Surface Points Research Articles

AI-Powered Approaches for Hypersurface Reconstruction in Multidimensional Spaces

The present article explores the possibilities of using artificial neural networks to solve problems related to reconstructing complex geometric surfaces in Euclidean and pseudo-Euclidean spaces, examining various approaches and techniques for training the networks. The main focus is on the possibility of training a set of neural networks with information about the available surface points, which can then be used to predict and complete missing parts. A method is proposed for using separate neural networks that reconstruct surfaces in different spatial directions, employing various types of architectures, such as multilayer perceptrons, recursive networks, and feedforward networks. Experimental results show that artificial neural networks can successfully approximate both smooth surfaces and those containing singular points. The article presents the results with the smallest error, showcasing networks of different types, along with a technique for reconstructing geographic relief. A comparison is made between the results achieved by neural networks and those obtained using traditional surface approximation methods such as Bézier curves, k-nearest neighbors, principal component analysis, Markov random fields, conditional random fields, and convolutional neural networks.

Efficient object recognition under cluttered scenes via descriptor-based matching and single point voting

This paper addresses the problem of recognizing multiple objects and multiple instances from point clouds. Whereas existing methods utilize descriptors on 3D fields or pointwise voting to achieve this task, our framework takes advantage of both descriptor-based and voting-based schemes to realize more robust and efficient prediction. Specifically, we propose a novel and robust descriptor called an orientation-enhanced fast point feature histogram (OE-FPFH) to describe points in both the object model and scene, and further to build the correspondence set. The OE-FPFH integrates an orientation vector through mining the geometric tensor of the local structure of a surface point, which is more representative than the original FPFH descriptor. To improve voting efficiency, we devise a novel single-point voting mechanism (SPVM), which constructs a unique local reference frame (LRF) on a single point using the orientation vector. The SPVM takes as input the corresponding point set and can generate a pose candidate for each correspondence. The process is realized by matching LRFs from two corresponding points. All pose candidates are subsequently divided into clusters and aggregated using the K-means clustering algorithm to deduce the poses for different objects or instances in the scene. Experiments on three challenging datasets demonstrate that our method is effective, efficient, and robust to occlusions and multiple instances.

Framework of acoustic analysis and shape optimization for three-dimensional doubly periodic multilayered structures

In this research, a framework of acoustic analysis and shape optimization, based on isogeometric boundary element method (IGA-BEM), is proposed for three-dimensional doubly periodic multilayered structures. The study addresses a gap in the literature by focusing on the shape optimization of such structures, which has not been extensively explored previously. The interface between different acoustic media is an infinite doubly periodic surface, which can be constructed by an open non-uniform rational B-splines. A periodic IGA-BEM is developed for the sound field analysis of the doubly periodic multilayered structure, in which the Ewald method is used to accelerate the calculation of periodic Green function. Furthermore, the shape derivative of the doubly periodic multiple boundaries is derived by imposing boundary perturbation and using the adjoint variable method. The control points of the NURBS surfaces are defined as the shape design variables, and all shape sensitivities can be quickly calculated by discretizing the shape derivative formula. Finally, in according with shape sensitivities, the corresponding shape optimization problem is solved by the method of moving asymptotes, so that the optimized shape design can be obtained. A series of numerical examples validates the accuracy and applicability of the proposed approaches.

Fatigue life prediction for Q420qFNH weathering steel welded joints considering the effect of multiple cracks

Multiple semi-elliptical cracks frequently develop at the weld toes of welded joints. These interfering multiple cracks significantly accelerate crack growth rates and reduce the fatigue life of a welded joint compared to a single crack. This study proposes a method for predicting the fatigue life of a welded joint with multiple cracks, considering weld toe amplification effect, multiple crack interference amplification effect, and crack closure effect. The method is validated through fatigue tests on Q420qFNH weathering steel welded joints. The main factors influencing the interference amplification effect are investigated, and theoretical formulas for the interference amplification factor of the stress intensity factor are derived using the finite element method and the superposition principle. The initiation, aggregation, and morphological evolution during the propagation process of multiple cracks is accurately simulated, and the fatigue life of both cruciform-welded and butt-welded joints is predicted. Additionally, a quantitative analysis is conducted to assess the impact of the number of fatigue cracks on fatigue strength. The results indicate that the interference amplification effect of cracks depends on their distance and mainly affects the surface point where the crack front is closest. The proposed fatigue life prediction method can accurately estimate the fatigue life of Q420qFNH steel welded joints considering the effect of multi-cracks. The interference and coalescence of multiple cracks significantly reduce the fatigue life of welded joints. An increase in the number of fatigue cracks notably decreases the fatigue strength.

A generalized model of cardiac surface motion for evaluating left anterior descending coronary artery dose in left breast cancer radiotherapy.

Retrospective studies indicate that radiation damage to left anterior descending coronary artery (LAD) may be critical for late-stage radiation-induced cardiac morbidity. Developing a method that accurately depicts LAD motion and perform dose assessment is crucial. To construct a generalized cardiac surface motion model for LAD dose assessment in left breast cancer radiotherapy. Cine MRI of 25 cases were divided into training and testing sets for model construction, and five external cases were gathered for generalization validation. Motion prediction from average intensity projection images (AIP) surface point cloud to that of each phase was realized by mapping the relationship between datum points and corresponding points with statistical shape modeling (SSM). Root mean square error (RMSE) for predicted corresponding points and Euclidean distance (ED) for predicted surface point cloud were used to assess model's accuracy. LAD dose assessment for 10 left breast cancer radiotherapy cases was perform by model application. The RMSE in testing cases and external cases were 0.209±0.020mm to 0.841±0.074mm and 0.895±0.093mm to 1.912±0.138mm, respectively; while the ED were 1.399±0.029mm to 1.658±0.100mm, 1.571±0.080mm to 1.779±0.104mm, respectively, proving the generalized model's high accuracy. The volume of LAD characterizing motion range (WPLAD) (2.392±0.639 cm3) was approximately twice that of LAD from superimposed images (SPLAD) (0.927±0.326 cm3) with p<0.05, and the former's Dmax (3582.06±575.92 cGy) was significantly larger than latter's (3222.71±665.37 cGy) (p<0.05). While WPLAD's Dmean (1408.06±413.06 cGy) was slightly smaller than that of SPLAD (1504.15±448.03 cGy), the difference did not reach statistical significance (p>0.05). WPLAD's V20 (23.42%±16.62%) was less than SPLAD's (29.18%±21.07%) with p<0.05, but their comparison in V30 and V40 did not yield statistically significant results. It implies the conventional LAD dose assessment ignores motion impact and may not be justified. The generalized cardiac surface motion model informs LAD dose accurate assessment in left breast cancer radiotherapy.

Maximum Lateral Expansion of Wetting Bulbs from Buried and Surface Point Sources: Implications for Drip Irrigation Design

Maximum Lateral Expansion of Wetting Bulbs from Buried and Surface Point Sources: Implications for Drip Irrigation Design

Accuracy of the geometric shape of the hole in the longitudinal section during honing

The wide application of honing as a finishing treatment of internal cylindrical surfaces for cylinder-piston systems, used in some structures, is caused by high accuracy measured in tenths of a micrometer, and high productivity of the process. The most important indicator of reliable operation of cylinder-piston systems are high requirements for the geometric accuracy of holes. Due to the lack of sufficient theoretical justification for the selection of honing parameters ensuring the accuracy of the geometric shape of the hole in the longitudinal section, the authors proposed a model for the formation of errors in the geometric shape of the hole. The model is built on the kinematic characteristics of the process including the ratio of the honing stone dimensions, the length of the hole, the stroke of the honing head, the ratio of the speeds of translational and rotational movements, and the force action in the processing zone, which changed due to the presence of an overrun of the honing stone. To obtain analytical dependencies ensuring the minimisation of form deviations, the conditions for stock removal for the points of the machined surface were considered, the value of which was taken proportional to the path of movement, and the pressure value. For this purpose, graphs of the distribution functions of displacements and pressure changes were constructed depending on the coordinate of the point location on the generating line of the hole being machined. Using the obtained analytical dependencies, the potential occurrence of a shape error in the form of a saddle shape was found, the dominant factor influencing the value of which is the value of the honing stone overrun. At the same time, it was identified that the ratio of the speeds of translational and rotational movements has an insignificant effect on the violation of the form in the longitudinal section.

Generation of arbitrarily patterned polarizers using 2-photon polymerization

Patterned polarizers are prepared using liquid crystals (LC) doped with a black dichroic dye and in combination with a linear polarizer. The pattern is achieved with a nanostructured LC alignment surface, that is generated using a two-photon polymerization direct laser write (2PP-DLW). This technique creates a pattern of high-resolution grooves in the photoresist at any arbitrary angle. The angle governs the LC orientation at any substrate surface point, determining the transmitted light linear polarization angle. This paper presents the first use of a 2PP-DLW cured positive tone photoresist for dichroic dye-doped LC alignment. Two complementary photoresists have been employed: conventional negative tone SU-8 photoresist and, in this context novel, positive tone S1805 photoresist. The alignment quality of the polarizers has been assessed by analyzing the transmission using an additional polarizer. For SU-8, the resulting grayscale pattern and a contrast ratio (CR) of 14 has measured. The uniformity of the alignment has been measured to be 65% using normalized Shannon entropy (H). For S1805, a CR of 37 was measured, and a uniformity of 63% was obtained. 2PP-DLW allows for shaping complex patterns in submicron dimensions and for the fabrication of arbitrarily patterned polarizers and other LC devices.

Point cloud data-driven modelling of high-strength steel wire corrosion pits considering orientation features

We propose a corrosion pit modelling approach of high-strength steel wires considering orientation features using surface point cloud data, collected by three-dimensional laser scanning. Corrosion pits were identified through density-based spatial clustering of applications with noise (DBSCAN). The identified corrosion pits could be modelled as a semiellipsoid considering orientation features. The Gaussian copula model was utilised to describe the joint distribution of the geometric parameters of the corrosion pits. This approach will be valuable for simulation of the surface morphology of corroded high-strength steel wires.

A Surface Determination Technique for Dimensional and Geometrical Analysis in Industrial X-ray Computed Tomography

Industrial X-ray computed tomography (XCT) is a nondestructive technique that can measure workpieces with non-accessible internal features or multimaterial components and assess the dimensional properties of assemblies in assembled states. Surface determination is one of its most crucial steps, which consists of determining boundary surfaces between a solid material and the surrounding air or between different solid materials. It allows for extracting surface points and assessing different features of the object from the data acquired through XCT scans. This task is particularly complex because of challenges associated with material properties, artefacts and noise. The main objective of this work is to assess not just the dimensional but also the geometric characteristics of industrial parts, which requires a more accurate definition of surface points. Therefore, we propose a new surface determination technique (SDT) in XCT to achieve subvoxel accuracy in determining surface points. We demonstrated the effectiveness and stability of our method by comparing it with other SDTs documented in the literature or with results from commercial software. The validation involved measuring various attributes, such as diameter, cylindricity and flatness, of a multi-stepped aluminium part calibrated by a coordinate measuring machine.

Four Different Build Angles in 3D-Printed Complete Denture Bases: A Comparative In Vitro Study

In this study, we aimed to investigate the differences in tissue surface adaptation and the variations in distances between reference points on the polished surfaces of 3D-printed denture bases produced at different build angles. The build angles were 0°, 30°, 60°, and 90°, with 15 denture bases printed for each angle. Using the Geomagic Control® software, a 3D best-fit alignment was conducted between the denture base tissue surface and the reference shape of the edentulous maxilla model to calculate the root mean square error. The distances between reference points on the polished surface were measured using digital calipers. A one-way analysis of variance was conducted for statistical analysis. The adaptation, as measured by the root mean square error, varied significantly among denture bases with different build angles. The distances between the anterior and posterior reference points of the polished surface were also significantly different. However, within the limitations of this study, the variations in adaptations and dimensional accuracy across different build angles were within clinically acceptable ranges. In clinical practice, the print angle can be adjusted based on factors such as printing time, resin consumption, and the number of denture bases being printed simultaneously.

Isogeometric topology optimization for maximizing band gap of two-dimensional phononic crystal structures

A smooth and efficient isogeometric topology optimization (ITO) method for maximizing band gaps in two-dimensional phononic crystals is developed in the paper. The band gaps of phononic crystals are computed by the NURBS-based isogeometric analysis, and the material distributions of two-dimensional phononic crystals are represented by the smooth, high-order continuity of the NURBS surface. The densities defined at each control point of the NURBS surface are employed as optimized design variables. The isogeometric analysis optimization using the same spline technique for both geometry and numerical analysis can benefit the optimization procedure and obtain smooth optimized structures, which can be easily used in 3D printing. The maximizing band gaps of phononic crystals for both out-of-plane and in-plane wave modes are obtained here using the present ITO approach. Numerical examples validated the effectiveness and reliability of the ITO method in broadening the band gaps and finding the optimal phononic crystals. And the numerical results show that the smooth optimized structures are obtained with fewer iterations.

Sigmoidal learning rate optimizer for deep neural network training using a two-phase adaptation approach

The optimization of machine learning models is an open research question since an optimal procedure to change the learning rate throughout training is still unknown. Manually defining a learning rate schedule involves troublesome, time-consuming try-and-error procedures to determine hyperparameters, such as learning rate decay epochs and learning rate decay rates, in order to navigate the intricate landscape of loss functions. Although adaptive learning rate optimizers automatize this process, recent studies suggest they may produce overfitting and reduce performance compared to fine-tuned learning rate schedules. Considering that the new machine learning loss function approaches present landscapes with much more saddle points than local minima, we proposed the Training Aware Sigmoidal Optimizer (TASO). This automated two-phase learning rate adaptation mechanism significantly reduces the need for manual hyperparameter tuning. The first phase uses a high learning rate to quickly traverse the numerous saddle points in the error surface, while the second phase uses a low learning rate to gradually approach the center of the local minimum previously found. We compared the proposed approach with commonly used adaptive learning rate schedules such as Adam, RMSProp, and Adagrad. The validation experiments were performed in image and text datasets and showed that TASO outperformed all competing methods in optimal (i.e., performing hyperparameter validation) and suboptimal (i.e., using default hyperparameters) scenarios. In our benchmark tests, TASO demonstrated promising performance, achieving an 8.32% increase in accuracy and a significant 46.62% decrease in training loss on average across various datasets and models. This remarkable performance positions TASO ahead of well-established adaptive optimizers, suggesting higher effectiveness and consistency in performance.

Partially invariant solution with an arbitrary surface of blow-up for the gas dynamics equations admitting pressure translation

We applied a method of symmetry reduction to the gas dynamics equations with a special form of the equation of state. This equation of state is a pressure represented as the sum of a density and an entropy functions. The symmetry Lie algebra of the system is 12-dimensional. One, two and three-dimensional subalgebras were considered. In this article, four-dimensional subalgebras are considered for the first time. Specifically, invariants are calculated for 50 four-dimensional subalgebras. Using invariants of one of the subalgebras, a symmetry reduction of the original system is calculated. The reduced system is a partially invariant submodel because one gas-dynamic function cannot be expressed in terms of the invariants. The submodel leads to two families of exact solutions, one of which describes the isochoric motion of the media, and the other solution specifies an arbitrary blow-up surface. For the first family of solutions, the particle trajectories are parabolas or rays; for the second family of solutions, the particles move along cubic parabolas or straight lines. From each point of the blow-up surface, particles fly out at different speeds and end up on a straight line at any other fixed moment in time. A description of the motion of particles for each family of solutions is given.

Compressing and Recovering Short-Range MEMS-Based LiDAR Point Clouds Based on Adaptive Clustered Compressive Sensing and Application to 3D Rock Fragment Surface Point Clouds.

Short-range MEMS-based (Micro Electronical Mechanical System) LiDAR provides precise point cloud datasets for rock fragment surfaces. However, there is more vibrational noise in MEMS-based LiDAR signals, which cannot guarantee that the reconstructed point cloud data are not distorted with a high compression ratio. Many studies have illustrated that wavelet-based clustered compressive sensing can improve reconstruction precision. The k-means clustering algorithm can be conveniently employed to obtain clusters; however, estimating a meaningful k value (i.e., the number of clusters) is challenging. An excessive quantity of clusters is not necessary for dense point clouds, as this leads to elevated consumption of memory and CPU resources. For sparser point clouds, fewer clusters lead to more distortions, while excessive clusters lead to more voids in reconstructed point clouds. This study proposes a local clustering method to determine a number of clusters closer to the actual number based on GMM (Gaussian Mixture Model) observation distances and density peaks. Experimental results illustrate that the estimated number of clusters is closer to the actual number in four datasets from the KEEL public repository. In point cloud compression and recovery experiments, our proposed approach compresses and recovers the Bunny and Armadillo datasets in the Stanford 3D repository; the experimental results illustrate that our proposed approach improves reconstructed point clouds' geometry and curvature similarity. Furthermore, the geometric similarity increases to 0.9 above in our complete rock fragment surface datasets after selecting a better wavelet basis for each dimension of MEMS-based LiDAR signals. In both experiments, the sparsity of signals was 0.8 and the sampling ratio was 0.4. Finally, a rock outcrop point cloud data experiment is utilized to verify that the proposed approach is applicable for large-scale research objects. All of our experiments illustrate that the proposed adaptive clustered compressive sensing approach can better reconstruct MEMS-based LiDAR point clouds with a lower sampling ratio.

Long-term releasing and migration characteristics of chloride ions in chloride-based asphalt mixtures

Chloride-based pavement lowers freezing point of pavement surface and delays ice formation by releasing chloride ions. However, the long-term effectiveness of chloride filler has not been well-understood. This study combined the experimental and simulation methods to investigate the long-term releasing characteristics of chloride ions inside chloride-based mixtures. In this study, two types of chloride-based asphalt mixtures (AC-13 and OGFC-13) were prepared with Mafilon (MFL) and immersed in deionized water. The electrical conductivity tests were conducted on leaching water to evaluate the long-term releasing characteristic of chloride ions. The migration simulation was carried out on MFL AC-13 subjected to wet-dry cycles to explore the migration characteristics of chloride ions inside MFL AC-13 mixture. Results show that chloride ions experiences a rapid release within 30d in water, followed by a gradual and sustained release. Half of the chloride ions in mixture containing 70 % MFL will released into water after immersion for 278d at 20°C or 74d at 60°C, respectively. The long-term release of chloride ions can be significantly improved by increasing the MFL dosage in asphalt mixtures. Chloride ions in mixture surface preferentially released into leaching water, resulting in a higher concentration of residual chloride in core of the mixture. During the drying phase, the chloride ions concentration throughout the asphalt mixture tends to become uniform as drying time increases. The findings achieved in this study would benefit and promote the better use of MFL in anti-icing pavement.

Fretting fatigue life of galvanized bridge support cable wire: Experimental study and strain-based fracture mechanics analysis

The galvanized wires used in cable bridges can fail due to fretting fatigue. Experimental results have shown that defects resulting from the galvanization process are a possible source of initiation for fatigue cracks and make the life shorter than that of a wire without a galvanized layer. The investigation presented in this paper uses strain-based fracture mechanics to analyze the influence of these defects on the fatigue life of galvanized wire. The presented analysis considers nonlinear material behaviour. A 3D finite element model is used to compute the required stress field. Stress intensity factors are obtained by a proposed numerical point load weight function, and shape factors are found for the surface and deepest points of the semielliptical crack. Plain fatigue tests of galvanized wires are performed to calibrate key model parameters. The calibrated model is then shown to provide reasonably accurate but systematically conservative estimates of the fatigue life under fretting conditions typical of bridge stay cable saddle supports.

Tessellation and interactive visualization of four-dimensional spacetime geometries

This paper addresses two problems needed to support four-dimensional (3d+t) spacetime numerical simulations. The first contribution is a general algorithm for producing conforming spacetime meshes of moving geometries. Here, the surface points of the geometry are embedded in a four-dimensional space as the geometry moves in time. The geometry is first tessellated at prescribed time steps and then these tessellations are connected in the parameter space of each geometry entity to form tetrahedra. In contrast to previous work, this approach allows the resolution of the geometry to be controlled at each time step. The only restriction on the algorithm is the requirement that no topological changes to the geometry are made (i.e. the hierarchical relations between all geometry entities are maintained) as the geometry moves in time. The validity of the final mesh topology is verified by ensuring the tetrahedralizations represent a closed 3-manifold. For some analytic problems, the 4d volume of the tetrahedralization is also verified. The second problem addressed in this paper is the design of a system to interactively visualize four-dimensional meshes when the 4d view changes, including tetrahedra (embedded in 4d) and pentatopes. Algorithms that either include or exclude a geometry shader are described, and the efficiency of each approach is then compared. Overall, the results suggest that visualizing tetrahedra (either those bounding the domain, or extracted from a pentatopal mesh) using a geometry shader achieves the highest frame rate, realizing interactive frame rates of at least 15 frames per second for meshes with about 50 million tetrahedra.

Damage mechanism and bending properties degradation of aviation composite honeycomb sandwich structures under laser irradiation

Damage mechanism and bending properties degradation of aviation composite honeycomb sandwich structures are studied under different laser conditions in this paper. Firstly, the damage test of composite honeycomb sandwich structures is conducted. Temperature field and ablation process during laser irradiation are analyzed. Damage morphology and mechanism are verified. Secondly, the influence of laser damage on the bending properties of composite honeycomb panels is studied. Progressive damage process and failure mechanism of honeycomb structures during loading are explored by digital image correlation (DIC) and strain trend. The results show that the temperature at the center point of front surface reaches more than 2000 °C within 1 s under the laser irradiation, while the temperature of back surface exhibits hysteresis. The ablation hole is funnel-shaped and has severe delamination. In the heat affected zone (HAZ), resin matrix has been basically sublimated and oxidized, leaving only carbon fiber bundles and some residual carbon. The honeycomb core in this area has been completely carbonized and deformed. During bending process, the honeycomb core breaks firstly, and strain appears peak at both crack ends, leading the crack extend along both sides. The ultimate load of damaged specimen is 2.35kN, which has a 42.26 % drop compared to that of healthy specimen 4.07kN. Bending properties of specimen are significantly degraded by laser damage.

Boundary points guided 3D object detection for point clouds

3D object detection in LiDAR point clouds is crucial for computer vision tasks such as autonomous driving. The two-stage approach with point cloud completion achieves remarkable performance by generating semantic surface points for foreground objects or learning bird’s eye view shape heat map labels. However, these methods require additional completion datasets, leading to substantial computation and memory demands. In this context, we propose a Boundary Points Guided 3D (BPG3D) object detection method that complements point cloud boundary information without the need for additional data. Specifically, we generate Region of Interest (RoI) boundary points to aggregate the neighbor voxel information at the RoI boundary during the refinement stage to complement the missing boundary information. Meanwhile, we design a Dual Feature Selection (DFS) module to adaptively fuse RoI grid point features and RoI boundary point features for bounding box refinement with negligible computational cost. Additionally, inspired by tensor decomposition theory, we use low-rank tensors to reconstruct high-rank tensors in the point cloud feature encoder to enhance contextual semantic information. The proposed method achieves 65.81% mAP on KITTI Test Set, obtaining a good trade-off between accuracy and efficiency.