Geometric Point Research Articles

Geometric and semantic point cloud data for quality control of bridge girder reinforcement cages

The reinforcement of bridge girders is critical to ensuring adequate strength, serviceability, and durability. Achievement of these criteria is assessed by quality control processes conducted throughout construction. This study explores two methods for processing point clouds of bridge girder reinforcement cages, to output positional and dimensional data utilised for quality control. An extended slicing method is first employed to enable the segmentation and classification of 3D rebar within complex bridge girder reinforcement cages. A semantic enrichment method is then used to infer data regarding the the individual rebar and rebar shapes, and improve the accuracy of prior identified information. The proposed algorithms were tested on two point clouds of bridge girder reinforcement cages collected on-site. Positional results, spacing and orientation, reported an average error of less than 2 mm and 0.1o. An average error of 5% was reported for the dimensional length of rebar, decreasing to 1% following the semantic enrichment algorithm. The basis of the presented methodology, including the identification, separation, and grouping for distinct placements of rebar (longitudinal, vertical, and transverse) can be extended for application to other common reinforcement cage archetypes.

Linking Off-Road Points to Routing Networks

Although graph theory has already been introduced in spatial reasoning, current spatial database systems do not provide out-of-the-box routing on geometric points that are not matched on the graph. Methods that connect new reference locations to the graph render different routing results. Moreover, current solutions break reasoning down to local analysis. We bridge the gap between routing networks and spatial geometry by a global matching of geometric points to routing networks.

A GLSM View on Homological Projective Duality

Given a gauged linear sigma model (GLSM) \({\mathcal {T}}_{X}\) realizing a projective variety X in one of its phases, i.e. its quantum Kähler moduli has a geometric point, we propose an extended GLSM \({\mathcal {T}}_{{\mathcal {X}}}\) realizing the homological projective dual category \({\mathcal {C}}\) to \(D^{b}Coh(X)\) as the category of B-branes of the Higgs branch of one of its phases. In most of the cases, the models \({\mathcal {T}}_{X}\) and \({\mathcal {T}}_{{\mathcal {X}}}\) are anomalous and the analysis of their Coulomb and mixed Coulomb-Higgs branches gives information on the semiorthogonal/Lefschetz decompositions of \({\mathcal {C}}\) and \(D^{b}Coh(X)\). We also study the models \({\mathcal {T}}_{X_{L}}\) and \({\mathcal {T}}_{{\mathcal {X}}_{L}}\) that correspond to homological projective duality of linear sections \(X_{L}\) of X. This explains why, in many cases, two phases of a GLSM are related by homological projective duality. We study mostly abelian examples: linear and Veronese embeddings of \({\mathbb {P}}^{n}\) and Fano complete intersections in \({\mathbb {P}}^{n}\). In such cases, we are able to reproduce known results as well as produce some new conjectures. In addition, we comment on the construction of the HPD to a nonabelian GLSM for the Plücker embedding of the Grassmannian G(k, N).

Scaling behaviour of braided active channels: a Taylor’s power law approach

At a channel (reach) scale, braided channels are fluvial, geomorphological, complex systems that are characterized by a shift of bars during flood events. In such events water flows are channeled in multiple and mobile channels across a gravel floodplain that remain in unmodified conditions. From a geometrical point of view, braided patterns of the active hydraulic channels are characterized by multicursal nature with structures that are spatially developed by either simple- and multi-scaling behavior. Since current studies do not take into account a general procedure concerning scale measurements, the latter behavior is still not well understood. The aim of our investigation is to analyze directly, through a general procedure, the scaling behavior of hydraulically active channels per transect and per reach analyzed. Our generalized stochastic approach is based on Taylor’s law, and the theory of exponential dispersion distributions. In particular, we make use of a power law, based on the variance and mean of the active channel fluctuations. In this way we demonstrate that the number of such fluctuations with respect to the unicursal behavior of the braided rivers, follows a jump-process of Poisson and compound Poisson–Gamma distributions. Furthermore, a correlation is also provided between the scaling fractal exponents obtained by Taylor’s law and the Hurst exponents.

Grain Boundary—A Route to Enhance Electrocatalytic Activity for Hydrogen Evolution Reaction

The electrocatalytic hydrogen evolution reaction (HER) of a given metal catalyst is intrinsically related to its electronic structure, which is difficult to alter for further improvement. Recently, it was discovered that the density of grain boundaries (GBs) is mechanistically of great importance for catalytic activity, implying that GBs are quantitatively correlated with the active sites in the HER. Here, by modeling the atomistic structure of GBs on a Au(110) surface, we find that HER performance is greatly enhanced by Au GBs, suggesting the feasibility of the HER mediated by GBs. The promoted HER performance is due to an increase in the capability of binding adsorbed hydrogen on the sites around GBs. A Au catalyst with a dominantly exposed (110) plane is synthesized, where considerable GBs exist for experimental verification. It is found that HER activity is inherently correlated with the density of the GBs in Au NPs. The improvement in HER activity can be elucidated from the geometrical and electronic points of view; the broken local spatial symmetry near a GB causes a decrease in the coordination numbers of the surface sites and the shift up of the d–band center, thereby reducing the limiting potential for each proton−electron transfer step. Our finding represents a promising means to further improve the HER activity of a catalyst.

Demonstrating the benefits of corrective intraoperative feedback in improving the quality of duodenal hydrogel spacer placement.

PurposePancreatic cancer is the fourth leading cause of cancer‐related death with a 10% 5‐year overall survival rate (OS). Radiation therapy (RT) in addition to dose escalation improves the outcome by significantly increasing the OS at 2 and 3 years but is hindered by the toxicity of the duodenum. Our group showed that the insertion of hydrogel spacer reduces duodenal toxicity, but the complex anatomy and the demanding procedure make the benefits highly uncertain. Here, we investigated the feasibility of augmenting the workflow with intraoperative feedback to reduce the adverse effects of the uncertainties.Materials and MethodsWe simulated three scenarios of the virtual spacer for four cadavers with two types of gross tumor volume (GTV) (small and large); first, the ideal injection; second, the nonideal injection that incorporates common spacer placement uncertainties; and third, the corrective injection that uses the simulation result from nonideal injection and is designed to compensate for the effect of uncertainties. We considered two common uncertainties: (1) “Narrowing” is defined as the injection of smaller spacer volume than planned. (2) “Missing part” is defined as failure to inject spacer in the ascending section of the duodenum. A total of 32 stereotactic body radiation therapy (SBRT) plans (33 Gy in 5 fractions) were designed, for four cadavers, two GTV sizes, and two types of uncertainties. The preinjection scenario for each case was compared with three scenarios of virtual spacer placement from the dosimetric and geometric points of view.ResultsWe found that the overlapping PTV space with the duodenum is an informative quantity for determining the effective location of the spacer. The ideal spacer distribution reduced the duodenal V33Gy for small and large GTV to less than 0.3 and 0.1cc, from an average of 3.3cc, and 1.2cc for the preinjection scenario. However, spacer placement uncertainties reduced the efficacy of the spacer in sparing the duodenum (duodenal V33Gy: 1.3 and 0.4cc). The separation between duodenum and GTV decreased by an average of 5.3 and 4.6 mm. The corrective feedback can effectively bring back the expected benefits from the ideal location of the spacer (averaged V33Gy of 0.4 and 0.1cc).ConclusionsAn informative feedback metric was introduced and used to mitigate the effect of spacer placement uncertainties and maximize the benefits of the EUS‐guided procedure.

FPCC: Fast point cloud clustering-based instance segmentation for industrial bin-picking

Instance segmentation is an important pre-processing task in numerous real-world applications, such as robotics, autonomous vehicles, and human–computer interaction. Compared with the rapid development of deep learning for two-dimensional (2D) image tasks, deep learning-based instance segmentation of 3D point cloud still has a lot of room for development. In particular, distinguishing a large number of occluded objects of the same class is a highly challenging problem, which is seen in robotic bin-picking. In a usual bin-picking scene, many identical objects are stacked together and the model of the objects is known. Thus, the semantic information can be ignored; instead, the focus in the bin-picking is put on the segmentation of instances. Based on this task requirement, we propose a Fast Point Cloud Clustering (FPCC) for instance segmentation of industrial bin-picking scene. FPCC includes a network named FPCC-Net and a fast clustering algorithm. FPCC-Net extracts features of each point and infers geometric center points of each instance simultaneously. After that, the proposed clustering algorithm clusters the remaining points to the closest geometric center in feature embedding space. Experiments show that FPCC also surpasses the existing works in bin-picking scenes and is more computationally efficient. Our code and data are available at (https://github.com/xyjbaal/FPCC).

Quasimusic: tilings and metre

In this paper, I try to explain how, by using concepts and ideas from the mathematical theory of tilings, we can approach metre in music through a geometric and algebraic point of view, being pinned down by a subgroup of with the hierarchical structure, leading to an abstract approach to rhythm, tempo and time signatures. I will also describe an algorithmic approach to write down sound using this structure which gives a way in which music can be written in an irrational metre.

Local spin base invariance from a global differential–geometrical point of view

This article gives a geometric interpretation of the spin base formulation with local spin base invariance of spinors on a curved space-time and, in particular, of a central element, the global Dirac structure, in terms of principal and vector bundles and their endomorphisms. It is shown that this is intimately related to Spin and SpinC structures in the sense that the existence of one of those implies the existence of a Dirac structure and allows for an extension to local spin base invariance. Vice versa, as a central result, the existence of a Dirac structure implies the existence of a SpinC structure. Nevertheless, the spin base invariant setting may be considered more general, allowing for more physical degrees of freedom. Furthermore, arguments are given that the Dirac structure is a more natural choice as a variable for (quantum) gravity than tetrads/vielbeins.

Measurement of constant radius swept features in cultural heritage

Abstract The dimensional characterization of archaeological fragment is a very complex operation and could prove to be useful for identifying the presence of standard attributes in the ceramics found from a specific archaeological site, or for making comparisons and analysis of similarities or for studying ancient technologies used for manufacture of objects. The dimensional analysis of the fragments is now carried out manually with traditional measuring devices. Typically, the results obtained are inaccurate and non-repeatable measurements. This paper focuses on the dimensional characterization of a specific geometric class of features: the constant radius swept features (called here CRS features). Several archaeological features, such as rims, bases, decorative motifs, processing marks and grooves are referable from a geometric point of view to the class of CRS features. These are detail features, which may be very interesting for the investigation of some aspects related to the historical-archaeological classification of the find. CRS features are often found on worn, damaged (e.g. chipped) or fragmented objects; they are frequently characterized, from a geometric point of view, by free form surfaces and by a limited cross sectional extension. In some cases, CRS features can be of axially symmetrical geometry: this occurs quite frequently in the case of archaeological pottery. For all these reasons, it is often difficult to apply traditional manual methods for the quantitative dimensional characterization of CRS features. This paper describes an original methodology for the measurement of CRS features acquired by scanning technologies. The algorithmic implementation of this methodology, consisting of a suitable processing of the feature nodes, allows to carry out automatically the dimensional characterization of the feature.

An iterative algorithm for inverse displacement analysis of Hyper-redundant elephant’s trunk robot

AbstractThis paper proposes an iterative algorithm to solve the inverse displacement for a hyper-redundant elephant’s trunk robot (HRETR). In this algorithm, each parallel module is regarded as a geometric line segment and point model. According to the forward approximation and inverse pose adjustment principles, the iteration process can be divided into forward and backward iteration. This iterative algorithm transforms the inverse displacement problem of the HRETR into the parallel module’s inverse displacement problem. Considering the mechanical joint constraints, multiple iterations are carried out to ensure that the robot satisfies the required position error. Simulation results show that the algorithm is effective in solving the inverse displacement problem of HRETR.

Design of Novel Cooling Systems Based on Metal Plates with Channels of Shapes Inspired by Nature

The effect of the channel shape of aluminum plates on cooling capacity was evaluated by studying different configurations. Common shapes of the channel, such as square and fork shapes, were compared with novel configurations inspired by shapes found in nature, specifically the shape of the outline of flowers, inspired these new configurations, consisting of channels with crateriform, salverform, and cruciform shapes. The aim of the study is to evaluate the effect of the channel shape on the cooling capacity of the metal plate. To that end, all the configurations were analyzed from a geometrical point of view, determining the minimum distance of each point across the plate to the channel. A finite difference method was implemented to study both transient and steady state heat dissipation across the plates for each configuration. Even though the effect of the channel shape on the average temperature of the plate is slight, the maximum temperature, the size and location of hot spots, and the temperature homogeneity of the plate are strongly affected by the shape of the channel through which the cooling fluid is circulated. A reduction in the maximum temperature of the plate during transient cooling of around 2 °C for the crateriform and salverform channels and approximately 4.5 °C for the cruciform channel can be attained, compared to the standard configurations. The steady state heat dissipation analysis concluded that the crateriform and salverform configurations reduced the maximum variation in temperature of the common configurations by roughly 15%, whereas a reduction of approximately 28% could be reached by the cruciform configuration. Regarding the homogeneity of temperature across the plate, a reduction up to 34.5% of the index of uniform temperature can be attained using the novel configurations during the steady state refrigeration of the plate. The cruciform channel is the optimal configuration for both transient and steady state cooling processes, reducing the size and temperature of hot spots and improving the temperature homogeneity of the plate, a result already anticipated by the geometrical analysis. In fact, the main conclusions attained from the cooling study are in good agreement with the results of the geometrical analysis. Therefore, the geometrical analysis was found to be a simple and reliable method to design the shape of channels of a cooling system.

Laser driven coherent white emission of graphene bulb

The laser-driven white emission of graphene foam in a vacuum bulb was investigated. Thanks to high brightness of light emission attributed to multiphoton ionization, it was possible to construct a compact, spatially coherent, white light source. A new graphene foam bulb was designed to efficiently couple white light into a multimode fiber. The efficiency of coupling light to multimode fibers with varying core diameters was measured. It is concluded that the performance of the graphene foam bulb is close to that simulated for an ideal geometrical point source.

Novel generation method of tooth surface points for variable transmission ratio gears

Variable transmission ratio gears have shown considerable potential as key components of variable speed transmission steering boxes that balance steering portability and sensitivity. The objective of this study is to develop a novel method for designing variable transmission ratio tooth surfaces to circumvent the shortcomings of the meshing theory method. The involute rack of the variable transmission ratio pinion-and-rack pair is considered as a set of countless and infinitely close transverse sections, each of which is referred to as a gear element. Assuming evenly distributed circles in the physical domain of the variable transmission ratio tooth surfaces of the pinion, the problem of generating a tooth surface point is transformed into solving the specific geometric feature intersection point of each circle and corresponding gear element during variable transmission ratio meshing. Thereafter, a mathematical model and algorithm are developed to generate tooth surface points in an approximately even pattern. The normal deviations of the gear-element–generated tooth surface points and the corresponding tooth surface points calculated using meshing theory show that the proposed design method has a sufficiently high accuracy. Finite element models are employed analyzing the contact pattern, contact stress, bending stress, and transmission ratio error. The results indicate that the layout of approximately even tooth surface points using the gear element method is beneficial for improving the fitting precision of tooth surfaces and reducing the contact stress and transmission ratio error. Further, the same derived law of the flank and fillet tooth surfaces is conducive to the continuity of the tooth surfaces, which contributes toward reducing the bending stress. Finally, a prototype is manufactured via CNC end milling. The major contributions lie in a robust and efficient modeling method for variable transmission ratio tooth surfaces, which combined forms a solid foundation for their application.

Viewing the network parameters and H‐factors from the perspective of geometry

Recent studies have shown that there is a profound connection between the existence of H -factors under attack circumstances and the parameters to measure the vulnerability of the network. The disadvantage of the previous theoretical conclusions is that the connectivity is often regarded as fixed, and the relationship between other network parameters and the H -factor is explored. However, in a real situation, as the network structure changes, connectivity becomes a dynamically variational parameter, and its changing will affect other parameters to make corresponding changes. In this study, we treat all parameters as a complex system that restricts each other, consider their mutual constraints from a geometric point of view, and apply high-dimensional surfaces to characterize their relationships. Seven network parameters including toughness and binding number are considered, and the concrete expression form of the surfaces in several specific settings are obtained. Furthermore, the local version for these seven network parameters are introduced.

Identifying Balls Feature in a Large-Scale Laser Point Cloud of a Coal Mining Environment by a Multiscale Dynamic Graph Convolution Neural Network.

In the process of coal mining, a certain amount of gas will be produced. Environmental perception is very important to realize intelligent and unmanned coal mine production and operation and to reduce the accident rate of gas explosion and other disasters. The identification of geometric features of the coal mine working face is the main part of the environmental perception of the working face. In this study, we identify geometric features in a large-scale coal mine working face point cloud (we take the ball as an example) so as to provide a method for the environmental perception of the coal mine working face. On the basis of previous research, we upgrade the dynamic graph convolution neural network (DGCNN) for directly processing point clouds from two aspects: extracting local features and global features of point clouds. First, a multiscale dynamic graph convolution neural network (MS-DGCNN) is proposed, and the combination of max-pooling and average-pooling is used as the symmetry function. Second, we use MS-DGCNN to learn the features of a variety of geometric point clouds in the point cloud data set we make and then look for the ball in the large-scale point cloud of the coal mining working face. Finally, we compare the performance of MS-DGCNN with that of other deep neural networks directly processing point clouds. This study enables MS-DGCNN to obtain more powerful feature expression ability and enhance the generalization of the model. In addition, this study provides a solid foundation for the geometric feature identification of MS-DGCNN in the environmental perception of the coal mine working face and creates a precedent for the application of MS-DGCNN in the field of energy. At the same time, this study makes a beneficial exploration for the development of a transparent coal mine working face.

Compression-after-impact effect on postbuckling behavior of thermoplastic composite laminated plates

This paper investigates the postbuckling behavior of carbon fiber reinforced thermoplastic composite (CFRTPC) laminated plates under uni-axial compression-after-impact (CAI). A physical model is proposed where both internal damage and local geometric imperfection of the plate caused by impact are taken into account. The distributed damage and impacted region of the plate are determined by using X-ray computed tomography analysis. An experiment-based approach is utilized to obtain the nonlinear constitutive law along with the stiffness degradation for the CFRTPC laminated plates. The experiments for two CFRTPC laminated plates under uni-axial compression-after-impact are carried out firstly. Then the experimental data are compared with finite element numerical results to validate the present method. The numerical results reveal that the postbuckling load-deflection curves of CFRTPC laminated plates under CAI are significantly influenced by the initial local geometric imperfection, impact point position, plate width-to-thickness ratio and boundary conditions. In contrast, the initial local geometric imperfection and impact point position only have a small effect on the postbuckling load-shortening curves of CFRTPC laminated plates under CAI.

Optimization of Airfoil Blend Limits With As-Manufactured Geometry Finite Element Models

Abstract Conventional airfoil blend repair limits are established using nominal, design intent geometry. This convention does not explicitly consider the inherent blade-to-blade structural response variation associated with geometric manufacturing deviations. In this work, we explore whether accounting for these variations leads to significant differences in blend depths and develop a novel approach to effectively predict blade-specific blend allowable. These blade-specific values maximize the part repairability according to their proximity to defined structural integrity constraints. The methodology is demonstrated on the as-manufactured geometry of an aerodynamic research rig compressor rotor. Geometric point cloud data of this rotor is used to construct as-built finite element models (FEMs) of each airfoil. The effect of two large blends on these airfoils demonstrates the opportunity of blade-specific blend limits. A new approach to determine each airfoil's blend repair capacity is developed that uses sequential least-squares quadratic programing and a parametric blended blade FEM that accounts for manufacturing geometry variations and variable blend geometry. A mesh morphing algorithm modifies a nominal geometry model to match the as-built airfoil surface and blend geometry. The numerical optimization maximizes blend depth values within the frequency, mode shape, and high cycle fatigue constraint boundaries. It is found that there are large variations in blend depth allowable between blades and competing structural integrity criteria are responsible for their limits. It is also found that, despite complex modal behavior caused by eigenvalue veering, the proposed optimization approach converges. The developed methodologies may be used in the future to extend blend limits, enable continued operations, and reduce sustainment costs.

3-D Contour Deformation for the Point Cloud Segmentation

The 3-D point cloud segmentation has played an important role in spatial structure analysis. Nowadays, segmentation methods either use a primitive-based strategy to fit points in predefined geometric shapes or group points based on their attributes (e.g., spatial distance). However, the required segmentation results, e.g., primitive level or object level, depend on the application. Therefore, this letter develops a semiautomatic method to extract contours for the users’ desired segmentation. First, we initialize a 3-D closed curve for the target. Second, we calculate the internal and external force based on the proposed vector flow to deform the curve. The deformation equation is solved based on the Euler equation and calculated iteratively. Finally, the curve is converged as object contours. After one removes contours, those disjoint points are grouped as the users’ desired instances. Experiments are conducted on various point clouds to demonstrate the effectiveness in terms of accuracy and consistency. Our quantitative evaluation outperformed selected primitive- and object-based methods, which presents a new viewpoint to the point cloud processing.

The First Draco 3D Object Crypto-Compression Scheme

3D objects have come to play an essential role in industry. They can also be very large, sometimes containing millions of vertices, and therefore it is vital that they are compressed, particularly when it comes to uploading them to the web and during real time rendering. The Draco 3D object compression system, proposed by Google, is becoming an industry standard for the compression of 3D objects structured as geometric meshes or point clouds. These 3D objects are important assets which also need to be secured. In this paper, we propose the first 3D object crypto-compression method, which integrates an encryption step into Google’s Draco compression scheme, by adding an AES encryption step during Draco’s entropy encoding step. Our proposed Draco 3D object crypto-compression scheme is format compliant, has no size expansion and does not require additional information such as an auxiliary file. After the entire decoding process (joint decryption and decompression), the reconstructed 3D object obtained is identical to the one after a standard compression by Draco. Experimental results on real 3D objects and a security analysis show our proposed method is efficient.