Planar Mesh Research Articles

SemanticMesh: parameterized fusion of semantic components for photogrammetric meshes

ABSTRACT The façades of photogrammetric building mesh models frequently lack detailed semantics, such as windows, doors, and balconies. To address this, we introduce SemanticMesh, a methodology designed to enrich façades with detailed semantics by integrating discrete components seamlessly. The process begins by transforming a localized area of the building surface into a 2D planar mesh using geodesic vectors, based on the component poses. This is followed by the application of 2D constrained triangulation to map the component boundaries onto the parameterized plane, after which the mesh is reconverted into 3D space. To achieve a smooth and aesthetically pleasing integration, we employ a Laplacian mesh deformation technique along the 3D embedding boundary. Our experiments across three distinct datasets – featuring near-planar, non-planar, and noisy surfaces – demonstrate that SemanticMesh provides superior modeling outcomes compared to conventional approaches.

Mode-shape magnification in high-speed camera measurements

If motion, identified using image-based methods, is too small to be seen with the naked eye, motion magnification can be used to help with the visualization. Established motion-magnification methods magnify (typically up to 1000 times) the band-passed content of the image data. Especially at higher frequencies, the amplitudes of measured displacements are often below the noise floor. In this research, a novel method for amplifying vibrations, based on experimental modal analysis (EMA), is introduced. The response of the examined structure to dynamic excitation is measured with a simplified, gradient-based, optical flow method and used to perform a hybrid modal analysis in conjunction with a reference accelerometer response measurement. Such a hybrid approach can: (a) identify structural dynamics significantly in the sub-pixel range, and (b) significantly below the image noise floor. The image of the vibrating structure is subdivided using a planar triangle mesh, which is then warped in accordance with the identified mode shape. A mesh-element-wise affine transformation is performed to obtain an image of the magnified mode shape. In the experimental part, the proposed method achieved magnification factors of approximately 40 thousand times, which is an order of magnitude deeper into noise than available before; additionally, the proposed approach is numerically significantly less demanding.The introduced mode-shape magnification presents an alternative to existing motion-magnification methods for applications where the harmonic displacement information is hidden by image noise.

Research and Application of Key Technologies for Assembling Design and Construction of Reinforcement in Super High Concrete Bridge Tower

Concrete bridge towers are widely used in long-span bridges. Aiming at the reinforcement process which requires the largest labor force and has the highest safety risk during the construction of the super high concrete bridge tower. The key technology of assembling design and construction of super high concrete bridge tower reinforcement characterized by “industrialized production of mesh, rapid section forming and on-site assembling installation” is creatively proposed. In terms of design, the three-dimensional bridge tower reinforcement is discretized into planar or 3D mesh. In order to facilitate the reinforcement segment, a new flush lapping is used for the circumferential connection of stirrup, and the tapered sleeve splicing is used for the connection of the reinforcement parts between the segments, and the reliability of the connection is verified by experiments. In terms of construction, industrial assembly lines are used for the production of steel mesh and overall bending forming. The bridge tower reinforcement segments are assembled on the special jig, and finally installed on the tower by the tower crane. At present, this technology has been successfully applied to projects such as Lingdingyang Bridge, reducing labor intensity, improving construction efficiency by 30%, and ensuring project quality.

Evaluation of Inner Products of Implicitly Defined Finite Element Functions on Multiply Connected Planar Mesh Cells

Evaluation of Inner Products of Implicitly Defined Finite Element Functions on Multiply Connected Planar Mesh Cells

Biomimetic Design of a New Semi-Rigid Spatial Mesh Antenna Reflector.

The reflective surface accuracy (RSA) of traditional space mesh antennas typically ranges from 0.2 to 6 mmRMS. To improve the RSA, an active control scheme can be employed, although it presents challenges in determining the installation position of the actuator. In this study, we propose a novel design for a semi-rigid cable mesh that combines rigid members and a flexible woven mesh, drawing inspiration from both rigid ribbed antennas and biomimicry. Initially, we investigate the planar mesh topology of spider webs and determine the bionic cable surface's mesh topology based on the existing hexagonal meshing method, with RSA serving as the evaluation criterion. Subsequently, through motion simulations and careful observation, we establish the offset angle as the key design parameter for the bionic mesh and complete the design of the bionic cable mesh accordingly. Finally, by analyzing the impact of the node quantity on RSA, we determine a layout scheme for the flexible woven mesh with a variable number of nodes, ultimately settling for 26 nodes. Our results demonstrate that the inclusion of numerous rigid components on the bionic cable mesh surface offers viable installation positions for the actuator of the space mesh antenna. The reflector accuracy achieved is 0.196 mmRMS, slightly surpassing the lower limit of reflector accuracy observed in most traditional space-space mesh antennas. This design presents a fresh research perspective on combining active control schemes with reflective surfaces, offering the potential to enhance the RSA of traditional rigid rib antennas to a certain extent.

A Discretize-then-Optimize Approach to PDE-Constrained Shape Optimization

We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a smooth manifold, termed the manifold of planar triangular meshes. The latter can be endowed with a complete Riemannian metric, which allows large mesh deformations without jeopardizing mesh quality; see R. Herzog and E. Loayza-Romero, Math. Comput. 92 (2022) 1-50. Nonetheless, the discrete shape optimization problem of finding optimal vertex positions does not, in general, possess a globally optimal solution. To overcome this ill-possedness, we propose to add a mesh quality penalization term to the objective function. This allows us to simultaneously render the shape optimization problem solvable, and keep track of the mesh quality. We prove the existence of a globally optimal solution for the penalized problem and establish first-order necessary optimality conditions independently of the chosen Riemannian metric. Because of the independence of the existence results of the choice of the Riemannian metric, we can numerically study the impact of different Riemannian metrics on the steepest descent method. We compare the Euclidean, elasticity, and a novel complete metric, combined with Euclidean and geodesic retractions to perform the mesh deformation.

Structured triangular mesh generation method for free-form gridshells based on conformal mapping and virtual interaction forces

With the rapid development of computer-aided design, manufacturing, and construction techniques, free-form single-layer reticulated shells (SLRSs) are increasingly applied in modern architectures. However, generating a uniform and smooth mesh directly on a three-dimensional free-form surface is challenging. This paper proposes a fast and automatic method to generate structured triangular mesh for free-form SLRSs. The difficulty is reduced by generating the mesh on the two-dimensional (2D) parametric plane obtained by conformal mapping. The virtual interaction forces (VIFs) combined with the area map are used to automatically adjust the distribution of the 2D structured base mesh to reduce distortions. Subsequently, mesh clipping and barycentric interpolation are used to map the planar mesh back to the original surface. Finally, the VIF-based mesh smoothing is conducted to improve the mesh uniformity and smoothness. Case studies show that the proposed method successfully generates high-quality structured triangular meshes on various types of free-form SLRSs. Moreover, this method can precisely control the overall size and direction of the mesh, providing architects and engineers with more choices of mesh patterns.

C1-smooth isogeometric spline functions of general degree over planar mixed meshes: The case of two quadratic mesh elements

Splines over triangulations and splines over quadrangulations (tensor product splines) are two common ways to extend bivariate polynomials to splines. However, combination of both approaches leads to splines defined over mixed triangle and quadrilateral meshes using the isogeometric approach. Mixed meshes are especially useful for representing complicated geometries obtained e.g. from trimming. As (bi-)linearly parameterized mesh elements are not flexible enough to cover smooth domains, we focus in this work on the case of planar mixed meshes parameterized by (bi-)quadratic geometry mappings. In particular we study in detail the space of C1-smooth isogeometric spline functions of general polynomial degree over two such mixed mesh elements. We present the theoretical framework to analyze the smoothness conditions over the common interface for all possible configurations of mesh elements. This comprises the investigation of the dimension as well as the construction of a basis of the corresponding C1-smooth isogeometric spline space over the domain described by two elements. Several examples of interest are presented in detail.

Planar Delaunay Mesh Smoothing Method Based on Angle and a Deep Q-Network

Mesh quality is critical to the accuracy and efficiency of finite element calculations, and mesh smoothing is an essential means of reducing the number of poor elements and improving mesh quality. The deep Q-network-based optimization algorithm for planar Delaunay mesh (unconstrained DQN) has attracted increasing attention due to its advantages in autonomous optimization. However, the unconstrained DQN model does not constrain the movement area of the central node during the training process, and element quality easily falls into a local optimum, resulting in a low generalization of the DQN model. In this paper, an updateable iterative inner polygon is proposed as a constraint to limit the central node’s movement and control the element’s angle. Next, the performance of different neural networks when training the same dataset is analyzed, and the appropriate neural network is selected. After that, the effectiveness and generalization of the method were analyzed. Finally, the results were compared with those obtained by existing methods. The results show that the proposed algorithm can improve the minimum angle of global elements and the shape of poor elements, and the trained DQN model has a high generalization.

BPM: Blended Piecewise Möbius Maps

AbstractWe propose a novel Möbius interpolator that takes as an input a discrete map between the vertices of two planar triangle meshes, and outputs a continuous map on the input domain. The output map interpolates the discrete map, is continuous between triangles, and has low quasi‐conformal distortion when the input map is discrete conformal. Our map leads to considerably smoother texture transfer compared to the alternatives, even on very coarse triangulations. Furthermore, our approach has a closed‐form expression, is local, applicable to any discrete map, and leads to smooth results even for extreme deformations. Finally, by working with local intrinsic coordinates, our approach is easily generalizable to discrete maps between a surface triangle mesh and a planar mesh, i.e., a planar parameterization. We compare our method with existing approaches, and demonstrate better texture transfer results, and lower quasi‐conformal errors.

Comparison of Mixing Plane, Frozen Rotor, and Sliding Mesh Methods on a Counter-Rotating Dual-Rotor Wind Turbine

Nowadays, there are numerous new features available in CFD (computational fluid dynamics) that can simulate complex physical phenomena, which used to be challenging to address. However, in current CFD software, certain problems can be simulated using different approaches. In our article, we chose different rotating motion methods to analyze a counter-rotating dual-rotor wind turbine (CO-DRWT). Using the different rotating motion approaches we selected (mixing plane, frozen rotor, and sliding mesh), we examined the torque on the rotors and compared them. The following conclusion was reached. If transient fluid flow must be examined, then the sliding mesh method provided the most realistic results, while the frozen rotor method was adequate if we investigated the effect of wake and vortex near the rotating blades or on its environment. The mixing plane method should be used when the focus is on the kinetics and kinematics of the rotating blade or structure.

SRL-assisted AFM: Generating planar unstructured quadrilateral meshes with supervised and reinforcement learning-assisted advancing front method

High-quality mesh generation is the foundation of accurate finite element analysis. Due to the vast interior vertices search space and complex initial boundaries, mesh generation for complicated domains requires substantial manual processing and has long been considered the most challenging and time-consuming bottleneck of the entire modeling and analysis process. In this paper, we present a novel computational framework named “SRL-assisted AFM” for meshing planar geometries by combining the advancing front method with neural networks that select reference vertices and update the front boundary using “policy networks”. These deep neural networks are trained using a unique pipeline that combines supervised learning with reinforcement learning to iteratively improve mesh quality. First, we generate different initial boundaries by randomly sampling points in a square domain and connecting them sequentially. These boundaries are used for obtaining input meshes and extracting training datasets in the supervised learning module. We then iteratively improve the reinforcement learning model performance with reward functions designed for special requirements, such as improving the mesh quality and controlling the number and distribution of extraordinary points. Our proposed supervised learning neural networks achieve an accuracy higher than 98% on predicting commercial software. The final reinforcement learning neural networks automatically generate high-quality quadrilateral meshes for complex planar domains with sharp features and boundary layers.

Robo-vision! 3D mesh generation of a scene for a robot for planar and non-planar complex objects.

This paper presents a novel architecture to generate a world model in terms of mesh from a continuous image stream with depth information extracted from a robot's ego-vision camera. We propose two algorithms for planar and non-planar mesh generation. A Cartesian grid-based mesh fitting algorithm is proposed for mesh generation of planar objects. For mesh generation of non-planar objects, we propose a Self Organization Map based algorithm. The proposed algorithm better approaches the boundary and overall shape of the objects compared to State-Of-the-Art (SOA). Extensive experiments done on three public datasets show that our method surpasses SOA both qualitatively and quantitatively.

Novel Approach for Umbilical Hernia Repair Using Mesh Strips.

Two-centimeter-wide strips of macroporous polypropylene mesh were passed through the abdominal wall and tied as simple interrupted sutures to achieve umbilical hernia repair. A retrospective review of all elective umbilical hernia repairs performed by a single surgeon using the mesh strip technique between 2016 and 2021 was conducted, and patient-reported outcomes were assessed via a telephonic survey. Thirty-three patients underwent an elective, open mesh strip repair of a primary umbilical hernia and met criteria for inclusion in the study. Of these patients, 60% responded to a patient-reported outcomes telephone survey. Ninety percent of survey responders reported a pain score of 0 of 10. Additionally, 90% reported being unable to feel or palpate the knot, and 80% reported an improvement in quality of life. Mean follow-up at 3 years revealed one recurrence in the setting of ascites, yielding a recurrence rate of 3%. Primary mesh strip repair of umbilical hernias combines the simplicity of suture repair with the advantageous force distribution properties of mesh, and constitutes a safe, efficient, and effective method of repair with a low recurrence rate at long-term follow-up that is comparable to planar mesh repair.

Dumanian Technique for Repair of Complex Incisional Hernias

Incisional hernia is protrusion of tissue at or near the site of an incision from a previous surgery. It is a challenging procedure to repair complex incisional hernias. Most of the numerous reconstructive techniques are unable to achieve goals of hernioplasty owing to various factors being planar mesh impose the risk of pain and infection whereas conventional suture repairs can fail due to suture pull through, rupture or slipping of knot. The open components separation technique (CST) creates large undermining skin flaps especially useful in patients with complex hernias who require judicial approximation of the midline fascia. Another novel technique for repair of such hernias is the Dumanian Technique : using mesh as a suture material and has been shown to improve the ultimate tensile strength (UTS) and thus prevent surgical failure. Both the techniques are implemented in our case to achieve successful abdominal closure.

Bio-inspired ultra-sensitive directional acoustic flow sensing using electro-spun nanofiber mesh over a close-back cavity

Nearly two decades ago, it is shown that the mechanically coupled tympanic membrane ear of the Ormia fly can detect directional sound from a distance [1]. It achieves that by sensing the pressure gradient across the two coupled membranes. The recently discovered acoustic flow sensing using spider silk [2], opens new perspectives in acoustic sensing of particle velocity. Here we demonstrate an ultra-sensitive directional sensing scheme using a nanofiber mesh that is uniformly placed over the surface of a close back micro cavity. The nanofiber mesh can capture sound-induced velocity fluctuation well enough to represent the acoustic air particle velocity. Our result shows that the uniform sound field, which travels parallel to the fiber mesh plane, can drive the fiber mesh in and out of the cavity underneath. Since the small size of the cavity makes the air inside incompressible, the front and rear sides of the fiber mesh will move out of phase, much like the directional ear of the Ormia fly. By sensing acoustic air particle velocity and adopting the practical design of a back volume, this work provides a new approach for ultra-sensitive directional acoustic sensing. [1] R. N. Miles, D. Robert, and R. R. Hoy, “Mechanically coupled ears for directional hearing in the parasitoid fly Ormia ochracea,” JASA, 98(6), 3059–3070 (1995). [2] J. Zhou and R. N. Miles, “Sensing fluctuating airflow with spider silk,” Proc. Natl. Acad. Sci. U. S. A. 114(46), 12120–12125 (2017).

Research on the computational method of creeping waves diffraction of arbitrary complex target based on the planar mesh model.

For a long time, due to the difficulty of obtaining accurate propagation trajectories, the research on creeping waves is limited to canonical geometries or simple targets, which leads to the situation that it is relatively mature in theoretical research on creeping waves, while the practical application scope of creeping waves for complex targets is narrow. In this paper, a thorough electromagnetic computation method for creeping waves on complex planar mesh model is systematically proposed. This approach broadens the field of creeping waves applications due to the generality of planar mesh models in electromagnetic engineering. The contents consist of the tracing of creeping waves, the calculation of the diffraction field, and the coupling effect with other scattering mechanisms. Aiming at the trajectory of creeping waves, we propose a set of tracing algorithms that enable rapid, real-time tracing based on analytical geometry and related computer graphics algorithms. Utilizing information such as vertices, triangles, and topological relations in the mesh model, one can recover the mathematical properties of the surfaces of the model and then, the corresponding parameters can be obtained. Therefore, the uniform geometrical theory of diffraction (UTD) can be used to accurately calculate the diffraction field. Moreover, for complex targets, the multiple coupling effect caused by creeping waves is the main source of radar echoes in many cases, which is not unimportant. Hence based on the electromagnetic accurate modeling, the coupling mechanism of creeping waves and various scattering mechanisms are studied. The research content is expected to have high application values in target recognition and characteristics.

SurfaceVoronoi

In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites P = { Pi } m i =1 on the surface. We propose two key techniques to solve this problem. First, as the partition is determined by minimizing the m distance fields, each of which rooted at a source site, we suggest keeping one or more distance triples, for each triangle, that may help determine the Voronoi bisectors when one uses a mark-and-sweep geodesic algorithm to predict the multi-source distance field. Second, rather than keep the distance itself at a mesh vertex, we use the squared distance to characterize the linear change of distance field restricted in a triangle, which is proved to induce an exact VD when the base surface reduces to a planar triangle mesh. Specially, our algorithm also supports the Euclidean distance, which can handle thin-sheet models (e.g. leaf) and runs faster than the traditional restricted Voronoi diagram (RVD) algorithm. It is very extensible to deal with various variants of surface-based Voronoi diagrams including (1) surface-based power diagram, (2) constrained Voronoi diagram with curve-type breaklines, and (3) curve-type generators. We conduct extensive experimental results to validate the ability to approximate the exact VD in different distance-driven scenarios.

Tuning the Roundabout of Four-Point-Star Tiles with the Core Arm Length of Three Half-Turns for 2D DNA Arrays.

By rationally adjusting the weaving modes of point-star tiles, the curvature inherent in the tiles can be changed, and various DNA nanostructures can be assembled, such as planar wireframe meshes, perforated wireframe tubes, and curved wireframe polyhedra. Based on the weaving and tiling architectures for traditional point-star tiles with the core arm length at two DNA half-turns, we improved the weaving modes of our newly reported four-point-star tiles with the core arm length at three half-turns to adjust their curvature and rigidity for assembling 2D arrays of DNA grids and tubes. Following our previous terms and methods to analyze the structural details of E-tiling tubes, we used the chiral indices (n,m) to describe the most abundant tube of typical assemblies; especially, we applied both one-locus and/or dual-locus biotin/streptavidin (SA) labelling strategies to define the configurations of two specific tubes, along with the absolute conformations of their component tiles. Such structural details of the DNA tubes composed of tiles with addressable concave and convex faces and packing directions should help us understand their physio-chemical and biological properties, and therefore promote their applications in drug delivery, biocatalysis, biomedicine, etc.

Structure simplification of planar quadrilateral meshes

In this paper, we present a structure simplification framework for planar all-quad meshes with open boundaries. Our simplification framework can handle quad meshes with complex structures (e.g., quad meshes obtained via Catmull–Clark subdivision of the triangle meshes) to produce simpler meshes while preserving the boundary features. To achieve that, we introduce a set of separatrix-based semi-global operations and combine them with existing local operations to develop a new simplification framework. Additionally, we organize and order the individual simplification operations into groups and employ ranking strategies for each group to sort these operations to produce quad meshes with better quality and simpler structure. We provide a comprehensive evaluation of our framework using different input parameters on a number of representative planar quad meshes with various boundary configurations. To demonstrate the advantages of our method, we compare it with a few existing frameworks. Our comparison shows that our simplification framework usually produces simpler structure with faster computation than the state-of-the-art methods.