Search Results (89)

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 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

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

Transfinite interpolation, originally proposed in the early 1970s as a global interpolation method, was first implemented using Lagrange polynomials and cubic Hermite splines. While initially developed for computer-aided geometric design (CAGD), the method also found application in global finite element analysis. With the advent of isogeometric analysis (IGA), Bernstein–Bézier polynomials have increasingly replaced Lagrange polynomials, particularly in conjunction with tensor product B-splines and non-uniform rational B-splines (NURBSs). Despite its early promise, transfinite interpolation has seen limited adoption in modern CAD/CAE workflows, primarily due to its mathematical complexity—especially when blending polynomials of different degrees. In this context, the present study revisits transfinite interpolation and demonstrates that, in four broad classes, Lagrange polynomials can be systematically replaced by Bernstein polynomials in a one-to-one manner, thus giving the same accuracy. In a fifth class, this replacement yields a robust dual set of basis functions with improved numerical properties. A key advantage of Bernstein polynomials lies in their natural compatibility with weighted formulations, enabling the accurate representation of conic sections and quadrics—scenarios where IGA methods are particularly effective. The proposed methodology is validated through its application to a boundary-value problem governed by the Laplace equation, as well as to the eigenvalue analysis of an acoustic cavity, thereby confirming its feasibility and accuracy. 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

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

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

In robotic-assisted laminectomy decompression, stable and precise vertebral plate cutting remains challenging due to manual dependency and the absence of adaptive skill-learning mechanisms. This paper presents an advanced robotic vertebral plate-cutting system that leverages patient-specific anatomical variations and replicates the surgeon’s cutting technique through a trajectory parameter prediction model. A spatial mapping relationship between artificial and patient vertebrae is first established, enabling the robot to mimic surgeon-defined trajectories with high accuracy. The robotic system’s trajectory planning begins with acquiring point cloud data of the vertebral plate, which undergoes preprocessing, Non-Uniform Rational B-Splines (NURBS) fitting, and parametric discretization. Using the processed data, a spatial mapping method translates the surgeon’s cutting path to the robotic coordinate system, with simulation validating the trajectory’s adherence to surgical requirements. To further enhance the accuracy and stability of trajectory planning, a Backpropagation(BP) neural network is implemented, providing predictive modeling for trajectory parameters. The analysis and training of the neural network confirm its effectiveness in capturing complex cutting trajectories. Finally, experimental validation, involving an artificial vertebral body model and cutting trials on patient vertebrae, demonstrates the proposed method’s capability to deliver enhanced cutting precision and stability. This skill-learning-based, personalized trajectory planning approach offers significant potential for improving the safety and quality of orthopedic robotic surgeries. Full article

This paper introduces an efficient and accurate interpolator for NURBS (non-uniform rational B-spline) curves, addressing the challenge of regulating feedrate under machining accuracy and dynamic constraints, particularly at sensitive corners. A recursive matrix representation and polynomial conversion are utilized to enhance the computation of NURBS curve intermediate points and derivatives. An improved adaptive planning method is presented to adjust the feedrate at sensitive corners, ensuring that chord error and dynamic constraints are met. The method integrates linear acceleration and deceleration stages to mitigate abrupt changes in acceleration and jerk. Additionally, a prediction–correction scheme-based interpolator is developed, employing an asynchronous mechanism to improve computational efficiency. The proposed method’s effectiveness and correctness are validated through simulation tests and machining experiments. Full article

In this research, an attempt was made to employ the Non-Uniform Rational B-Splines (NURBS) method for a challenging computational fluid dynamics (CFD) problem of aerodynamics around NACA 2412 airfoils. The comparison was carried out thoroughly by using the same boundary conditions and geometry, comparing NURBS to standard FEM implementations. Our study was interested in demonstrating the foreseeable functionalities of NURBS for solving complex CFD problems and conducting a comparative effectiveness performance evaluation between them with traditional FEM methodologies. Full article

Novel freeform optical design methods can be classified in two categories, depending on whether they focus on the generation of a starting point or the development of new optimization tools. In this paper, we design a freeform three-mirror anastigmat (TMA) and compare different surface representations using either a differential ray tracer as a new optimization tool or a commercial ray tracer (ANSYS-ZEMAX OpticStudio). For differential ray tracing, we used FORMIDABLE (Freeform Optics Raytracer with Manufacturable Imaging Design cApaBiLitiEs), an optical design library with differential ray tracing and Non-Uniform Rational B-Splines (NURBS) optimization capabilities, available under the European Software Community License (ESCL). NURBS allow a freeform surface to be represented without needing any prior knowledge of the surface, such as the polynomial degree in polynomial descriptions. OpticStudio and other commercial optical design software are designed to optimize polynomial surfaces but are not well-suited to optimize NURBS surfaces, requiring a custom optical design library. In order to demonstrate the interest in using NURBS representation, we designed and independently optimized two freeform telescopes over different iteration cycles; with NURBS using FORMIDABLE or with XY polynomials using OpticStudio. We then compared the resulting systems using their root mean square field maps to assess the optimization quality of each surface representation. We also provided a full-system comparison, including mirror freeform departures. This study shows that NURBS can be a relevant alternative to XY polynomials for the freeform optimization of reflective three-mirror telescopes as it achieves more a uniform imaging quality in the field of view. Full article

In this paper, we implement the finite detail technique primarily based on T-Splines for approximating solutions to the linear elasticity equations in the connected and bounded Lipschitz domain. Both theoretical and numerical analyses of the Dirichlet and Neumann boundary problems are presented. The Reissner–Mindlin (RM) hypothesis is considered for the investigation of the mechanical performance of a 3D cylindrical shell pipe without and with preformed hole problems under concentrated and compression loading in the linear elastic behavior for trimmed and untrimmed surfaces in structural engineering problems. Bézier extraction from T-Splines is integrated for an isogeometric analysis (IGA) approach. The numerical results obtained, particularly for the displacement and von Mises stress, are compared with and validated against the literature results, particularly with those for Non-Uniform Rational B-Spline (NURBS) IGA and the finite element method (FEM) Abaqus methods. The obtained results show that the computation time of the IGA based on the T-Spline method is shorter than that of the IGA NURBS and FEM Abaqus/CAE (computer-aided engineering) methods. Furthermore, the highlighted results confirm that the IGA approach based on the T-Spline method shows more success than numerical reference methods. We observed that the NURBS IGA method is very limited for studying trimmed surfaces. The T-Spline method shows its power and capability in computing trimmed and untrimmed surfaces. Full article

An isogeometric topology optimization (ITO) model for multi-material structures under thermal-mechanical loadings using neural networks is proposed. In the proposed model, a non-uniform rational B-spline (NURBS) function is employed for geometric description and analytical calculation, which realizes the unification of the geometry and computational models. Neural networks replace the optimization algorithms of traditional topology optimization to update the relative densities of multi-material structures. The weights and biases of neural networks are taken as design variables and updated by automatic differentiation without derivation of the sensitivity formula. In addition, the grid elements can be refined directly by increasing the number of refinement nodes, resulting in high-resolution optimal topology without extra computational costs. To obtain comprehensive performance from ITO for multi-material structures, a weighting coefficient is introduced to regulate the proportion between thermal compliance and compliance in the loss function. Some numerical examples are given and the validity is verified by performance analysis. The optimal topological structures obtained based on the proposed model exhibit both excellent heat dissipation and stiffness performance under thermal-mechanical loadings. Full article