Search Results (139)

Banana (Musa spp.) fruit morphology is a key determinant of yield and quality, yet modeling its 3D structural dynamics across genotypes remains difficult. To address this challenge, we developed a generic, biomass-driven 3D structural model for banana fruit fingers that quantitatively links growth and morphology. Field experiments were conducted over two growing seasons in Hainan, China, using three representative genotypes. Morphological traits, including outer and inner arc length, circumference, and pedicel length, along with dry (W_d) and fresh weight (W_f), were measured every 10 days after flowering until 110 days. Quantitative relationships between morphological traits and W_f, as well as between W_d and W_f, were fitted using linear or Gompertz functions with genotype-specific parameters. Based on these functions, a parameterized 3D reconstruction method was implemented in Python, combining biomass-driven growth equations, curvature geometry, and cross-sectional interpolation to simulate the fruit’s bending, tapering, and volumetric development. The resulting dynamic 3D models accurately reproduced genotype-specific differences in curvature, length, and shape with average fitting R² > 0.95. The proposed biomass-driven 3D structural model provides a methodological framework for integrating banana fruit morphology into functional–structural plant models. Full article

The design of smart skin with lightweight requirements utilizes high-performance composite materials, resulting in thin structural characteristics. When subjected to complex aerodynamic loads, the smart skin structure experiences warping deformation, which significantly impacts both flight efficiency and structural integrity. However, this deformation behavior has been largely overlooked in current shape sensing methods embedded within the structural health monitoring (SHM) systems of smart skin, leading to insufficient monitoring capabilities. To address this issue, this paper proposes a novel shape sensing methodology for the real-time monitoring of warping deformation in smart skin. Initially, the structural displacement field of the smart skin and the warping function are mathematically defined, incorporating constitutive relations and considering the influence of material parameters on sectional strains. Subsequently, the inverse finite element method (iFEM) is employed to establish a shape sensing model. The interpolation function and the actual sectional strains, derived from discrete strain measurements, are calculated based on the current constitutive equations. Finally, to validate the accuracy of the proposed iFEM for monitoring warping deformation, numerical tests are conducted on curved skin structures. The results indicate that the proposed methodology enhances reconstruction capability, with a 10% improvement in accuracy compared to traditional iFEM methods. Consequently, the shape sensing algorithm can be seamlessly integrated into the SHM system of smart skin to ensure the predicted performance. Full article

This paper presents a novel implementation of the Polynomial Point Interpolation Collocation Method (PPCM) for analyzing the coupled electrothermal and thermomechanical behavior of V-shaped microactuators. Within the PPCM framework, the governing equations for heat transfer and structural mechanics are discretized over the computational domain. The resulting discrete electrothermal system is solved in a fully coupled manner via an incremental load method to determine the temperature field. Subsequently, the displacement field is computed by solving the discrete mechanical equation, which incorporates terms from the natural boundary conditions. The MQ radial basis function behaves well in convergence when its parameters p_a and p_q are 1 and 1.8. Under a 6 V voltage, the difference between the PPCM and FEM temperature values is less than 1 °C. Meanwhile, the discrepancy between the PPCM and experimental temperature values is approximately 20 °C, corresponding to an approximate error of 10%. Furthermore, the displacement error between the PPCM and FEM is as low as approximately 2 μm under an applied voltage of 12 V. These results validate the PPCM for predicting the driving characteristics of V-shaped microactuators. Full article

In this paper, we introduce and investigate a novel family of parameter-dependent operators incorporating multiple shape parameters ${\left\{{\lambda }_k\right\}}_{k=1}^n$, whose underlying basis functions include these parameters and exhibit a symmetry property. This parameter-dependent formulation provides a unified and flexible framework for constructing positive linear operators with enhanced approximation and shape-preserving capabilities. We establish fundamental properties of the proposed operators, including nonnegativity, linearity, end-point interpolation, monotonicity preservation and partition of unity; derive their central moments; and determine direct approximation theorems and Voronovskaja-type results. Finally, numerical experiments and graphical illustrations demonstrate the improved performance and adaptability of the proposed scheme compared with existing Bernstein-type variants. The presented framework unifies several classical and generalized operator families while providing additional shape control for practical applications in computer-aided geometric design and function approximation. Full article

Maritime remote sensing ship detection has long been plagued by two major issues: the failure of geometric priors due to the extreme length-to-width ratio of ships; and the sharp drop in edge signal-to-noise ratio caused by the overlapping chromaticity domain between ships and seawater, which leads to unsatisfactory accuracy of existing detectors in such scenarios. Therefore, this paper proposes an optical remote sensing ship detection model combining channel shuffling and bilinear interpolation, named CSBI-YOLO. The core innovations include three aspects: First, a group shuffling feature enhancement module is designed, embedding parallel group bottlenecks and channel shuffling mechanisms into the interface between the YOLOv8 backbone and neck to achieve multi-scale semantic information coupling with a small number of parameters. Second, an edge-gated upsampling unit is constructed, using separable Sobel magnitude as structural prior and a learnable gating mechanism to suppress low-contrast noise on the sea surface. Third, an R-IoU-Focal loss function is proposed, introducing logarithmic curvature penalty and adaptive weights to achieve joint optimization in three dimensions: location, shape, and scale. Dual validation was conducted on the self-built SlewSea-RS dataset and the public DOTA-ship dataset. The results show that on the SlewSea-RS dataset, the mAP₅₀ and mAP_50–95 values of the CSBI-YOLO model increased by 6% and 5.4%, respectively. On the DOTA-ship dataset, comparisons with various models demonstrate that the proposed model outperforms others, proving the excellent performance of the CSBI-YOLO model in detecting maritime ship targets. Full article

This study presents a reduced-order modeling framework for the shape optimization of a centrifugal pump. A database of CFD solutions is generated using Latin Hypercube Sampling over five design parameters to construct a reduced-order model based on proper orthogonal decomposition with radial basis function interpolation. The model predicts the flow field at the impeller–diffuser interface and pump outlet, enabling the estimation of impeller torque and total pressure rise. The active subspaces method is applied to reduce the dimensionality of the input space from five to four modified parameters. The sensitivity of the ROM is assessed with respect to further dimensionality reductions in the parameter space, POD mode truncation, and adaptive sampling. The model is then used to perform pump shape optimization via a quasi-Newton method, identifying the combination of the parameters that minimizes the impeller torque while satisfying a constraint on the head. The optimal result is validated through CFD analysis and compared against the Pareto front generated by a genetic algorithm. The work highlights the potential of model-order reduction techniques in centrifugal pump optimization. Full article

Enhancing solar cell performance is effectively attainable through optimization of the front electrode layout. This research tackles the electrode design problem via a geometry-driven optimization framework to discover high-efficiency front electrode patterns. The introduced methodology employs wide quadratic curves for representing the electrode geometry, wherein both the interpolation points and the widths of these curves function as design variables. Two solar cell configurations are utilized to test the optimization technology. In contrast to traditional shape optimization, the current strategy provides enhanced design flexibility, promoting novel and high-performance electrode configurations. Key parameters analyzed encompass the initial geometry, the count of wide quadratic curves, mesh resolution, and the size of the solar cell. Results demonstrate that the presented approach constitutes a viable and efficient design pathway for elevating solar cell operation. The performance of solar cells optimized using this technology outperforms those processed with a modified Solid Isotropic Material with Penalization (SIMP) approach. Furthermore, relative to typical H-pattern electrode grids, the optimized layouts not only achieve superior efficiency but also considerably minimize the consumption of electrode materials. Full article

This paper presents an effective method for generating blending meshes by leveraging geodesic curves on triangular meshes. Depending on whether the input meshes intersect, the blending regions are automatically initialized using either minimum-distance points or intersection curves, while allowing users to intuitively adjust boundary curves directly on the mesh. Each blending region is parameterized via geodesic linear interpolation, and a reparameterization strategy is employed to establish optimal correspondences between boundary curves, ensuring smooth, twist-free connections. The resulting blending mesh is merged with the input meshes through subdivision, trimming, and co-refinement along the boundaries. The proposed method is applicable to both intersecting and non-intersecting meshes and offers flexible control over the shape and curvature of the blending region through various user-defined parameters, such as boundary radius, scaling factor, and blending function parameters. Experimental results demonstrate that the method produces stable and smooth transitions even for complex geometries, highlighting its robustness and practical applicability in diverse domains including digital fabrication, mechanical design, and 3D object modeling. Full article

Knee osteoarthritis (KOA) is a most prevalent chronic muscoloskeletal disorder causing pain and functional impairment. Accurate predictions of KOA evolution are important for early interventions and preventive treatment planning. In this paper, we propose a novel dynamic hypergraph-based risk model (DyHRM) which integrates the encoder–decoder (ED) architecture with hypergraph convolutional neural networks (HGCNs). The risk model is used to generate longitudinal forecasts of KOA incidence and progression based on the knee evolution at a historical stage. DyHRM comprises two main parts, namely the dynamic hypergraph gated recurrent unit (DyHGRU) and the multi-view HGCN (MHGCN) networks. The ED-based DyHGRU follows the sequence-to-sequence learning approach. The encoder first transforms a knee sequence at the historical stage into a sequence of hidden states in a latent space. The Attention-based Context Transformer (ACT) is designed to identify important temporal trends in the encoder’s state sequence, while the decoder is used to generate sequences of KOA progression, at the prediction stage. MHGCN conducts multi-view spatial HGCN convolutions of the original knee data at each step of the historic stage. The aim is to acquire more comprehensive feature representations of nodes by exploiting different hyperedges (views), including the global shape descriptors of the cartilage volume, the injury history, and the demographic risk factors. In addition to DyHRM, we also propose the HyGraphSMOTE method to confront the inherent class imbalance problem in KOA datasets, between the knee progressors (minority) and non-progressors (majority). Embedded in MHGCN, the HyGraphSMOTE algorithm tackles data balancing in a systematic way, by generating new synthetic node sequences of the minority class via interpolation. Extensive experiments are conducted using the Osteoarthritis Initiative (OAI) cohort to validate the accuracy of longitudinal predictions acquired by DyHRM under different definition criteria of KOA incidence and progression. The basic finding of the experiments is that the larger the historic depth, the higher the accuracy of the obtained forecasts ahead. Comparative results demonstrate the efficacy of DyHRM against other state-of-the-art methods in this field. Full article

The Thin-Plate Splines (TPS) technique, using Kybic et al.’s generalized interpolation approach, is extended to differentiable manifolds. The initial application to surface mesh deformation resulting from parameterized Computer Aided Design (CAD) used in the framework of shape optimization is given. Coming to RSM (Response Surface Model), we give a comparison with Kriging and RBF (Radial Basis Functions), and an enrichment methodology is proposed. The new approach proposed is a breakthrough for UAV shape design of high-curvature areas. Full article

In the context of the deep integration of digital art and geometric computing, this paper proposes a digital art pattern generation method with arbitrary quadrilateral tiling. The aim is to break through the limitations of traditional fixed tiling templates in terms of adaptability to irregular tiling shapes, controllability of local deformations, and naturalness of boundary transitions. By decoupling the topological stability of quadrilaterals from deformation parameters and combining the Coons surface interpolation method, a smooth invariant mapping for the fundamental region of arbitrary quadrilaterals is constructed, solving the seamless splicing problem of irregular fundamental region. This method supports real-time editing of quadrilateral shape and colors the fundamental region based on the dynamical system model to generate periodic seamless patterns with global symmetry and controllable local details. Experiments show that the proposed method can be adapted to any quadrilateral structure, from regular rectangles to non-convex polygons. By adjusting the interpolation parameters and dynamical system functions, the symmetry, texture complexity, and visual rhythm of the patterns can be flexibly regulated. The algorithm achieves efficient computation under GPU parallel optimization (with an average generation time of 0.25 s per pattern), providing a new solution for the pattern generation and personalized design of digital art patterns. Full article

We introduce a novel family of compactly supported basis functions, termed Legendre Delta-Shaped Functions (LDSFs), constructed using the eigenfunctions of the Legendre differential equation. We begin by proving that LDSFs form a basis for a Haar space. We then demonstrate that interpolation using classical Legendre polynomials is a special case of interpolation with the proposed Legendre Delta-Shaped Basis Functions (LDSBFs). To illustrate the potential of LDSBFs, we apply the corresponding series to approximate a rectangular pulse. The results reveal that Gibbs oscillations decay rapidly, resulting in significantly improved accuracy across smooth regions. This example underscores the effectiveness and novelty of our approach. Furthermore, LDSBFs are employed within the collocation framework to solve Poisson-type equations and systems of nonlinear differential equations arising in energy transfer problems. We also derive new error bounds for interpolation polynomials in a special case, expressed in both the discrete ${(L}_2)$ norm and the Sobolev $\left(H_p\right)$ norm. To validate the proposed method, we compare our results with those obtained using the Legendre pseudospectral method. Numerical experiments confirm that our approach is accurate, efficient, and highly competitive with existing techniques. Full article

Given a triangular mesh in ${\mathbb{R}}^3$ with a family of points associated with its vertices along with vectors associated with its edges, we propose a novel technique for the construction of locally generated fitting parametrized G1-spline interpolation surfaces. The method consists of a G1 correction over the mesh edges of the mesh triangles, produced using reduced side derivatives (RSDs) introduced earlier by the author in terms of the barycentric weight functions. In the case of polynomial RSD shape functions, we establish polynomial edge corrections via an algorithm with an independent interest in determining the optimal GCD cofactors with the lowest degree for arbitrary families of polynomials. Full article

In this paper, a new approach to topology optimization using the parameterized level set function and genetic algorithm optimization methods is presented. The impact of a number of parameters describing the level set function in the representation of the model was examined. Using the B-spline interpolation function, the number of variables describing the level set function was decreased, enabling the application of evolutionary methods (genetic algorithms) in the topology optimization process. The traditional level set method is performed by using the Hamilton–Jacobi transport equation, which implies the use of gradient optimization methods that are prone to becoming stuck in local minima. Furthermore, the resulting optimal shapes are strongly dependent on the initial solution. The proposed topology optimization procedure, written in MATLAB R2013b, utilizes a genetic algorithm for global optimization, enabling it to locate the global optimum efficiently. To assess the acceleration and convergence capabilities of the proposed topology optimization method, a new genetic algorithm penalty operator was tested. This operator addresses the slow convergence issue typically encountered when the genetic algorithm optimization procedure nears a solution. By penalizing similar individuals within a population, the method aims to enhance convergence speed and overall performance. In complex examples (3D), the method can also function as a generator of good initial solutions for faster topology optimization methods (e.g., level set) that rely on such initial solutions. Both the proposed method and the traditional methods have their own advantages and limitations. The main advantage is that the proposed method is a global search method. This makes it robust against entrapment in local minima and independent of the initial solution. It is important to note that this evolutionary approach does not necessarily perform better in terms of convergence speed compared to gradient-based or other local optimization methods. However, once the global optimum has been found using the genetic algorithm, convergence can be accelerated using a faster local method such as gradient-based optimization. The application and usefulness of the method were tested on typical 2D cantilever beams and Michell beams. Full article

In this work, we introduce a novel class of $C^1$ rational quadratic interpolation splines defined by two symmetric parameters. This generalization encompasses the rational quadratic interpolation schemes given by Schmidt in 1987 as a special case. For data sets with convexity, monotonicity, or positivity constraints, we derive the necessary and sufficient conditions, ensuring that the interpolant preserves these properties. Furthermore, we propose an algorithm for selecting visually appealing and shape-preserving spline curves by minimizing a particular approximated curvature functional. Full article