %. Besides, textures such as RPrt-s (Rectangular prism textured) and TPrt-s (Triangular prism textured) show surface improvement but still result in high values greater than 42 Å. The amorphous transition rate (ATR) and material removal rate (MRR) closely correlate and display similar variations. The material's triangular prism textured surface enables for minimal SDL (subsurface damage layer) thickness, dislocation density, and atom removal while preserving low groove surface roughness.

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.

Lattice Boltzmann simulation of droplets accelerate shedding on an inverted triangular surface with wettability gradient

The droplet combining and shedding on a gradient-wetting inverted triangle surface is investigated using the lattice Boltzmann method based on the Shan-Chen pseudo-potential model. The impacts of the tip angle, wetting gradient, and Bond number are investigated. The study shows that the smaller the tip angle, the better for the droplets to merge and shed. The droplet combining and shedding process can be sped up by the triangular surface’s wetting gradient. As the wetting gradient increases, the droplet combining and shedding becomes easier. Applying a wetting gradient to speed drainage is better when the original surface is more hydrophilic. The combination and shedding of droplets on the wet surface are significantly influenced by the Bond number as well.

Investigation of the Shear Mechanism at Sand-Concrete Interface under the Influence of the Concave Groove Angle of the Contact Surface

A “random-type” sand–concrete interface shear test was developed based on the sand cone method, with a focus on the most commonly encountered triangular contact surface morphology. A “regular-type” triangular interface, matched in roughness to the “random-type”, was meticulously designed. This “regular-type” interface features five distinct triangular groove inclinations: 18°, 33°, 50°, 70°, and 90°. A series of sand–concrete interface direct shear tests were conducted under consistent compaction conditions to investigate the impact of varying compaction densities and triangular groove inclinations on the shear strength at the interface. Particle flow simulations were utilized to examine the morphology of the shear band and the characteristics of particle migration influenced by the triangular contact surface. This analysis is aimed at elucidating the influence of the inclination of the triangular groove on the shear failure mechanism at the sand–concrete interface. The findings indicate that: (1) The morphology of the interface significantly impacts the shear strength of the sand–concrete interface, while the shape of the stress-displacement curve experiences minimal alteration. (2) At smaller inclination angles, particle contact forces are arranged in a wave-like configuration around the sawtooth tip, resulting in a non-uniform stress distribution along the sawtooth slope. However, as the inclination angle grows, the stress concentration at the sawtooth tip diminishes, and the stress distribution across the sawtooth slope becomes more consistent. (3) Particle migration is significantly influenced by the sawtooth’s inclination angle. At lower angles, particles climb the structure’s tip through sliding and rolling. As the angle increases, particle motion shifts to shear, accompanied by a transition in friction from surface friction to internal shear friction. This leads to the formation of a wider shear band and an increase in shear strength.

Experimental Investigation of the Effects of Grooves in Fe2O4/Water Nanofluid Pool Boiling

In this study, we systematically explored how changing groove surfaces of iron oxide/water nanofluid could affect the pool boiling heat transfer. We aimed to investigate the effect of three types of grooves, namely rectangular, circular, and triangular, on the boiling heat transfer. The goal was to improve heat transfer performance by consciously changing surface structure. Comparative analyses were conducted with deionized water to provide valuable insights. Notably, the heat transfer coefficient (HTC) exhibited a significant increase in the presence of grooves. For deionized water, the HTC rose by 91.7% and 48.7% on circular and rectangular grooved surfaces, respectively. Surprisingly, the triangular-grooved surface showed a decrease of 32.9% in HTC compared to the flat surface. On the other hand, the performance of the nanofluid displayed intriguing trends. The HTC for the nanofluid diminished by 89.2% and 22.3% on rectangular and triangular grooved surfaces, while the circular-grooved surface exhibited a notable 41.2% increase in HTC. These results underscore the complex interplay between groove geometry, fluid properties, and heat transfer enhancement in nanofluid-based boiling. Hence, we thoroughly examine the underlying mechanisms and elements influencing these observed patterns in this research. The results provide important insights for further developments in this area by shedding light on how surface changes and groove geometry may greatly affect heat transfer in nanofluid-based pool boiling systems.

Impact of intermittent sputtering on the ordering of triangular surface topography

It is demonstrated that the quality of nanoscale triangular structures on Si (100) surfaces can be improved by applying intermittent ion beam sputtering. This investigation is conducted along the work of Rakhi et al. (2023), which introduces an additional physical parameter space related to intermittent sputtering. Through this approach, we have observed the minimum surface defect density associated with higher-order surface structures, particularly at tT = 8 min. This can have large potential applications in modern cutting-edge technology demands of controlled growth of nanostructures, especially the low dimensional high aspect ratio nanostructures.

Response Characteristics of Pressure-Sensitive Conductive Elastomer Sensors Using OFC Electrode with Triangular Wave Concavo-Convex Surfaces.

The sensor response of pressure-sensitive conductive elastomers using polymeric materials can be adjusted by altering the type and quantity of fillers used during manufacturing. Another method involves modifying the surface shape of the elastomer. This study investigates the sensor response by altering the surface shape of an electrode using a readily available pressure-sensitive conductive elastomer. By employing an oxygen-free copper electrode with a flat surface (with surface roughness parameters Ra = 0.064 μm and Rz = 0.564 μm) as a baseline, we examined the sensor system's characteristics. Electrodes were fabricated with triangular wave concavo-convex surfaces, featuring tip angles of 60, 90, and 120°. Improved sensor responses were observed with electrodes having tip angles of 60 and 90°. Additionally, even with varying conductive properties of elastomers, the conductance of the elastomer sensor increased similarly when using an electrode with a 90° tip angle. This study demonstrates the potential for expanding the applications of conductive elastomer sensors, highlighting the noteworthy improvement in sensor response and performance achieved by altering the surface shape of electrodes used with commercially available conductive elastomers.

Trajectory optimization for automated tape placement on triangular mesh surfaces considering gap requirements

Abstract Automated tape placement (ATP) is an important automated process adopted for the fabrication of large composite components. Trajectory planning is the key link of ATP, which directly affects the precision and efficiency of the layup process, and the quality of final products. Presently, most existing trajectory optimization methods for ATP focus on smooth surfaces. Nevertheless, as commercial CAD/CAM software generally uses NURBS (Non-uniform Rational B-Splines) for modelling, the difficulty of finding the solution and the low efficiency associated with the calculation process are inevitable. The discrete methods provide alternatives for designing layup trajectories, whereas their accuracy is seldom analyzed. Furthermore, a path optimization algorithm for eliminating gap problems while preventing wrinkles on discrete models is rarely reported. In this paper, the adjustment of layup trajectories for ATP is considered on triangular meshes. Firstly, the triangular mesh is reconstructed as a Nagata patch to recover the original geometry with good accuracy. Then, a numerical method for tracing desired paths on the Nagata patch set is provided, and the computation efficiency is validated. Next, two optimization methodologies are proposed to improve the layup of composite tapes while avoiding wrinkles. Finally, the presented two strategies are examined on a discrete hyperbolic surface and a discrete freeform surface, and some of the results are delivered.

Mesh neural networks for SE(3)-equivariant hemodynamics estimation on the artery wall

Computational fluid dynamics (CFD) is a valuable asset for patient-specific cardiovascular-disease diagnosis and prognosis, but its high computational demands hamper its adoption in practice. Machine-learning methods that estimate blood flow in individual patients could accelerate or replace CFD simulation to overcome these limitations. In this work, we consider the estimation of vector-valued quantities on the wall of three-dimensional geometric artery models. We employ group-equivariant graph convolution in an end-to-end SE(3)-equivariant neural network that operates directly on triangular surface meshes and makes efficient use of training data. We run experiments on a large dataset of synthetic coronary arteries and find that our method estimates directional wall shear stress (WSS) with an approximation error of 7.6% and normalised mean absolute error (NMAE) of 0.4% while up to two orders of magnitude faster than CFD. Furthermore, we show that our method is powerful enough to accurately predict transient, vector-valued WSS over the cardiac cycle while conditioned on a range of different inflow boundary conditions. These results demonstrate the potential of our proposed method as a plugin replacement for CFD in the personalised prediction of hemodynamic vector and scalar fields.

Steady and Unsteady Dynamics of Magneto-Nanofluidic Flow in a Bottom-Heated Top-Cooled Recto-Triangular Thermal System

This work numerically explores the evolution flow features during the journey through unsteady to steady dynamics in a magneto-nanofluidic thermal system of recto-triangular shape. This system, which is partially heated using the triangular surface and employs a top-cooling configuration, features an upper rectangular and a lower triangular part. The study addresses laminar flow for various Rayleigh numbers (Ra) up to 105 considering uniform magnetic fields at different inclination angles and utilizing a 0.1% nanoparticle concentration (fixed) CuO-water nanofluid along with a finite element-based solver. The results reveal the formation of multi-vortical structures with varying numbers of circulation cells. The most important observation is the transformation of cells from a four-cell configuration to a one-cell configuration, and finally to a two-cell configuration as Ra changes from 103 to 104 to 105 without a magnetic field. The one-cell structure sustains over a narrow range of Ra and is sensitive to the Hartmann number (Ha). The inclined magnetic fields have a severe impact on the flow structure. Starting from a quiescent state and progressing through the unsteady flow stages, the system rapidly reaches a steady state under different temperature differences (simulated by Ra), except for a few exceptions of Ra and Ha values. The analysis of the unsteady stages of flow development provides deeper insights into the dynamics of multi-cellular flows.

Studying the influence of surface roughness with different shapes and quantities on convective heat transfer of fluid within nanochannels using molecular dynamics simulations.

In the past decade, rapid advancements in microtechnology and nanotechnology have propelled modern science and technology into the nanoscale domain, where miniaturization and high integration have found extensive applications across various fields, including industry, biotechnology, and information technology. Mechanisms of nanofluid flow and heat transfer properties have received increasing attention. In the flow and convective heat transfer of fluids at the nanoscale, the shape and dimensions of the surfaces play a crucial role. So, the main purpose of our paper is to investigate the influence of surface roughness with different shapes and quantities on fluid flow and convective heat transfer. In this study, we have chosen argon atoms as the fluid and used copper atoms to simulate the nanochannel walls. In order to investigate the influence of the shape and quantity of roughness on the convective heat transfer of fluids within nanochannels, we computed and analyzed the velocity, temperature, and density distributions of fluids inside channels with triangular, hemispherical, and rectangular roughness. Through simulation results, we found that triangular, hemispherical, and rectangular surface roughness at the same height can result in differences in temperature and velocity of the fluid within nanochannels. With a nanochannel roughness number of 5, the temperature and velocity of the fluid at the middle position of the nano-channel for the triangular roughness increased by 6% and 25% compared to the rectangular roughness, and by 4% and 10% compared to the hemispherical roughness. The fluid temperature and velocity are highest in channels with triangular surface roughness and lowest in those with rectangular roughness. Furthermore, increasing the quantity of surface roughness decreases the temperature and velocity of the fluid within nanochannels. When the quantity of rectangular surface roughness is 5, the fluid temperature within the nanochannel decreases by 12%, and the velocity decreases by 38% compared to a roughness quantity of 1. We also found, through velocity contours, that the presence of roughness increases the local fluid velocity in the rough regions of nanochannels. Roughness also reduces the density fluctuations of the fluid near the walls within the nanochannel. Roughness significantly affects the heat transfer performance of the fluid during its flow, and this influence should not be overlooked. In this study, molecular dynamics theory was employed, and simulations were conducted using the open-source software LAMMPS to investigate the influence of different shapes and quantities of surface roughness on fluid flow within nanochannels. The model in this paper was constructed using the LAMMPS software, and the surface roughness shapes on the walls were implemented as rectangular, hemispherical, and triangular. The wall surfaces were composed of copper atoms, while the fluid consisted of argon atoms. The copper atoms were arranged in a face-centered cubic (FCC) lattice with a lattice constant of 3.615 Å. Similarly, the argon atoms were arranged in a face-centered cubic (FCC) lattice with a lattice constant of 5.62 Å. The interactions between copper atoms were modeled using the EAM (Embedded Atom Method) potential, while the interactions between argon atoms were described using the LJ (Lennard-Jones) potential. The LJ potential was also employed to represent interactions between argon and copper atoms.

A Novel Radial Basis Function Description of a Smooth Implicit Surface for Musculoskeletal Modelling

As musculoskeletal illnesses continue to increase, practical computerised muscle modelling is crucial. This paper addresses this concern by proposing a mathematical model for a dynamic 3D geometrical surface representation of muscles using a Radial Basis Function (RBF) approximation technique. The objective is to obtain a smoother surface while minimising data use, contrasting it from classical polygonal (e.g. triangular) surface mesh models or volumetric (e.g. tetrahedral) mesh models. The paper uses RBF implicit surface description to describe static surface generation and dynamic surface deformations based on its spatial curvature preservation during the deformation. The novel method is tested on multiple data sets, and the experiments show promising results according to the introduced metrics.

Structural Outlier Detection and Zernike-Canterakis Moments for Molecular Surface Meshes-Fast Implementation in Python.

Object retrieval systems measure the degree of similarity of the shape of 3D models. They search for the elements of the 3D model databases that resemble the query model. In structural bioinformatics, the query model is a protein tertiary/quaternary structure and the objective is to find similarly shaped molecules in the Protein Data Bank. With the ever-growing size of the PDB, a direct atomic coordinate comparison with all its members is impractical. To overcome this problem, the shape of the molecules can be encoded by fixed-length feature vectors. The distance of a protein to the entire PDB can be measured in this low-dimensional domain in linear time. The state-of-the-art approaches utilize Zernike-Canterakis moments for the shape encoding and supply the retrieval process with geometric data of the input structures. The BioZernike descriptors are a standard utility of the PDB since 2020. However, when trying to calculate the ZC moments locally, the issue of the deficiency of libraries readily available for use in custom programs (i.e., without relying on external binaries) is encountered, in particular programs written in Python. Here, a fast and well-documented Python implementation of the Pozo-Koehl algorithm is presented. In contrast to the more popular algorithm by Novotni and Klein, which is based on the voxelized volume, the PK algorithm produces ZC moments directly from the triangular surface meshes of 3D models. In particular, it can accept the molecular surfaces of proteins as its input. In the presented PK-Zernike library, owing to Numba's just-in-time compilation, a mesh with 50,000 facets is processed by a single thread in a second at the moment order 20. Since this is the first time the PK algorithm is used in structural bioinformatics, it is employed in a novel, simple, but efficient protein structure retrieval pipeline. The elimination of the outlying chain fragments via a fast PCA-based subroutine improves the discrimination ability, allowing for this pipeline to achieve an 0.961 area under the ROC curve in the BioZernike validation suite (0.997 for the assemblies). The correlation between the results of the proposed approach and of the 3D Surfer program attains values up to 0.99.