3D Triangle Research Articles

A Three-Dimensional Triangle Mesh Integration Method for Oblique Photography Model Data

Oblique photography 3D models are increasingly used in 3D modeling and visualization, urban planning and design, smart cities, smart mines, and other fields. To ensure that 3D models can be replaced and updated, it is necessary to deal with the model holes and incomplete areas caused by the incorrect matching of feature points in the modeling process. Moreover, in 3D models of the planning and management of certain mining areas or urban areas to be developed, regions can also be delineated for replacements and updates. Due to the unsatisfactory display effect of the manually modeled models used to replace and update, the authenticity of the model texture and the detail characteristics of the model triangle meshes cannot be guaranteed during integration. Therefore, this paper proposes a 3D model triangle mesh integration method for oblique photography data which integrates the real and complete 3D models used for replacement with the incomplete part or the part of the original model that needs to be replaced. The experimental results show that this method can integrate the original terrain model and the replacement model efficiently and quickly, the integrated model has no gap, and the display effect is good, effectively achieving model repair or model update and replacement.

Mechanical and bandgap properties of 3D bi-material triangle re-entrant honeycomb

In the aerospace industry, precision components need to serve in a comprehensive environment of severe temperature changes, vibrations, and noise. Therefore, it is necessary to design a multifunctional mechanical metamaterial that integrates a tunable coefficient of thermal expansion (CTE), Poisson's ratio (PR), and bandgap. Here, a 3D bi-material triangle re-entrant honeycomb (3D-BTRH) with adjustable Poisson's ratio is proposed. Due to the geometric symmetry, the 3D-BTRH realizes the isotropy of mechanical properties in the three coordinate axes. The intrinsic mechanisms of tunable CTE and PR of the 3D-BTRH are revealed by building theoretical models. The accuracy of the theoretical analysis of PR and Young's modulus is verified by simulation and experiment. The finite element analysis is used to calculate the band structures and width of the total effective bandgap utilizing Bloch's theorem and Bloch's periodic boundary conditions. The accuracy of the band structure calculations is verified by calculating the transmission characteristic curve. The parametric analysis shows that the 3D-BTRH can achieve tunable CTE and PR in the directions of the three axes, and has a large width of the total effective bandgap. Moreover, this work provides a design idea for 3D metamaterials to simultaneously regulate CTE, PR, and the bandgap, which offers opportunities for better engineering practice.

Zero watermarking scheme for 3D triangle mesh model based on global and local geometric features

Zero watermarking scheme for 3D triangle mesh model based on global and local geometric features

Diffusion-Mediated Nucleation and Growth of fcc and bcc Nanocrystal Superlattices with Designable Assembly of Freestanding 3D Supercrystals.

Diffusion-mediated assembly of octahedral PbS nanocrystals (NCs) in a confined antisolvent environment displays a primary burst nucleation and Ostwald ripening growth of rhombic bcc supercrystals, followed by a secondary seed-based nucleation and oriented attachment growth of triangle fcc supercrystals. As the diffusion proceeds from ethanol across a sharp interface into NC-suspended toluene, a burst nucleation of supercrystal seeds occurs, and such supercrystals are quickly developed into rhombic grains that have a bcc structure. At a critical size of 10 μm, an Ostwald ripening event appears to guide the supercrystal growth. Upon grain growth above 30 μm, the fcc supercrystals start a nucleation at two symmetrical tips of individual rhombic crystals. Such fcc supercrystals are developed with a triangle shape, and two triangles are combined with one bcc rhombus in-between to form a butterfly-like bowtie stacking structure. The fcc triangle wings grow larger at a reduction of bcc rhombus cores. As the bcc cores gradually fade, such butterfly-like bowtie crystals aggregate and undergo an oriented attachment process, leading to the formation of freestanding 3D triangle crystals that have a single fcc lattice. Analysis of experimental observations and defined diffusion parameters reveals that fast solvent diffusion and high-NC concentration promote the growth of rhombic bcc supercrystals, while slow solvent diffusion and low-NC concentration accelerate the development of triangle fcc supercrystals. Upon succeeding in designable growth of 3D fcc supercrystals, this study provides designing principles for controlled fabrication of supercrystals with desired superlattices for additional engineering and applications.

NGD-Transformer: Navigation Geodesic Distance Positional Encoding with Self-Attention Pooling for Graph Transformer on 3D Triangle Mesh

Following the significant success of the transformer in NLP and computer vision, this paper attempts to extend it to 3D triangle mesh. The aim is to determine the shape’s global representation using the transformer and capture the inherent manifold information. To this end, this paper proposes a novel learning framework named Navigation Geodesic Distance Transformer (NGD-Transformer) for 3D mesh. Specifically, this approach combined farthest point sampling with the Voronoi segmentation algorithm to spawn uniform and non-overlapping manifold patches. However, the vertex number of these patches was inconsistent. Therefore, self-attention graph pooling is employed for sorting the vertices on each patch and screening out the most representative nodes, which were then reorganized according to their scores to generate tokens and their raw feature embeddings. To better exploit the manifold properties of the mesh, this paper further proposed a novel positional encoding called navigation geodesic distance positional encoding (NGD-PE), which encodes the geodesic distance between vertices relatively and spatial symmetrically. Subsequently, the raw feature embeddings and positional encodings were summed as input embeddings fed to the graph transformer encoder to determine the global representation of the shape. Experiments on several datasets were conducted, and the experimental results show the excellent performance of our proposed method.

An explicit symplectic approach to solving the wave equation in moving media

AbstractAn explicit approach using symplectic time integration in conjunction with traditional finite difference spatial derivatives to solve the wave equation in moving media is presented. A simple operator split of this second order wave equation into two coupled first order equations is performed, allowing these split equations to be solved symplectically. Orders of symplectic time integration ranging from first to fourth along with orders of spatial derivatives ranging from second to sixth are explored. The case of cylindrical acoustic spreading in air under a constant velocity in a 2D square structured domain is considered. The variation of the computed time‐of‐flight, frequency, and wave length are studied with varying grid resolution and the deviations from the analytical solutions are determined. It was found that symplectic time integration interferes with finite difference spatial derivatives higher than second order causing unexpected results. This is actually beneficial for unstructured finite volume tools like OpenFOAM where second order spatial operators are the state‐of‐the art. Cylindrical acoustic spreading is simulated on an unstructured 2D triangle mesh showing that symplectic time integration is not limited to the spatial discretization paradigm and overcomes the numerical diffusion arising with the in‐built numerical methods which hinder wave propagation.

Maneuvering Angle Rigid Formations With Global Convergence Guarantees

Angle rigid multi-agent formations can simultaneously undergo translational, rotational, and scaling maneuvering, therefore combining the maneuvering capabilities of both distance and bearing rigid formations. However, maneuvering angle rigid formations in 2D or 3D with global convergence guarantees is shown to be a challenging problem in the existing literature even when relative position measurements are available. Motivated by angle-induced linear equations in 2D triangles and 3D tetrahedra, this paper aims to solve this challenging problem in both 2D and 3D under a leader-follower framework. For the 2D case where the leaders have constant velocities, by using local relative position and velocity measurements, a formation maneuvering law is designed for the followers governed by double-integrator dynamics. When the leaders have time-varying velocities, a sliding mode formation maneuvering law is proposed by using the same measurements. For the 3D case, to establish an angle-induced linear equation for each tetrahedron, we assume that all the followers' coordinate frames share a common <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Z$</tex> direction. Then, a formation maneuvering law is proposed for the followers to globally maneuver <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$Z$</tex> -weakly angle rigid formations in 3D. The extension to Lagrangian agent dynamics and the construction of the desired rigid formations by using the minimum number of angle constraints are also discussed. Simulation examples are provided to validate the effectiveness of the proposed algorithms.

Structural phase-field crystal model for Lennard–Jones pair interaction potential

A modification of the structural phase-field crystal model for a Lennard–Jones (LJ) pair interaction potential is presented. Formation of 1D and 2D structures for the LJ-potential was studied numerically. The equilibrium lattice parameters for the obtained structures were found consistent to the correspondent LJ-distance parameters. The lattice parameter of 2D triangle’s structure matches the periodical in 1D, which is consistent to the theory of freezing from the isotropic liquids. Numerically obtained phase diagram of two-dimensional structures qualitatively reproduces classical PFC diagram and coincides with the melting region of high-temperature part of LJ diagram.

A GAMIFICATION APPROACH FOR THE IMPROVEMENT OF PAID CROWD-BASED LABELLING OF GEOSPATIAL DATA

Abstract. Non-commercial, unpaid crowdsourcing is the basis of many non-profit projects on the Internet such as Wikipedia or OpenStreetMap. A prerequisite for such projects to be successful is to find a sufficient number of volunteer crowdworkers who are intrinsically motivated to participate. In the field of geodata collection, many tasks exist that in principle could be solved with crowdsourcing; however, finding a large number of volunteers is problematic. There is also paid crowdsourcing in addition to crowdsourcing based on voluntary collaboration. The main incentive for participating in paid crowdsourcing projects is primarily payment for the work. Thus, intrinsic motivation is replaced by extrinsic motivation. However, intrinsic motivation simply replaced by extrinsic motivation can lead to a reduction in performance. If there are no additional intrinsic incentives in addition to monetary payment, it can happen that crowdworkers only perform exactly as much work as is necessary to satisfy the employers. Gamification may positively influence the motivation of paid crowdworkers. The goal of this paper is to investigate whether it is possible to increase the performance of paid crowdworkers with gamification. To this end, we have developed a web-based tool for the labelling of 3D triangle meshes. We presented this tool with and without game elements to paid crowdworkers and investigated to what extent gamification influenced the quality and quantity of the collected data.

Precomputed fast rejection ray-triangle intersection

We propose a ray-triangle intersection algorithm with fast-rejection strategies. We intersect the ray with the triangle plane, then transform the intersection problem into 2D by applying a transformation matrix to the ray-plane intersection point. For 2D transformation, we study two different approaches. The first approach uses a transformation matrix which transforms the triangle into a unit triangle. Then, simple 2D tests are performed. The second approach transforms the triangle into a 2D triangle while preserving similarity. This allows us to prune (i.e., to clip away) areas surrounding the triangle, determining whether the transformed intersection point lies within the triangle. We discuss several optimizations for this pruning approach. We implemented both approaches into the CPU-based ray-tracing framework PBRT, version 3, and we performed a time-based comparison against PBRT’s default intersection algorithm and Baldwin and Weber’s algorithm. The results show that our algorithms are faster than the default algorithm. They are comparable to or slightly slower than Baldwin and Weber’s algorithm, however, the pruning approach produces watertight results and may be further optimized. Moreover, additional CPU/GPU experiments outside of PBRT document promising speedup over the standard Möller–Trumbore algorithm in areas like ray-casting or collision detection.

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.

Subdivision-based Mesh Convolution Networks

Convolutionalneural networks (CNNs) have made great breakthroughs in two-dimensional (2D) computer vision. However, their irregular structure makes it hard to harness the potential of CNNs directly on meshes. A subdivision surface provides a hierarchical multi-resolution structure in which each face in a closed 2-manifold triangle mesh is exactly adjacent to three faces. Motivated by these two observations, this article presents SubdivNet , an innovative and versatile CNN framework for three-dimensional (3D) triangle meshes with Loop subdivision sequence connectivity. Making an analogy between mesh faces and pixels in a 2D image allows us to present a mesh convolution operator to aggregate local features from nearby faces. By exploiting face neighborhoods, this convolution can support standard 2D convolutional network concepts, e.g., variable kernel size, stride, and dilation. Based on the multi-resolution hierarchy, we make use of pooling layers that uniformly merge four faces into one and an upsampling method that splits one face into four. Thereby, many popular 2D CNN architectures can be easily adapted to process 3D meshes. Meshes with arbitrary connectivity can be remeshed to have Loop subdivision sequence connectivity via self-parameterization, making SubdivNet a general approach. Extensive evaluation and various applications demonstrate SubdivNet’s effectiveness and efficiency.

Fast Barycentric-Based Evaluation Over Spectral/hp Elements

As the use of spectral/hp element methods, and high-order finite element methods in general, continues to spread, community efforts to create efficient, optimized algorithms associated with fundamental high-order operations have grown. Core tasks such as solution expansion evaluation at quadrature points, stiffness and mass matrix generation, and matrix assembly have received tremendous attention. With the expansion of the types of problems to which high-order methods are applied, and correspondingly the growth in types of numerical tasks accomplished through high-order methods, the number and types of these core operations broaden. This work focuses on solution expansion evaluation at arbitrary points within an element. This operation is core to many postprocessing applications such as evaluation of streamlines and pathlines, as well as to field projection techniques such as mortaring. We expand barycentric interpolation techniques developed on an interval to 2D (triangles and quadrilaterals) and 3D (tetrahedra, prisms, pyramids, and hexahedra) spectral/hp element methods. We provide efficient algorithms for their implementations, and demonstrate their effectiveness using the spectral/hp element library Nektar++ by running a series of baseline evaluations against the ‘standard’ Lagrangian method, where an interpolation matrix is generated and matrix-multiplication applied to evaluate a point at a given location. We present results from a rigorous series of benchmarking tests for a variety of element shapes, polynomial orders and dimensions. We show that when the point of interest is to be repeatedly evaluated, the barycentric method performs at worst 50% slower, when compared to a cached matrix evaluation. However, when the point of interest changes repeatedly so that the interpolation matrix must be regenerated in the ‘standard’ approach, the barycentric method yields far greater performance, with a minimum speedup factor of 7times . Furthermore, when derivatives of the solution evaluation are also required, the barycentric method in general slightly outperforms the cached interpolation matrix method across all elements and orders, with an up to 30% speedup. Finally we investigate a real-world example of scalar transport using a non-conformal discontinuous Galerkin simulation, in which we observe around 6times speedup in computational time for the barycentric method compared to the matrix-based approach. We also explore the complexity of both interpolation methods and show that the barycentric interpolation method requires {mathcal {O}}(k) storage compared to a best case space complexity of {mathcal {O}}(k^2) for the Lagrangian interpolation matrix method.

Lattice mismatch induced tunable dimensionality of transition metal Di-chalcogenides

Low-dimensional materials have excellent properties which are closely related to their dimensionality. However, the growth mechanism underlying tunable dimensionality from 2D triangles to ID ribbons of such materials is still unrevealed. Here, we establish a general kinetic Monte Carlo model for transition metal dichalcogenides (TMDs) growth to address such an issue. Our model is able to reproduce several key ñndings in experiments, and reveals that the dimensionality is determined by the lattice mismatch and the interaction strength between TMDs and the substrate. We predict that the dimensionality can be well tuned by the interaction strength and the geometry of the substrate. Our work deepens the understanding of tunable dimensionality of low-dimensional materials and may inspire new concepts for the design of such materials with expected dimensionality.

Tetrahedra of varying density and their applications

We propose concepts to utilize basic mathematical principles for computing the exact mass properties of objects with varying densities. For objects given as 3D triangle meshes, the method is analytically accurate and at the same time faster than any established approximation method. Our concept is based on tetrahedra as underlying primitives, which allows for the object’s actual mesh surface to be incorporated in the computation. The density within a tetrahedron is allowed to vary linearly, i.e., arbitrary density fields can be approximated by specifying the density at all vertices of a tetrahedral mesh. Involved integrals are formulated in closed form and can be evaluated by simple, easily parallelized, vector-matrix multiplications. The ability to compute exact masses and centroids for objects of varying density enables novel or more exact solutions to several interesting problems: besides the accurate analysis of objects under given density fields, this includes the synthesis of parameterized density functions for the make-it-stand challenge or manufacturing of objects with controlled rotational inertia. In addition, based on the tetrahedralization of Voronoi cells we introduce a precise method to solve L_{2|infty } Lloyd relaxations by exact integration of the Chebyshev norm. In the context of additive manufacturing research, objects of varying density are a prominent topic. However, current state-of-the-art algorithms are still based on voxelizations, which produce rather crude approximations of masses and mass centers of 3D objects. Many existing frameworks will benefit by replacing approximations with fast and exact calculations.Graphic abstract

Multi-objective optimization of adhesively bonded single-lap joints of carbon fiber reinforced polymer laminates based on genetic algorithm

To improve its structural performance, the multi-objective optimization of adhesively bonded single-lap joints of carbon fiber reinforced polymer (CFRP) laminates was carried out based on genetic algorithm. Firstly, finite element (FE) models were constructed using 3D Hashin damage criteria and triangle cohesive zone model (CZM), those well capture the intra-laminar, inter-laminar and adhesive damages during the tensile loads, respectively. And its effectiveness was verified through experiments. Secondly, using the Latin hypercube sampling (LHS) method and polynomial response surface method (RSM), a multi-objective optimization agent model with tensile strength and shear strength as the objective function was established based on lap the length, the adhesive thickness and the width of the bonded parts. Finally, the tensile strength and shear strength agent model was optimized to obtain Pareto solution set based on genetic algorithm (GA), and the Pareto solution set was sequenced by technique for order preference by similarity to ideal solution (TOPSIS) method to obtain the optimized single-bonded joint structure design scheme. The result shows that the experimental measurements of tensile load tests concur with the numerical predictions and validate the FE models. The tensile strength and shear strength of the adhesively bonded single-lap joints of CFRP laminates have a significant correlation with the lap length, the thickness of the adhesive layer and the width of the bonded parts. Compared with the numerical simulation results, the error of the quadratic response surface proxy model results is less than 2.3%. Compared with the conventional single lap bonding structure, the tensile strength and shear strength are increased by 2.65% and 17.24%, respectively.

Modeling of Personalized Anatomy Using Plastic Strains

We present a method for modeling solid objects undergoing large spatially varying and/or anisotropic strains, and use it to reconstruct human anatomy from medical images. Our novel shape deformation method uses plastic strains and the finite element method to successfully model shapes undergoing large and/or anisotropic strains, specified by sparse point constraints on the boundary of the object. We extensively compare our method to standard second-order shape deformation methods, variational methods, and surface-based methods, and demonstrate that our method avoids the spikiness, wiggliness, and other artifacts of previous methods. We demonstrate how to perform such shape deformation both for attached and un-attached (“free flying”) objects, using a novel method to solve linear systems with singular matrices with a known nullspace. Although our method is applicable to general large-strain shape deformation modeling, we use it to create personalized 3D triangle and volumetric meshes of human organs, based on magnetic resonance imaging or computed tomography scans. Given a medically accurate anatomy template of a generic individual, we optimize the geometry of the organ to match the magnetic resonance imaging or computed tomography scan of a specific individual. Our examples include human hand muscles, a liver, a hip bone, and a gluteus medius muscle (“hip abductor”).

Au5Br: A new member of highly stable 2D-type doped gold nanomaterial

A new potential relatively highly stable two-dimensional (2D) type naonomaterial of doped gold nanoclusters, Au5Br, is reported. The nanomaterial is obtained by searching bromine-doped neutral gold clusters through the CALYPSO software together with DFT method. The structural study of AunBr (n = 2–13) nanoclusters indicates that the geometrical transition size of the lowest energy structures from 2D to three-dimensional (3D) is Au6Br, and the 3D structures of AunBr (n = 7–13) are all based on the multilayer pyramid-type. The research on the relative stability of the ground state of the AunBr (n = 2–13) clusters reveals that these clusters are odd-sized number stable. Interestingly, the most special one is Au5Br with 2D triangle geometry, which has the strongest local stability and can be used as a candidate for magic cluster. The calculations of the natural charge population (NCP) in all the lowest energy clusters show that all bromine atoms are negatively charged. Polarization analysis strongly suggests that Au4Br nanocluster’s nonlinear optic properties is probably particular better than other nanoclusters. Finally, in order to further understand the high stability properties of Au5Br nanocluster, its molecular orbitals (MOs), electronic localization function (ELF), infrared (IR) and Raman spectra are also studied in detail.

&amp;lt;i&amp;gt;In-Silico&amp;lt;/i&amp;gt; Identification of Anticancer Compounds; Ligand-Based Pharmacophore Approach against EGFR Involved in Breast Cancer

Objective: Breast cancer is a public health challenge on a global scale that is caused by environmental or genetic factors. Breast cancer is affecting both males and females, but there is still a lack of effective drugs with improved potency and admissibility against breast cancer as many of the breast cancer drugs have severe side effects. Methods: The docking approach has been used to find a new compound for breast cancer with more efficacy and tolerance and with lesser side effects. A ligand-based pharmacophore approach has been generated for 39 anticancer compounds with significance for the development of new drugs. Result: Through docking, the approach found new lead compounds for breast cancer. The proposed pharmacophore model in this study contains two HBAs and one HYD, one hydrophobic domain and two Aromatic rings and the estimated distance range is minimum to maximum of derived pharmacophore features. Conclusion: Based on this research, it is proposed that these two lead compounds may be able to be used against EGFR in breast cancer. New compounds can be identified based on common features in the Pharmacophore model. 3D pharmacophore triangle could be used for further studies because this pharmacophore has better merging and in the future for more studies can suggest the same distance range of pharmacophore features as this pharmacophore.

Deterministic Approach to Achieve Full-Polarization Cloak.

Achieving full-polarization (σ) invisibility on an arbitrary three-dimensional (3D) platform is a long-held knotty issue yet extremely promising in real-world stealth applications. However, state-of-the-art invisibility cloaks typically work under a specific polarization because the anisotropy and orientation-selective resonant nature of artificial materials made the σ-immune operation elusive and terribly challenging. Here, we report a deterministic approach to engineer a metasurface skin cloak working under an arbitrary polarization state by theoretically synergizing two cloaking phase patterns required, respectively, at spin-up (σ+) and spin-down (σ−) states. Therein, the wavefront of any light impinging on the cloak can be well preserved since it is a superposition of σ+ and σ− wave. To demonstrate the effectiveness and applicability, several proof-of-concept metasurface cloaks are designed to wrap over a 3D triangle platform at microwave frequency. Results show that our cloaks are essentially capable of restoring the amplitude and phase of reflected beams as if light was incident on a flat mirror or an arbitrarily predesigned shape under full polarization states with a desirable bandwidth of ~17.9%, conceiving or deceiving an arbitrary object placed inside. Our approach, deterministic and robust in terms of accurate theoretical design, reconciles the milestone dilemma in stealth discipline and opens up an avenue for the extreme capability of ultrathin 3D cloaking of an arbitrary shape, paving up the road for real-world applications.