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Traffic network design is a pivotal aspect of urban planning, necessitating a harmonious blend of theoretical and practical approaches. In this paper, we propose a novel network design methodology utilizing Delaunay triangulation. We address the limitations of raw Delaunay networks, particularly their triangular configurations, by introducing edge-reduction techniques guided by a newly developed metric, detour redundancy. This metric is instrumental in assessing edge importance, facilitating the transformation of the network to better mirror real-world traffic scenarios. The efficacy and practical application of the designed networks are then evaluated through traffic simulations using the principles of cellular automata. Our findings underscore the potential of this approach in enriching traffic network design and pave the way for future investigations into diverse network characteristics and their implications in urban environments. [ABSTRACT FROM AUTHOR]

Sequential sampling methods are often used to estimate functions describing models subjected to time‐intensive simulations or expensive experiments. These methods provide guidelines for point selection in the domain to capture maximum information about the function. However, in most sequential sampling methods, determining a new point is a time‐consuming process. In this paper, we propose a new method, named Sieve, to sequentially select points of an initially unknown function based on the definition of proper intervals. In contrast with existing methods, Sieve does not involve function estimation at each iteration. Therefore, it presents a greater computational efficiency for achieving a given accuracy in estimation. Sieve brings in tools from computational geometry to subdivide regions of the domain efficiently. Further, we validate our proposed method through numerical simulations and two case studies on the calibration of internal combustion engines and the optimal exploration of an unknown environment by a mobile robot. [ABSTRACT FROM AUTHOR]

Positioning, coverage, and connectivity play important roles in next-generation wireless network applications. The coverage in a wireless sensor network (WSN) is a measure of how effectively a region of interest (ROI) is monitored and targets are detected by the sensor nodes. The random deployment of sensor nodes results in poor coverage in WSNs. Additionally, battery depletion at the sensor nodes creates coverage holes in the ROI and affects network coverage. To enhance the coverage, determining the optimal position of the sensor nodes in the ROI is essential. The objective of this study is to define the optimal locations of sensor nodes prior to their deployment in the given network terrain and to increase the coverage area using the proposed version of an enhanced particle swarm optimization (EPSO) algorithm for different frequency bands. The EPSO algorithm avoids the deployment of sensor nodes in close proximity to each other and ensures that every target is covered by at least one sensor node. It applies a probabilistic coverage model based on the Euclidean distances to detect the coverage holes in the initial deployment of sensor nodes and guarantees a higher coverage probability. Delaunay triangulation (DT) helps to enhance the coverage of a given network terrain in the presence of targets. The combination of EPSO and DT is applied to cover the holes and optimize the position of the remaining sensor nodes in the WSN. The fitness function of the EPSO algorithm yielded converged results with the average number of iterations of 78, 82, and 80 at 3.6 GHz, 26 GHz, and 38 GHz frequency bands, respectively. The results of the sensor deployment and coverage showed that the required coverage conditions were met with a communication radius of 4 m compared with 6–120 m with the existing works. [ABSTRACT FROM AUTHOR]

Ship detection and formation recognition in remote sensing have increasingly garnered attention. However, research remains challenging due to arbitrary orientation, dense arrangement, and the complex background of ships. To enhance the analysis of ship situations in channels, we model the ships as the key points and propose a context-aware DGCN-based ship formation recognition method. First, we develop a center point-based ship detection subnetwork, which employs depth-separable convolution to reduce parameter redundancy and combines coordinate attention with an oriented response network to generate direction-invariant feature maps. The center point of each ship is predicted by regression of the offset, target scale, and angle to realize the ship detection. Then, we adopt the spatial similarity of the ship center points to cluster the ship group, utilizing the Delaunay triangulation method to establish the topological graph structure of the ship group. Finally, we design a context-aware Dense Graph Convolutional Network (DGCN) with graph structure to achieve formation recognition. Experimental results on HRSD2016 and SGF datasets demonstrate that the proposed method can detect arbitrarily oriented ships and identify formations, attaining state-of-the-art performance. [ABSTRACT FROM AUTHOR]

Given a set of dot pattern point set P with the size n in the plane, we propose a Delaunay triangulation-based shape reconstruction algorithm, entitled prudent carving, that can reconstruct the inner boundaries (holes) and outer boundaries of P with the same approach. Our prudent carving algorithm is a parameter-free algorithm that has the ability to detect multiple components, sharp corners, and nested holes independent from the number of them in the total O (n log n) time. The qualitative and quantitative comparison of the results with the state-of-the-art algorithms shows that the prudent carving algorithm provides an enhancement over the previously best-known algorithms for reconstructing the boundaries of points. [ABSTRACT FROM AUTHOR]

The article considers the problem of estimating the error in calculating the gradient of functions of Sobolev classes for piecewise linear approximation on triangulations. Traditionally, problems of this kind are considered for continuously differentiable functions. In this case, the corresponding estimates reflect both the smoothness class of the functions and the quality of the triangulation simplexes. However, in problems of substantiating the existence of a solution to a variational problem in the nonlinear theory of elasticity, conditions arise for permissible deformations in terms of generalized derivatives. Therefore, for the numerical solution of these problems, conditions are required that provide the necessary approximation of the derivatives of continuous functions of the Sobolev classes. In this article, an integral estimate of the indicated error for continuously differentiable functions is obtained in terms of the norms of the corresponding spaces for functions that reflect, on the one hand, the quality of triangulation of the polygonal region, and on the other hand, the class of functions with generalized derivatives. The latter is expressed in terms of the majorant of the modulus of continuity of the gradient. To obtain the final estimate, the possibility of passing to the limit using the norm of the Sobolev space is proven.

In this work, we introduce a new approach for computing Delaunay triangulations. Delaunay triangulations have numerous applications in geolocation, communications and other ICT systems or practical applications. Having available various types of approaches for computing such structures is rather desired from an implementation and computational point of view. We adopt Genetic Algorithms for computing Delaunay triangulations and present the design and evaluation of our novel approach. We consider a set of points in the plane as vertices and connect them with edges, creating the point graph. We have developed in C++ an application framework based on genetic algorithms, called Delaunay_Genetic, which produces the Delaunay triangulation structure of a given set of points in the plane. Delaunay_Genetic considers a novel graph-based chromosome representation of desired solutions, creates an initial population of individuals (chromosomes), an initial generation, and produces from the original population (generation) new generations of individuals in each repetition of the genetic process of Reproduction. Each new generation emerges more robust than the previous one. Our evaluations have revealed that the Delaunay triangulation yielded by Delaunay_Genetic, achieves an accuracy of 98–100% of the optimal Delaunay triangulation, while maintaining good convergence speed. Despite its limitations in computational time and space, the proposed novel approach exhibits several complementary benefits to computational geometry based approaches, such as allowing the insertion of new points in the triangulation dynamically, leading to seamless adaptation to new conditions, parallelization of the computational process and tolerance to noise regarding the coordinates of the points. Therefore, this work provides a useful alternative approach for computing Delaunay triangulations. [ABSTRACT FROM AUTHOR]

This paper is dedicated to developing a cost-effective ground-moving object detection method in aerial videos. Without limitations on types, quantity, and distribution of moving objects, which were required by the previous methods, the proposed approach can detect various ground-moving objects in aerial videos captured through diverse flying states in various ground appearances. The proposed method is mainly composed of generation of the appropriate feature points, detection of moving objects, and target tracking. In the originality of our work, a novel detection strategy designed for ground-moving objects is based on change detection of Delaunay triangulation (CDDT) and a three-step motion vector search-based tracking algorithm is further exploited for enhancing the detection rate. Experimental results show that our method can achieve the detection rate of at least 95% (roughly similar to the famous existing state-of-the-art methods) and 0.03 second/frame (far less than the famous existing methods) using test videos (containing only several moving objects distributed in a sparse space) in the previous methods compared. Besides, the average detection rate of 86.81%, average false detection rate of 9.44%, and a frame rate of about 33 fps can be obtained using our test videos captured in the complicated ground appearances. This result makes the proposed method more attractive for detecting various ground-moving objects in aerial videos, when compared to other approaches, and can also achieve cost-effective performance. [ABSTRACT FROM AUTHOR]

Compared with the single or even multiple targets, the group targets exhibit complex and time-varying structure, making the group shape estimation and evaluation quite challenging. This paper proposes a data-driven multi-sensor target group shape modeling and recognition approach to arbitrary shape estimation for group targets, and a group target shape fitting evaluation metric. The proposed approach consists of three parts. Firstly, the information flooding method is used to realize the collection and dissemination of the target information in the field of view by strongly connected sensors. Secondly, a density peak clustering method is utilized to cluster the data set. Finally, an improved Delaunay triangular network algorithm is used to fit the shape of group targets. The proposed group shape fitting evaluation metric can quantitatively evaluate the accuracy of any group target shape estimate. The effectiveness and reliability of the proposed algorithm are verified in comparison with the classic target shape fitting methods such as the hypersurface and random matrices.

Due to their unstructured characteristics, mature convolutional neural network (CNN) models often have difficulty performing spatial analysis with vector data. Current studies used graph neural network (GCN) models to address this problem. However, the definition of cognition factors involves uncertainties, making it challenging to accurately and comprehensively define these factors. In this paper, the road interchange detection task is taken as an example to introduce the MeshCNN, a deep learning model based on triangular mesh data, aiming to provide a new solution for spatial analysis of vector data. A triangular edge classification model is first trained with simple input features. Then, interchanges are detected based on the classification results with an adaptive method. Experiments were conducted on real-world road network data from four cities. The results reveal that the proposed method outperformed the existing methods with precision and recall rate of 89.36% and 79.25% for interchange detection on the total datasets. Furthermore, our proposed method can also detect interchanges in other regions more easily than the GCN method.

Robust and fast image recognition and matching is an important task in the underwater domain. The primary focus of this work is on extracting subsea features with sonar sensor for further Autonomous Underwater Vehicle navigation, such as the robotic localization and landmark mapping applications. With the assistance of high-resolution underwater features in the Side Scan Sonar (SSS) images, an efficient feature detector and descriptor, Speeded Up Robust Feature, is employed to seabed sonar image fusion task. In order to solve the nonlinear intensity difference problem in SSS images, the main novelty of this work is the proposed Underwater Wireless Sensor Network-based Delaunay Triangulation (UWSN-DT) algorithm for improving the performances of sonar map fusion accuracy with low computational complexity, in which the wireless nodes are considered as underwater feature points, since nodes could provide sufficiently useful information for the underwater map fusion, such as the location. In the simulated experiments, it shows that the presented UWSN-DT approach works efficiently and robustly, especially for the subsea environments where there are few distinguishable feature points. [ABSTRACT FROM AUTHOR]

A wireless data collection network (DCN) is the key constituent of the IoT. It is used in many applications such as transport, logistics, security and monitoring. Despite the continuous development of DCN, communication between nodes in such network presents several challenges. The major issue is the deployment of connected objects and, more precisely, how numerous nodes are appropriately positioned to attain full coverage. The current work presents a hybrid technique, named DTABC, combining a geometric deployment method, called Delaunay Triangulation diagram DT, and an optimization algorithm named the Artificial Bee Colony (ABC) algorithm. In the centralized approach, this hybrid method is executed on a single node while, in a distributed approach, it is executed in parallel on different nodes deployed in a wireless data collection network. This study aims at enhancing the coverage rate in data collection networks utilizing less sensor nodes. The Delaunay Triangulation diagram is utilized to produce solutions showing the first locations of the IoT objects. Then, the Artificial Bee Colony algorithm is used to improve the node deployment coverage rate. The developed DTABC approach performance is assessed experimentally by prototyping M5StickC nodes on a real testbed. The obtained results reveal that the coverage rate, the number of the objects' neighbors, the RSSI and the lifetime of the distributed approach are better than those of the algorithms introduced in previous research works. [ABSTRACT FROM AUTHOR]

Copyright of Aero Weaponry is the property of Aero Weaponry Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The Earth's crust is exposed by tectonic processes and is not static over time. Modelling of the Earth's surface velocities is of utmost importance for research in geodesy, geophysics, structural geology, and other geosciences. It may support positioning, navigation, seismic risk, and volcano notification services, for example. Space geodetic techniques can be used to provide high-quality velocities in a network of geodetic sites. Velocity field modelling should, however, expand the velocities from a discrete set of points to any location in-between. This paper presents four new methods for the Earth's surface velocity interpolation. Contrary to the widely used approach dividing the velocity field to the horizontal and vertical components, a full 3D interpolation approach is proposed based on the Delaunay triangulation and the n-simplex interpolation. The use of a combination of all three components is advantageous for geophysical interpretation. The proposed interpolation approach is entirely local but enables global modelling, which does not suffer from map projection distortions and singularities at the poles. Various global and regional position/velocity datasets are used to evaluate the performance of the proposed velocity interpolation methods. The latter provide practically the same results when applied to regional velocity field modelling. However, the so-called continuous piecewise quasi-radial 3D velocity field interpolation method is recommended for its favourable properties. It introduces an ellipsoidal Earth model, appropriately considers vertical/up and horizontal velocity components, tends to radial symmetry, and provides continuity for the interpolated velocity components as well as for the estimated uncertainties. [ABSTRACT FROM AUTHOR]

An interface-preserving moving mesh algorithm in two or higher dimensions is presented. It resolves a moving (d-1)-dimensional manifold directly within the d-dimensional mesh, which means that the interface is represented by a subset of moving mesh cell-surfaces. The underlying mesh is a conforming simplicial partition that fulfills the Delaunay property. The local remeshing algorithms allow for strong interface deformations. We give a proof that the given algorithms preserve the interface after interface deformation and remeshing steps. Originating from various numerical methods, data is attached cell-wise to the mesh. After each remeshing operation, the interface-preserving moving mesh retains valid data by projecting the data to the new mesh cells. An open source implementation of the moving mesh algorithm is available at Reference [1]. [ABSTRACT FROM AUTHOR]

The diverse nature of hull components in shipbuilding has created a demand for intelligent robots capable of performing various tasks without pre-teaching or template-based programming. Visual perception of a target's outline is crucial for path planning in robotic edge grinding and other processes. Providing the target's outline from point cloud or image data is essential for autonomous programming, requiring a high-performance algorithm to handle large amounts of data in real-time construction while preserving geometric details. The high computational cost of triangulation has hindered real-time industrial applications, prompting efforts to improve efficiency. To address this, a new improvement called Directive Searching has been proposed to enhance search efficiency by directing the search towards the target triangle cell and avoiding redundant searches. Another improvement, Heritable Initial, reduces the search amount by inheriting the start position from the last search. Combining Directive Searching and Heritable Initial into a new method called DSHI has led to a significant efficiency advancement, with a calculation efficiency improvement of nearly 300–3000 times compared to the ordinary Bowyer–Watson method. In terms of outlines extraction, DSHI has improved the extraction efficiency by 4–16 times compared to the ordinary Bowyer–Watson methods, while ensuring stable outlines results, and has also increased the extraction efficiency by 2–4 times compared to PCL. The DSHI method is also applied to actual ship component edge-grinding equipment, and its effect meets the shipbuilding process requirements. It could be inferred that the new method has potential applications in shipbuilding and other industries, offering satisfying efficiency and robustness for tasks such as automatic edge grinding. [ABSTRACT FROM AUTHOR]

Wireless Sensor Networks (WSNs) are critical for various applications ranging from environment monitoring to industrial monitoring. The varying and continuously growing interest in this field demands an understanding of the sensor node distribution to ensure robustness and to improve resource utilization for data processing and decision making. In this paper, we focus on reconstructing the boundaries of a wireless sensor network, which also has a lot of applications in IoT and Robotics. As these sensor node locations can be considered as a set of points in the 2D plane, boundary detection of a WSN can be related to classical shape reconstruction problem in Computational Geometry. In this paper, we extend a simple and generic strategy for hole detection to a geometric solution for boundary/shape reconstruction. Furthermore, we introduce a simple and controllable heuristic algorithm to patch the coverage holes identified by our boundary reconstruction algorithm. Not only does this study improve the reliability of WSNs, but it also provides a useful tool for the extensive domain of computational geometry and shape analysis. Our different experiments show that the proposed reconstruction algorithm outperforms the existing state-of-the-art methods, and hole patching gives a simple and controllable solution for mobile node placement.

Abstract Numerous computational methods, including evolutionary-based, energy-based, and geometrical-based methods, are utilized to identify cavities inside proteins. Cavity information aids protein function annotation, drug design, poly-pharmacology, and allosteric site investigation. This article introduces “flow transfer algorithm” for rapid and effective identification of diverse protein cavities through multidimensional cavity scan. Initially, it identifies delimiter and susceptible tetrahedra to establish boundary regions and provide seed tetrahedra. Seed tetrahedron faces are precisely scanned using the maximum circle radius to transfer seed flow to neighboring tetrahedra. Seed flow continues until terminated by boundaries or forbidden faces, where a face is forbidden if the estimated maximum circle radius is less or equal to the user-defined maximum circle radius. After a seed scanning, tetrahedra involved in the flow are clustered to locate the cavity. The CRAFT web interface integrates this algorithm for protein cavity identification with enhanced user control. It supports proteins with cofactors, hydrogens, and ligands and provides comprehensive features such as 3D visualization, cavity physicochemical properties, percentage contribution graphs, and highlighted residues for each cavity. CRAFT can be accessed through its web interface at http://pitools.niper.ac.in/CRAFT , complemented by the command version available at https://github.com/PGlab-NIPER/CRAFT/ . Scientific contribution Flow transfer algorithm is a novel geometric approach for accurate and reliable prediction of diverse protein cavities. This algorithm employs a distinct concept involving maximum circle radius within the 3D Delaunay triangulation to address diverse van der Waals radii while existing methods overlook atom specific van der Waals radii or rely on complex weighted geometric techniques.

Delaunay triangulation is an effective way to build a triangulation of a cloud of points, i.e., a partitioning of the points into simplices (triangles in 2D, tetrahedra in 3D, and so on), such that no two simplices overlap and every point in the set is a vertex of at least one simplex. Such a triangulation has been shown to have several interesting properties in terms of the structure of the simplices it constructs (e.g., maximising the minimum angle of the triangles in the bi-dimensional case) and has several critical applications in the contexts of computer graphics, computational geometry, mobile robotics or indoor localisation, to name a few application domains. This review paper revolves around three main pillars: (I) algorithms, (II) implementations over central processing units (CPUs), graphics processing units (GPUs), and field programmable gate arrays (FPGAs), and (III) applications. Specifically, the paper provides a comprehensive review of the main state-of-the-art algorithmic approaches to compute the Delaunay Triangulation. Subsequently, it delivers a critical review of implementations of Delaunay triangulation over CPUs, GPUs, and FPGAs. Finally, the paper covers a broad and multi-disciplinary range of possible applications of this technique.

Positioning, coverage, and connectivity play important roles in next-generation wireless network applications. The coverage in a wireless sensor network (WSN) is a measure of how effectively a region of interest (ROI) is monitored and targets are detected by the sensor nodes. The random deployment of sensor nodes results in poor coverage in WSNs. Additionally, battery depletion at the sensor nodes creates coverage holes in the ROI and affects network coverage. To enhance the coverage, determining the optimal position of the sensor nodes in the ROI is essential. The objective of this study is to define the optimal locations of sensor nodes prior to their deployment in the given network terrain and to increase the coverage area using the proposed version of an enhanced particle swarm optimization (EPSO) algorithm for different frequency bands. The EPSO algorithm avoids the deployment of sensor nodes in close proximity to each other and ensures that every target is covered by at least one sensor node. It applies a probabilistic coverage model based on the Euclidean distances to detect the coverage holes in the initial deployment of sensor nodes and guarantees a higher coverage probability. Delaunay triangulation (DT) helps to enhance the coverage of a given network terrain in the presence of targets. The combination of EPSO and DT is applied to cover the holes and optimize the position of the remaining sensor nodes in the WSN. The fitness function of the EPSO algorithm yielded converged results with the average number of iterations of 78, 82, and 80 at 3.6 GHz, 26 GHz, and 38 GHz frequency bands, respectively. The results of the sensor deployment and coverage showed that the required coverage conditions were met with a communication radius of 4 m compared with 6–120 m with the existing works.

Ship detection and formation recognition in remote sensing have increasingly garnered attention. However, research remains challenging due to arbitrary orientation, dense arrangement, and the complex background of ships. To enhance the analysis of ship situations in channels, we model the ships as the key points and propose a context-aware DGCN-based ship formation recognition method. First, we develop a center point-based ship detection subnetwork, which employs depth-separable convolution to reduce parameter redundancy and combines coordinate attention with an oriented response network to generate direction-invariant feature maps. The center point of each ship is predicted by regression of the offset, target scale, and angle to realize the ship detection. Then, we adopt the spatial similarity of the ship center points to cluster the ship group, utilizing the Delaunay triangulation method to establish the topological graph structure of the ship group. Finally, we design a context-aware Dense Graph Convolutional Network (DGCN) with graph structure to achieve formation recognition. Experimental results on HRSD2016 and SGF datasets demonstrate that the proposed method can detect arbitrarily oriented ships and identify formations, attaining state-of-the-art performance.

In this paper, we present an efficient algorithm, namely Orienting and Final Circles (OFC)-Delaunay Triangulation, for constructing the Delaunay triangulation of a finite planar point set using the idea of the Method of Orienting Curves (introduced by Phu in Zur Lösung einer regulären Aufgabenklasse der optimalen Steuerung im Groen mittels Orientierungskurven, Optimization 18(1) (1987) 65–81 and Ein konstruktives Lösungsverfahren für das Problem des Inpolygons kleinsten Umfangs von J. Steiner, Optimization 18(3) (1987) 349–359). The concepts of orienting and final circles are introduced. The Delaunay edges are determined by orienting circles and a final circle. Our algorithm has O (n log n) worst-case running time. The algorithm is implemented in Python and some numerical examples are presented. [ABSTRACT FROM AUTHOR]

We investigate the dynamic phase transition in two-dimensional Ising models whose equilibrium characteristics are influenced by either anisotropic interactions or quenched defects. The presence of anisotropy reduces the dynamical critical temperature, leading to the expected result that the critical temperature approaches zero in the full-anisotropy limit. We show that a comprehensive understanding of the dynamic behavior of systems with quenched defects requires a generalized definition of the dynamic order parameter. By doing so, we demonstrate that the inclusion of quenched defects lowers the dynamic critical temperature as well, with a linear trend across the range of defect fractions considered. We also explore if and how it is possible to predict the dynamic behavior of specific magnetic systems with quenched randomness. Various geometric quantities, such as a defect potential index, the defect dipole moment, and the properties of the defect Delaunay triangulation, prove useful for this purpose. [ABSTRACT FROM AUTHOR]

Adaptive sampling and mesh representation of images play an important role in image compression and vectorization. In this paper, a multi-points stochastic gradient multi-armed bandits algorithm, a generalization of the gradient bandit algorithm, is presented to adaptively sample points in images. By modeling the adaptive image sampling as a multi-arm selection decision-making problem, we first propose an efficient action selection strategy based on a parameterized probability distribution, and then define an adaptive reward function according to the restored image of Delaunay triangulation and a feature map function, and the reward function can overcome the sparse reward issue effectively. As a result, the proposed multi-points stochastic gradient multi-armed bandits algorithm is used to evaluate the reward of each action. At last, a prescribed number of sampling points are selected using a simple and effective strategy according to the average reward of each pixel. The quality of reconstructed images based on sampled points is estimated, and experimental results demonstrate the proposed algorithm achieves a better reconstruction accuracy than that of existing methods. [ABSTRACT FROM AUTHOR]

Copyright of Journal of China University of Petroleum is the property of China University of Petroleum and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is hyperbolic if there exists a constant δ ≥ 0 such that any side of any geodesic triangle in X is contained in the d-neighborhood of the union of the two other sides. In this paper, we study the hyperbolicity of an important kind of Euclidean graphs called Delaunay triangulations. Furthermore, we characterize the Delaunay triangulations contained in the Euclidean plane that are hyperbolic. [ABSTRACT FROM AUTHOR]

The increase in maritime traffic and vessel size has strengthened the need for economical and safe maritime transportation networks. Currently, ship path planning is based on past experience and shortest route usage. However, the increasing complexity of the marine environment and the development of autonomous ships require automatic shortest path generation based on maritime traffic networks. This paper proposes an efficient shortest path planning method using Dijkstra's algorithm based on a maritime traffic network dataset created by extracting maritime traffic routes through a spatial-temporal density analysis of large-scale AIS data and Delaunay triangulation. Additionally, the depth information of all digital charts in Korea was set as a safety contour to support safe path planning. The proposed network-based shortest path planning method was compared with the path planning and sailing distance of a training ship, and compliance with maritime laws was verified. The results demonstrate the practicality and safety of the proposed method, which can enable the establishment of a safe and efficient maritime transportation network along with the development of autonomous ships. [ABSTRACT FROM AUTHOR]

Given an initial set of planar nodes, the problem is to build a minimum spanning tree connecting the maximum possible number of nodes by not exceeding the maximum edge length. To obtain a set of edges, a Delaunay triangulation is performed over the initial set of nodes. Distances between every pair of the nodes in respective edges are calculated used as graph weights. The edges whose length exceeds the maximum edge length are removed. A minimum spanning tree is built over every disconnected graph. The minimum spanning trees covering a maximum of nodes are selected, among which the tree whose length is minimal is the solution. It is 1.17 % shorter on average for 10 to 80 nodes compared to a nonselected tree.

If $ X $ is a geodesic metric space and $ x_1, x_2, x_3\in X $, a geodesic triangle $ T = \{x_1, x_2, x_3\} $ is the union of the three geodesics $ [x_1 x_2] $, $ [x_2 x_3] $ and $ [x_3 x_1] $ in $ X $. The space $ X $ is hyperbolic if there exists a constant $ \delta \ge 0 $ such that any side of any geodesic triangle in $ X $ is contained in the $ \delta $-neighborhood of the union of the two other sides. In this paper, we study the hyperbolicity of an important kind of Euclidean graphs called Delaunay triangulations. Furthermore, we characterize the Delaunay triangulations contained in the Euclidean plane that are hyperbolic.

A variational problem for the minimum of the stored energy functional is considered in the framework of the nonlinear theory of elasticity, taking into account admissible deformations. An algorithm for solving this problem is proposed, based on the use of a polygonal partition of the computational domain by the Delaunay triangulation method. Conditions for the convergence of the method to a local minimum in the class of piecewise affine mappings are found.

Using the recoupling theory, we define a representation of the pure braid group and show that it is not trivial. [ABSTRACT FROM AUTHOR]

ABSTRACTDigital Elevation Models (DEMs) play a crucial role in civil and environmental applications, such as hydrologic and geologic analyses, hazard monitoring, natural resources exploration, etc. Generally, DEMs can be generated from various data sources, such as ground surveys, photogrammetric stereo methods, satellite images, laser scanning, and digitized contour lines. Compared with other data sources, contour lines are still the cheapest and more common data source becausethey cover all areas, at different scales, in most countries. Although there are different algorithms and technologies for interpolation in between contour lines, DEMs extracted solely from contours still suffer from poor terrain quality representation, which in turn negatively affects the quality of analytical applications results. In this paper, an approach for improving the digital terrain modeling based on contour line densification and Delaunay triangulation is presented to acquire a more suitable DEM for hydrographic modeling and its applications. The proposed methodology was tested using a variety of terrain patterns in terms of intensity: hilly, undulated, and plain (1:25,000 topographic map, 5 m contour interval). The precision of the extracted GRID model increases as the number of added contours increases. Adding four contour lines, the Root Mean Square Error (RMSE) of examining points were 0.26 m, 0.29 m, and 0.05 m for hilly, undulated, and plain samples, respectively, and the Mean Absolute Error (MAE) were 0.50 m, 0.48 m, and 0.17 m. The convergence probabilities between extracted and original flow lines for the same regions were 96.91%, 94.93%, and 84.03%. Applying the methodology, experimental results indicate that the developed approach provides a significant advantage in terrain modeling enhancement, generates DEMs smoothly and effectively from contours, mitigates problems and reduces uncertainties.

Abstract Background In tissues and organisms, the coordination of neighboring cells is essential to maintain their properties and functions. Therefore, knowing which cells are adjacent is crucial to understand biological processes that involve physical interactions among them, e.g. cell migration and proliferation. In addition, some signaling pathways, such as Notch or extrinsic apoptosis, are highly dependent on cell–cell communication. While this is straightforward to obtain from membrane images, nuclei labelling is much more ubiquitous for technical reasons. However, there are no automatic and robust methods to find neighboring cells based only on nuclear markers. Results In this work, we describe Nfinder, a method to assess the cell’s local neighborhood from images with nuclei labeling. To achieve this goal, we approximate the cell–cell interaction graph by the Delaunay triangulation of nuclei centroids. Then, links are filtered by automatic thresholding in cell–cell distance (pairwise interaction) and the maximum angle that a pair of cells subtends with shared neighbors (non-pairwise interaction). We systematically characterized the detection performance by applying Nfinder to publicly available datasets from Drosophila melanogaster, Tribolium castaneum, Arabidopsis thaliana and C. elegans. In each case, the result of the algorithm was compared to a cell neighbor graph generated by manually annotating the original dataset. On average, our method detected 95% of true neighbors, with only 6% of false discoveries. Remarkably, our findings indicate that taking into account non-pairwise interactions might increase the Positive Predictive Value up to + 11.5%. Conclusion Nfinder is the first robust and automatic method for estimating neighboring cells in 2D and 3D based only on nuclear markers and without any free parameters. Using this tool, we found that taking non-pairwise interactions into account improves the detection performance significantly. We believe that using our method might improve the effectiveness of other workflows to study cell–cell interactions from microscopy images. Finally, we also provide a reference implementation in Python and an easy-to-use napari plugin.

In the era of big data, from digital cities to digital earth, the exponential growth of spatial information due to the development of diverse data collection technologies has been a significant concern. Delaunay triangulation has garnered widespread attention and application in geomorphological analysis, topographic simulation, and cartographic synthesis due to its minimal data redundancy and excellent stability. However, as the application fields of Delaunay triangular mesh models continue to expand and application requirements deepen, especially with the urgent need to address real-time large-scale scene rendering and terrain visualization, the efficiency, accuracy, and stability of Delaunay triangulation meshes are increasingly demanded. This paper proposes a parallel optimization algorithm based on the insertion point method, following an analysis of the traditional insertion point method, and demonstrates its effectiveness through a series of experiments.

Cultural and creative products through the visual expression of cultural elements, spirit, symbols, etc., to give the product outside the function of a unique aesthetic experience and spiritual enjoyment, modern three-dimensional printing technology and traditional arts and crafts integration, greatly liberating the traditional fine arts in the shape of the limitations of the designers to facilitate the creative creation. In this paper, the lag in cultural creative products is studied, and the entire process of three-dimensional printing of cultural creative products integrated with the concept of traditional fine arts is designed. Specifically, parametric 3D modeling of cultural and creative products is carried out. Then the dense point cloud model of cultural and creative products is reconstructed by ICP fine alignment. Delaunay triangulation is used to complete the conversion from dense point cloud model to mesh model, and texture mapping is carried out so as to make the generated cultural and creative products more lifelike. The printing of cultural and creative products is completed using SLA technology and printing materials, and their design effectiveness is evaluated by combining with the KANO model. The values of SI and |DSI| are between 31.17%~62.03% and 12.81%~56.02, respectively, and the users’ satisfaction with the cultural and creative 3D printed products integrating the concepts of traditional fine arts is relatively high. Designers can further optimize the 3D printed cultural creative products integrating traditional art concepts on the basis of the original products according to the order of “Basic > Expectation > Charm”.