Search Results (62)

This paper presents a novel method for designing manufacturable porous infill structures using a Voronoi-based topology optimization framework. By integrating discrete Voronoi representations into density-based topology optimization in a differentiable manner, the method enables variable-thickness edge structures, with Euclidean distance fields generated from seed points. The material distribution and structural shape are determined by the seed point locations and the distance tensor, which serve as the design variables in this work. As the seed points are directly associated with the dual graph of the Voronoi diagram (VD), namely the Delaunay triangulation (DT), a constraint is formulated based on the DT to ensure the manufacturability of the infill structure. This is achieved by constraining all edge angles of the DT to satisfy the overhang requirement. Since 3D printers can fabricate overhanging structures up to a certain length, VD edges shorter than this threshold are exempt from the self-supporting constraint. To reduce the number of design variables and simplify the manufacturability constraint, a merging strategy is introduced to combine seed points that are sufficiently close during the optimization process. To ensure manufacturability of the outer surface, a set of seed points is additionally sampled on the outer boundary and kept fixed throughout optimization. The proposed method is validated on both regular and irregular 2D design domains, and the results demonstrate its capability to generate manufacturable porous infill structures with satisfactory mechanical performance. Full article

We characterize the combinatorial structure of the Voronoi cell of the ${\mathcal{A}}_n$ lattice in arbitrary dimensions. Based on the well-known fact that the Voronoi cell is the disjoint union of $(n+1)!$ congruent simplices, we show that it is the disjoint union of $(n+1)$ congruent hyper-rhombi, which are the generalized rhombi or trigonal trapezohedra. The explicit structure of the faces is investigated, including the fact that all the k-dimensional faces, $2\le k\le n-1$, are hyper-rhombi. Based on our explicit algebraic representation, we re-derive the classical geometric result that the Voronoi cell is the vertex-first orthogonal projection of the $(n+1)$-dimensional unit cube and therefore a zonotope. We prove that in low dimensions ($n\le 3$) the Voronoi cell of the ${\mathcal{A}}_n$ lattice can be understood as the section of the Voronoi cell of the ${\mathcal{D}}_{n+1}$ lattice with the hyperplane orthogonal to the diagonal direction. We provide all the explicit coordinates and transformation matrices associated with our analysis. Most of our analysis is algebraic and easily accessible to those less familiar with the Coxeter–Dynkin diagrams. Full article

To address the lagging construction and irrational spatial distribution of current electric vehicle (EV) charging infrastructure, scientific location and capacity planning has emerged as a critical research focus in transportation electrification. Through a systematic review of domestic and international literature, this paper analyzes the evolution of charging station planning models from single economic indicators to multi-objective frameworks incorporating grid constraints, carbon emission benefits, and user behavior. Research indicates that while geometric spatial partitioning and swarm intelligence algorithms are widely utilized, existing methods face limitations in handling iterative spatial service area matching and overcoming the premature convergence of standard Particle Swarm Optimization (PSO). Consequently, this study proposes an integrated technical route utilizing Voronoi diagrams to adaptively partition service areas based on demand density, and constructing a comprehensive model encompassing construction and maintenance costs, environmental costs, and generalized user costs. To solve this highly complex spatial allocation problem, a Catfish Particle Swarm Optimization (CPSO) algorithm is employed as an efficient computational tool. Ultimately, this approach aims to provide practical, quantitative decision support for urban EV charging network planning by balancing the conflicting interests of operators, users, and the power grid within a comprehensive ‘Total Social Cost’ framework. Full article

In robot motion planning in a space with obstacles, the goal is to find a collision-free path for robots from the start to the target position. Numerous fundamentally different approaches, and their many variants, address this problem depending on the types of obstacles, the dimensionality of the space and the restrictions on robot movements. We present a hierarchical motion planning framework for snake-like robots navigating cluttered environments. At the global level, a bounded Generalized Voronoi Diagram (GVD) generates a maximal-clearance path through complex terrain. To overcome the limitations of pure avoidance strategies, we incorporate a local trajectory optimization layer that enables Obstacle-Aided Locomotion (OAL). This is realized through a simulation-in-the-loop system in CoppeliaSim, where gait parameters are optimized using Particle Swarm Optimization (PSO) based on contact forces and energy efficiency. By coupling high-level deliberative planning with low-level contact-aware control, our approach enhances both adaptability and locomotion efficiency. Experimental results demonstrate improved motion performance compared to conventional planners that neglect environmental contact. Full article

Aiming at the problems of large search space, unstable computational efficiency, and lack of safety of generated paths in complex environments of traditional HybridA* algorithms, this paper proposes an improved HybridA* algorithm based on Voronoi diagrams and safe corridors (GCHybridA*) to overcome these challenges. The method first reduces ineffective node expansion by constructing a Voronoi path away from obstacles and smoothing it, followed by selecting key guidance points to provide stage-like goals for path search. Then, an innovative safe corridor is generated and the path search is restricted to the safe corridor area to guarantee the safety of the path, and an adaptive step-size mechanism is designed to balance the search efficiency and path quality. The experimental results show that the GCHybridA* algorithm significantly outperforms the conventional HybridA* algorithm, with an average reduction of 83.7% in node expansions while maintaining zero potential collision points across all four typical maps. This study provides an innovative and robust solution for efficient and safe path planning in autonomous driving systems. This study provides an innovative and robust solution for global path planning in autonomous driving systems, focusing on static environment navigation with safety guarantees. Full article

Based on the goal of achieving a classified promotion of rural revitalization in China’s Comprehensive Rural Revitalization Plan (2024–2027), this study presents a framework for a comprehensive sustainable development assessment system using multi-source data. This framework mainly adheres to the principles of settlement-type identification and spatial optimization strategies. The proposed framework is applied to Sangxu Town in eastern China to divide the settlements into five types and then optimize the spatial layout of rural settlements by employing spatial point pattern analysis, weighted Voronoi diagrams, and an extended breakpoint combination model. This study shows that, firstly, the overall development level of settlements in Sangxu Town is relatively high, but the distribution is uneven, with higher levels in the central and eastern regions and lower levels in the west. Secondly, based on the sustainable comprehensive development levels, 14 removal-type settlements (accounting for 27.45%), 21 control and retention-type settlements (41.18%), 7 agglomeration and upgrading-type settlements (13.73%), and 5 suburban integration-type settlements (9.80%) were identified. Thirdly, the activity intensity of residents is generally low in areas with low nighttime light intensity. The number of rural settlements was reduced to 37 after relocation, freeing up 94.91 hectares of homestead land—a reduction of 9.51%. This research improves the application of big data technology in identifying types of rural settlements and optimizing layout, providing experience for achieving sustainable development in rural areas in China. Full article

The innovation of multi-material offers significant benefits to architectural systems. The fusion of multiple materials, transitioning from one to another in a graded manner, enables the creation of fused space without the need for mechanical connections. Given that plastic is a major contributor to ecological imbalance, this research on fused space aims to recycle plastic and use it as a multi-material for building applications, due to its capacity for being 3D printed and fused with other materials. Furthermore, to generate diverse properties for the fused space, several nature-inspired forming algorithms are employed, including Swarm Behavior, Voronoi, Game of Life, and Shortest Path, to shape the building enclosure. Subsequently, digital analyses, such as daylight analysis, structural analysis, porosity analysis, and openness analysis, are conducted on the enclosure, forming the color mapping digital diagram, which determines the distribution of varying thickness, density, transparency, and flexibility gradation parameters, resulting in spatial diversity. During the fabrication process, Dual Force V1 and Dual Force V2 were developed to successfully print multi-material gradations with fused plastic following an upgrade to the cooling system. Finally, three test sites in London were chosen to implement the fused space concept using multi-material. Full article

This paper presents a theoretical framework for constructing generalized weighted Voronoi diagrams (GWVDs) of weighted points and straight-line segments (“sites”) in the Euclidean plane, based on lower envelopes constructed in three-dimensional space. Central to our approach is an algebraic distance function that defines the minimum weighted distance from a point to a site. We also introduce a parameterization for the bisectors, ensuring a precise representation of Voronoi edges. The connection to lower envelopes allows us to derive (almost tight) bounds on the combinatorial complexity of a GWVD. We conclude with a short discussion of implementation strategies, ranging from leveraging computational geometry libraries to employing graphics hardware for approximate solutions. Full article

We investigated patterns formed during the polymerization process of bifunctional monomers in a liquid crystal for both large polymer concentrations (polymer-dispersed liquid crystals, PDLC) and small concentrations (polymer-stabilized liquid crystals, PSLC). The resulting experimental patterns are reminiscent of Voronoi diagrams, so a reverse Voronoi algorithm was developed that provides the seed locations of cells, thus allowing a computational reproduction of the experimental patterns. Several metrics were developed to quantify the commonality between the faithful experimental patterns and the idealized and generated ones. This led to descriptions of the experimental patterns with accuracies better than 90% and showed that the curvature or concavity of the cell edges was below 2%. Possible reasons for the discrepancies between the original and generated Voronoi diagrams are discussed. The introduced algorithm and quantification of the patterns could be transferred to many other experimental problems, for example, melting of thin polymer films, ultra-thin metal films, or bio-membranes. The discrepancies between the experimental and ideal Voronoi diagrams are quantified, which may be useful in the quality control of privacy windows, reflective displays, or smart glass. Full article

With the widespread application of unmanned aerial vehicles (UAV) in surveying, disaster search and rescue, agricultural spraying, war reconnaissance, and other fields, coverage path planning is one of the most important problems to be explored. In this paper, a large-area coverage path planning (CCP) method based on vehicle–UAV collaboration is proposed. The core idea of the proposed method is adopting a divide-and conquer-strategy to divide a large area into small areas, and then completing efficient coverage scanning tasks through the collaborative cooperation of vehicles and UAVs. The supply points are generated and adjusted based on the construction of regular hexagons and a Voronoi diagram, and the segmentation and adjustment of sub-areas are also achieved during this procedure. The vehicle paths are constructed based on the classical ant colony optimization algorithm, providing an efficient way to traverse all supply points within the coverage area. The classic zigzag CCP method is adopted to fill the contours of each sub-area, and the UAV paths collaborate with vehicle supply points using few switching points. The simulation experiments verify the effectiveness and feasibility of the proposed vehicle–UAV collaboration CCP method, and two comparative experiments demonstrate that the proposed method excels at large-scale CCP scenarios, and achieves a significant improvement in coverage efficiency. Full article

The study of unmanned aerial vehicle (UAV) coverage path planning is of great significance for ensuring maritime situational awareness and monitoring. In response to the problem of maritime multi-region coverage surveillance in complex obstacle environments, this paper proposes a global path planning method capable of simultaneously addressing the multiple traveling salesman problem, coverage path planning problem, and obstacle avoidance problem. Firstly, a multiple traveling salesmen problem–coverage path planning (MTSP-CPP) model with the objective of minimizing the maximum task completion time is constructed. Secondly, a method for calculating obstacle-avoidance path costs based on the Voronoi diagram is proposed, laying the foundation for obtaining the optimal access order. Thirdly, an improved discrete grey wolf optimizer (IDGWO) algorithm integrated with variable neighborhood search (VNS) operations is proposed to perform task assignment for multiple UAVs and achieve workload balancing. Finally, based on dynamic programming, the coverage path points of the area are solved precisely to generate the globally coverage path. Through simulation experiments with scenarios of varying scales, the effectiveness and superiority of the proposed method are validated. The experimental results demonstrate that this method can effectively solve MTSP-CPP in complex obstacle environments. Full article

Designing scaffolds similar to the structure of trabecular bone requires specialised algorithms. Existing scaffold designs for bone tissue engineering have repeated patterns that do not replicate the random stochastic porous structure of the internal architecture of bones. In this research, the Voronoi tessellation method is applied to create random porous biomimetic structures. A volume mesh created from the shape of a Zygoma fracture acts as a boundary for the generation of random seed points by point spacing to create Voronoi cells and Voronoi diagrams. The Voronoi lattices were obtained by adding strut thickness to the Voronoi diagrams. Gradient Voronoi scaffolds of pore sizes (19.8 µm to 923 µm) similar to the structure of the trabecular bone were designed. A Finite Element Method-based computational fluid dynamics (CFD) simulation was performed on all designed Voronoi scaffolds to predict the pressure drops and permeability of non-Newtonian blood flow behaviour using the power law material model. The predicted permeability (0.33 × 10⁻⁹ m² to 2.17 × 10⁻⁹ m²) values of the Voronoi scaffolds from the CFD simulation are comparable with the permeability of scaffolds and bone specimens from other research works. Full article

Matched line segments are crucial geometric elements for reconstructing the desired 3D structure in stereo satellite imagery, owing to their advantages in spatial representation, complex shape description, and geometric computation. However, existing line segment matching (LSM) methods face significant challenges in effectively addressing co-linear interference and the misdirection of parallel line segments. To address these issues, this study proposes a “continuous–discrete–continuous” cyclic LSM method, based on the Voronoi diagram, for stereo satellite images. Initially, to compute the discrete line-point matching rate, line segments are discretized using the Bresenham algorithm, and the pyramid histogram of visual words (PHOW) feature is assigned to the line segment points which are detected using the line segment detector (LSD). Next, to obtain continuous matched line segments, the method combines the line segment crossing angle rate with the line-point matching rate, utilizing a soft voting classifier. Finally, local point-line homography models are constructed based on the Voronoi diagram, filtering out misdirected parallel line segments and yielding the final matched line segments. Extensive experiments on the challenging benchmark, WorldView-2 and WorldView-3 satellite image datasets, demonstrate that the proposed method outperforms several state-of-the-art LSM methods. Specifically, the proposed method achieves F1-scores that are 6.22%, 12.60%, and 18.35% higher than those of the best-performing existing LSM method on the three datasets, respectively. Full article

Assessing the quality of maize seedlings is crucial for field management and germplasm evaluation. Traditional methods for evaluating seedling quality mainly rely on manual field surveys, which are not only inefficient but also highly subjective, while large-scale satellite detection often lacks sufficient accuracy. To address these issues, this study proposes an innovative approach that combines the YOLO v8 object detection algorithm with Voronoi spatial analysis to rapidly evaluate maize seedling quality based on high-resolution drone imagery. The YOLO v8 model provides the maize coordinates, which are then used for Voronoi segmentation of the field after applying the Convex Hull difference method. From the generated Voronoi diagram, three key indicators are extracted: Voronoi Polygon Uniformity Index (VPUI), missing seedling rate, and repeated seedling rate to comprehensively evaluate maize seedling quality. The results show that this method effectively extracts the VPUI, missing seedling rate, and repeated seedling rate of maize in the target area. Compared to the traditional plant spacing variation coefficient, VPUI performs better in representing seedling uniformity. Additionally, the R² for the estimated missing seedling rate and replanting rate based on the Voronoi method were 0.773 and 0.940, respectively. Compared to using the plant spacing method, the R² increased by 0.09 and 0.544, respectively. The maize seedling quality evaluation method proposed in this study provides technical support for precision maize planting management and is of great significance for improving agricultural production efficiency and reducing labor costs. Full article

The modeling of the concrete matrix serves as a foundation for mesoscale analysis of concrete, which provides a crucial avenue for investigating the crack propagation and strength characteristics of concrete. However, the primary prerequisite for conducting such analyses is the generation of aggregate models. By combining the advantages of Voronoi diagrams and the random walk algorithm (RWA), a Voronoi–random walk algorithm is proposed in this paper. The algorithm overcomes the limitations of traditional methods, including constraints on aggregate volume fraction, low computational efficiency, and insufficient randomness in aggregate distribution. The meso-structure of a concrete block was modeled by the proposed method, and then its failure behavior under uniaxial compression was simulated using the finite element method. The numerical results agreed well with the experimental observations, indicating the effectiveness and accuracy of the proposed approach. Full article