Search Results (145)

In the realm of 3D curve reconstruction, Non-Uniform Rational B-Splines (NURBSs) offer a versatile mathematical tool due to their ability to precisely represent complex geometries. However, achieving high fitting accuracy in stereo-based applications remains challenging, primarily due to the nonlinear nature of weight optimization. This study introduces an enhanced iterative strategy that leverages the geometric significance of NURBS weights to incrementally refine curve fitting. By formulating an inverse optimization problem guided by model deformation principles, the proposed method progressively adjusts weights to minimize reprojection error. Experimental evaluations confirm the method’s convergence and demonstrate its superiority in fitting accuracy when compared to conventional optimization techniques. Full article

Deep-sea navigation represents the future trend of maritime navigation; however, complex seakeeping conditions often lead to unconventional ship attitudes. Conventional calculation methods are insufficient for accurately assessing hull performance under heeled or extreme trim conditions. Drawing inspiration from Bonjean curve principles, this study proposes a Quasi-Bonjean (QB) method to compute ship performance elements in arbitrary attitudes. Specifically, the QB method first constructs longitudinally distributed hull sections from the Non-Uniform Rational B-Spline (NURBS) surface model, then simulates arbitrary attitudes through dynamic waterplane adjustments, and finally calculates performance elements via sectional integration. Furthermore, an Adaptive Surface Tessellation (AST) method is proposed to optimize longitudinal section distribution by minimizing the number of stations while maintaining high geometric fidelity, thereby enhancing the computational efficiency of the QB method. Comparative experiments reveal that the AST-generated 100-station sections achieve computational precision comparable to 200-station uniform distributions under optimal conditions, and the performance elements calculated by the QB method under multi-attitude conditions meet International Association of Classification Societies accuracy thresholds, particularly excelling in the displacement and vertical center of buoyancy calculations. These findings confirm that the QB method effectively addresses the critical limitations of traditional hydrostatic tables, providing a theoretical foundation for analyzing damaged ship equilibrium and evaluating residual stability. Full article

This paper extends Woźny and Chudy’s linear-complexity Bézier evaluation algorithm (2020) to all parametric curves/surfaces with normalized basis functions via a novel basis function matrix decomposition. The unified framework covers the following: (i) B-spline/NURBS models; (ii) Bézier-type surfaces (tensor-product, rational, and triangular); (iii) enhanced models with shape parameters or non-polynomial basis spaces. For curves, we propose sequential and reverse corner-cutting modes. Surface evaluation adapts to type: non-tensor-product surfaces are processed through index-linearization to match the curve format, while tensor-product surfaces utilize nested curve evaluation. This approach reduces computational complexity, resolves cross-model compatibility issues, and establishes an efficient evaluation framework for diverse parametric geometries. Full article

This research describes a multi-objective trajectory planning method for robotic arms based on time, energy, and impact. The quintic Non-Uniform Rational B-Spline (NURBS) curve was employed to interpolate the trajectory in joint space. The quintic NURBS interpolation curve can make the trajectory become constrained within the kinematic limits of velocity, acceleration, and jerk while also satisfying the continuity of jerk. Then, based on the Parrot Optimization (PO) algorithm, through improvements to reduce algorithmic randomness and the introduction of appropriate multi-objective strategies, the algorithm was extended to the Multi-Objective Parrot Optimization (MOPO) algorithm, which better balances global search and local convergence, thereby more effectively solving multi-objective optimization problems and reducing the impact on optimization results. Subsequently, by integrating interpolation curves, the multi-objective optimization of joint trajectories could be performed under robotic kinematic constraints based on time–energy-jerk criteria. The obtained Pareto optimal front can provide decision-makers in industrial robotic arm applications with flexible options among non-dominated solutions. Full article

The conservation of cultural heritage is fundamental, and it is difficult to predict how heritage objects will relate with structural damages. For these objects, the most used process for the analyses involves NURBS models that may introduce an excessive level of approximation leading to wrong simulation results. This work presents the preliminary review of literature and first tests regarding denoising and voxel algorithms and their application for the creation of volumetric models of a reconstruction of an ancient scorpionide, to identify the bottlenecks of the post-processing method for the creation of volumetric data for the FEA of cultural heritage. Full article

To assess the condition of cultural heritage assets for conservation, reality-based 3D models can be analyzed using FEA (finite element analysis) software, yielding valuable insights into their structural integrity. Three-dimensional point clouds obtained through photogrammetric and laser scanning techniques can be transformed into volumetric data suitable for FEA by utilizing voxels. When directly using the point cloud data in this process, it is crucial to employ the highest level of accuracy. The fidelity of r point clouds can be compromised by various factors, including uncooperative materials or surfaces, poor lighting conditions, reflections, intricate geometries, and limitations in the precision of the instruments. This data not only skews the inherent structure of the point cloud but also introduces extraneous information. Hence, the geometric accuracy of the resulting model may be diminished, ultimately impacting the reliability of any analyses conducted upon it. The removal of noise from point clouds, a crucial aspect of 3D data processing, known as point cloud denoising, is gaining significant attention due to its ability to reveal the true underlying point cloud structure. This paper focuses on evaluating the geometric precision of the voxelization process, which transforms denoised 3D point clouds into volumetric models suitable for structural analyses. Full article

Real-time parametric interpolation plays a crucial role in achieving high-speed and high-precision multi-axis CNC machining. In the interpolation cycle, the position of the next interpolation point is required to be calculated in real-time to guide the action of the machining process. Due to the existence of the positioning error of the interpolation point, it is extremely difficult to eliminate the feedrate fluctuation, which may lead to dramatic decreases in machining quality and the driving capabilities’ saturation of each axis. A computationally efficient and precise feedrate fluctuation minimization method is proposed for the NURBS tool path interpolation in the CNC milling process. The model for the arc length and curvature, with respect to the parameter of the NURBS tool path, is established to reduce the calculation amount required by interpolation points determination. The deviation between the theoretical and actual interpolation step length is decreased by the proposed arc length compensation method to minimize the feedrate fluctuation. In addition, the interpolation points derived from the arc length compensation process are further corrected by performing the Newton iteration to restrict the feedrate fluctuation within the preset accuracy threshold. The effectiveness and superiorities of the proposed feedrate fluctuation minimization method are verified by simulation and milling experiments. Full article

Resistance is a key index of a ship’s hydrodynamic performance, and studying the design of the bulbous bow is an important method to reduce ship resistance. Based on the ship resistance sample data obtained from computational fluid dynamics (CFD) simulation, this study uses a machine learning method to realize the fast prediction of ship resistance corresponding to different bulbous bows. To solve the problem of insufficient accuracy in the single surrogate model, this study proposes a CBR surrogate model that integrates convolutional neural networks with backpropagation and radial basis function models. The coordinates of the control points of the NURBS surface at the bulbous bow are taken as the design variables. Then, a convergence factor is introduced to balance the global and local search abilities of the whale algorithm to improve the convergence speed. The sample space is then iteratively searched using the improved whale algorithm. The results show that the mean absolute error and root mean square error of the CBR model are better than those of the BP and RBF models. The accuracy of the model prediction is significantly improved. The optimized bulbous bow design minimizes the ship resistance, which is reduced by 4.95% compared with the initial ship model. This study provides a reliable and efficient machine learning method for ship resistance prediction. Full article

This paper proposes a specifically parametric design method for planing hulls using longitudinal functions and shape coefficients in order to meet the requirements for optimizing the hydrodynamic performance of planing hulls. To fully define the geometry of the planing hull, a series of design parameters and a set of longitudinal functions and shape coefficients are introduced to define key geometric features. The main frame curves of the hull are designed from bottom to top to ensure the priority and independence of parameters related to the planing surface. The mathematical equations of the control points of the keel curve, chine curve, sheer curve, and surface station curve of the hull framework are established and solved based on B-spline theory. This configures the basis for generating a continuous smooth surface of the hull. Finally, based on the frame curves, the hull surface was generated by using NURBS surface interpolation. The design parameters, especially the longitudinal functions and shape coefficients, can intuitively and independently control the key features of the hull form, which allow control over key geometric features that are highly relevant to the hydrodynamics of the planing hull. By utilizing this approach, rapid production of deep-V and radial planing hulls is achievable, resulting in closed and smooth hull surfaces. Case studies have provided evidence that the modeling of monohull unstepped planing hulls with diverse characteristics can be effectively accomplished through the definition of these parameters. Full article

An air-lubricated planing hull with integrated air channels presents a transformative approach for enhancing marine vessel performance by significantly reducing hydrodynamic resistance. Within the framework of air-layer drag reduction research, the precise definition and optimization of geometric design parameters are critical, as they directly influence the formation and stability of the air layer and the hydrodynamic characteristics of the hull. Applying a fully parameterized modeling approach to the air-lubricated planing hull is highly relevant and pivotal for advancing systematic, performance-driven hull design and optimization in modern naval architecture. This study proposes a fully parameterized modeling method specifically designed for such crafts. The method utilizes B-spline curves to represent the planar projections of the primary hull contours and the sectional lines of key hull surfaces. The hull surfaces are fitted using non-uniform rational B-Spline (NURBS) surfaces, and the design parameters are smoothed according to the principle of minimum strain energy, leading to fair and smooth hull surfaces. A dedicated program is developed based on this method. It facilitates the rapid generation of smooth hull forms for an air-lubricated planing hull solely from design parameters without depending on parent hull forms. This approach provides geometric hull samples for optimizing the hydrodynamic performance of the air-lubricated planing hull. Full article

This paper presents a novel adaptive crack-tip extended isogeometric analysis (adaptive CT XIGA) framework based on locally refined B-splines (LR B-splines) for efficient and accurate fracture modeling in two-dimensional solids. The XIGA method facilitates crack modeling without requiring the specific locations of crack faces and enables crack propagation simulation without remeshing by employing localized enrichment functions. LR B-splines, as an advanced extension of B-splines and NURBS, offer high-order continuity, precise geometric representation, and local refinement capabilities, thereby enhancing computational accuracy and efficiency. Various local mesh refinement strategies, designed based on crack and crack-tip locations, are investigated. Among these strategies, the crack-tip topological refinement strategy is adopted for local refinement in the adaptive CT XIGA framework. Stress intensity factors (SIFs) are evaluated using the contour interaction integral technique, while the maximum circumferential stress criterion is adopted to predict the crack growth direction. Numerical examples demonstrate the accuracy, efficiency, and robustness of adaptive CT XIGA. The results confirm that the proposed framework achieves superior error convergence rates and significantly reduces computational costs compared to a-posteriori-error-based adaptive XIGA methods, particularly in crack propagation simulations. These advantages establish adaptive CT XIGA as a powerful and efficient tool for addressing complex fracture problems in solid mechanics. Full article

Collision avoidance and path planning are essential for ensuring safe and efficient UAV operations, particularly in applications like drone delivery and Advanced Air Mobility (AAM). This study introduces an improved algorithm for three-dimensional path planning in obstacle-rich environments, such as urban and industrial areas. The proposed approach integrates the A* search algorithm with a customized heuristic function which incorporates local obstacle density. This modification not only guides the search towards more efficient paths but also minimizes altitude variations and steers the UAV away from high-density obstacle regions. To achieve this, the A* algorithm was adapted to output obstacle density information at each path node, enabling a subsequent refinement process. The path refinement applies a truncation algorithm that considers both path angles and obstacle density, and the refined waypoints serve as control points for Non-Uniform Rational B-Splines (NURBS) interpolation. This process ensures smooth and dynamically feasible trajectories. Numerical simulations were performed using a quadrotor model with integrated PID controllers in environments with varying obstacle densities. The results demonstrate the algorithm’s ability to effectively balance path efficiency and feasibility. Compared to traditional methods, the proposed approach exhibits superior performance in high-obstacle-density environments, validating its effectiveness and practical applicability. Full article

This paper extends the well-known transfinite interpolation formula, which was developed in the late 1960s by the applied mathematician William Gordon at the premises of General Motors as an extension of the pre-existing Coons interpolation formula. Here, a conjecture is formulated, which claims that the meaning of the involved blending functions can be enhanced, such that it includes any linear independent and complete set of functions, including piecewise-linear, trigonometric functions, Bernstein polynomials, B-splines, and NURBS, among others. In this sense, NURBS-based isogeometric analysis and aspects of T-splines may be considered as special cases. Applications are provided to illustrate the accuracy in the interpolation through the L₂ error norm of closed-formed functions prescribed at the nodal points of the transfinite patch, which represent the solution of partial differential equations under boundary conditions of the Dirichlet type. Full article

Sandwich structures with triply periodic minimal surface (TPMS) cores have garnered research attention due to their potential to address challenges in lightweight solutions, high-strength designs, and energy absorption capabilities. This study focuses on performing finite element analyses (FEAs) on eight novel TPMS cores and one stochastic topology. It presents a method of analysis obtained through implicit modeling in Ansys simulations and examines whether the results obtained differ from a conventional method that uses a non-uniform rational B-spline (NURBS) approach. The study further presents a sensitivity analysis and a qualitative analysis of the meshes and four material models are evaluated to find the best candidate for polymeric parts created by additive manufacturing (AM) using a stereolithography (SLA) method. The FEA results from static and explicit simulations are compared with experimental data and while discrepancies are identified in some of the specimens, the failure mechanism of the proposed topologies can generally be estimated without the need for an empirical investigation. Results suggest that implicit modeling, while more computationally expensive, is as accurate as traditional methods. Additionally, insights into numerical simulations and optimal input parameters are provided to effectively validate structural designs for sandwich-type engineering applications. Full article

To achieve efficient and accurate thick plate welding, as well as to precisely extract and plan the paths of complex three-dimensional weld seams in large steel structures, this study introduces a novel vision-guided approach for robotic welding systems utilizing a constant-focus laser sensor. This methodology specifically targets and mitigates several critical shortcomings inherent in conventional vision-guided welding techniques, including limited detection ranges, diminished precision in both detection and tracking, and suboptimal real-time performance. For preprocessed weld images, an improved grayscale extreme centroid method was developed to extract the center of the light stripe. Furthermore, a sophisticated feature point extraction algorithm, which integrates a maximum distance search strategy with a least-squares fitting procedure, was developed to facilitate the precise and timely identification of weld seam characteristic points. To further optimize the outcomes, a cylindrical filtering mechanism was employed to eliminate substantial discrepancies, whereas local Non-Uniform Rational B-Spline (NURBS) curve interpolation was utilized for the generation of smooth and accurate trajectory plans. A spatial vector-based pose adjustment strategy was then implemented to provide robust guidance for the welding robot, ensuring the successful execution of the welding operations. The experimental results indicated that the proposed algorithm achieved a tracking error of 0.3197 mm for welding workpieces with a thickness of 60 mm, demonstrating the method’s substantial potential in the manufacturing sector, especially in the domain of automated welding. Full article