Pub Date : 2025-09-08DOI: 10.1016/j.cad.2025.103955
Longdu Liu , Xiangjun Wu , Jiqiang Huang , Lingxin Cao , Xiaokang Liu , Changhe Tu , Lin Lu
Shell structures are widely used in architecture and engineering for their efficient load-bearing behavior. However, large-span, thin-shell designs often suffer from insufficient stiffness and strength. Rib-reinforced shells can enhance both stiffness and spatial efficiency, but they commonly rely on inefficient principal-stress-field (PSF)–guided quadrilateral partitioning. We present a direct computational framework that optimizes rib layouts from the PSF without intermediate partitioning. Our approach uses centroidal Voronoi tessellation to generate ribs directly on the optimized principal stress field, enabling adaptive rib refinement on arbitrary freeform surfaces. We also optimize rib cross-sectional profiles to minimize material usage while preserving structural performance, improving both mechanical efficiency and sustainability. Numerical simulations and physical experiments show that, under equivalent load and volume constraints, structures optimized with our method achieve a 78% reduction in deformation compared to conventional approaches, validating the effectiveness of the framework.
{"title":"Principal stress field-guided optimization for rib structure generation","authors":"Longdu Liu , Xiangjun Wu , Jiqiang Huang , Lingxin Cao , Xiaokang Liu , Changhe Tu , Lin Lu","doi":"10.1016/j.cad.2025.103955","DOIUrl":"10.1016/j.cad.2025.103955","url":null,"abstract":"<div><div>Shell structures are widely used in architecture and engineering for their efficient load-bearing behavior. However, large-span, thin-shell designs often suffer from insufficient stiffness and strength. Rib-reinforced shells can enhance both stiffness and spatial efficiency, but they commonly rely on inefficient principal-stress-field (PSF)–guided quadrilateral partitioning. We present a direct computational framework that optimizes rib layouts from the PSF without intermediate partitioning. Our approach uses centroidal Voronoi tessellation to generate ribs directly on the optimized principal stress field, enabling adaptive rib refinement on arbitrary freeform surfaces. We also optimize rib cross-sectional profiles to minimize material usage while preserving structural performance, improving both mechanical efficiency and sustainability. Numerical simulations and physical experiments show that, under equivalent load and volume constraints, structures optimized with our method achieve a 78% reduction in deformation compared to conventional approaches, validating the effectiveness of the framework.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103955"},"PeriodicalIF":3.1,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-02DOI: 10.1016/j.cad.2025.103964
Will Thacher , Yulong Pan , Per-Olof Persson
In this work we introduce a triangular Delaunay mesh generator that can be trained using reinforcement learning to maximize a given mesh quality metric. Our mesh generator consists of a graph neural network that distributes and modifies vertices, and a standard Delaunay algorithm to triangulate the vertices. We explore various design choices and evaluate our mesh generator on diverse tasks including mesh generation, mesh improvement, and producing variable resolution meshes. The learned mesh generator outputs meshes that are comparable in quality to those produced by Triangle and DistMesh, two popular Delaunay-based mesh generators.
{"title":"Optimization of a Triangular Delaunay Mesh Generator using Reinforcement Learning","authors":"Will Thacher , Yulong Pan , Per-Olof Persson","doi":"10.1016/j.cad.2025.103964","DOIUrl":"10.1016/j.cad.2025.103964","url":null,"abstract":"<div><div>In this work we introduce a triangular Delaunay mesh generator that can be trained using reinforcement learning to maximize a given mesh quality metric. Our mesh generator consists of a graph neural network that distributes and modifies vertices, and a standard Delaunay algorithm to triangulate the vertices. We explore various design choices and evaluate our mesh generator on diverse tasks including mesh generation, mesh improvement, and producing variable resolution meshes. The learned mesh generator outputs meshes that are comparable in quality to those produced by Triangle and DistMesh, two popular Delaunay-based mesh generators.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103964"},"PeriodicalIF":3.1,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-02DOI: 10.1016/j.cad.2025.103946
Jiahao Li , Xin Zhao , Lin Wang , Shuangrong Liu , Haozhong Gao , Zeming Cheng , Chaoran Pang , Bo Yang
The design of phase distribution in cement microstructure has significant research and educational value. It aids in correlation studies, expands knowledge boundaries, and guides production processes. However, current methods for controllable microstructure synthesis cannot customize the location, size, and shape of phases in the synthesized microstructure, limiting research on cement-based materials. To address this limitation, this paper proposes a diffusion-based synthesis framework, MCCMS, which introduces multi-scale constraints at different diffusion steps to achieve fine-grained customization of phases. The MCCMS framework divides the cement microstructure into super-voxels of varying sizes at each diffusion step, imposing constraint rules to regulate their variation. Users can modify these super-voxels at different steps to customize the phases under varying constraint strengths. Experimental results demonstrate that the MCCMS framework can precise control over the position, size, and shape of phases within the microstructure, showcasing the high fidelity of the synthetic results.
{"title":"MCCMS: Achieve fine-grained phase distribution design in cement microstructure using diffusion models","authors":"Jiahao Li , Xin Zhao , Lin Wang , Shuangrong Liu , Haozhong Gao , Zeming Cheng , Chaoran Pang , Bo Yang","doi":"10.1016/j.cad.2025.103946","DOIUrl":"10.1016/j.cad.2025.103946","url":null,"abstract":"<div><div>The design of phase distribution in cement microstructure has significant research and educational value. It aids in correlation studies, expands knowledge boundaries, and guides production processes. However, current methods for controllable microstructure synthesis cannot customize the location, size, and shape of phases in the synthesized microstructure, limiting research on cement-based materials. To address this limitation, this paper proposes a diffusion-based synthesis framework, MCCMS, which introduces multi-scale constraints at different diffusion steps to achieve fine-grained customization of phases. The MCCMS framework divides the cement microstructure into super-voxels of varying sizes at each diffusion step, imposing constraint rules to regulate their variation. Users can modify these super-voxels at different steps to customize the phases under varying constraint strengths. Experimental results demonstrate that the MCCMS framework can precise control over the position, size, and shape of phases within the microstructure, showcasing the high fidelity of the synthetic results.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103946"},"PeriodicalIF":3.1,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144988421","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-02DOI: 10.1016/j.cad.2025.103962
Kaloyan S. Kirilov , Jingtian Zhou , Joaquim Peiró , David Moxey
Established a posteriori mesh generation, high-order mesh curving and some mesh optimisation approaches often rely on an accurate CAD parametrisation of the boundary of the computational domain. This information, however, is not always available, especially when composite multi-software workflows are employed. To deal with such cases, we propose a method for reconstructing the missing connectivity information between the mesh and the CAD geometry when importing an arbitrarily sourced mesh. The reconstruction is followed by curving methods for order elevation, projections or subsequently optimisations with boundary-conforming node sliding. Lastly, mesh modification techniques are used to achieve the desired mesh resolution and quality for meshes incorporating boundary layers. We illustrate the steps of the proposed end-to-end workflow through two simple geometries coming from different sources and an end-to-end complex automotive mesh generation test case.
{"title":"High-order curvilinear mesh generation from third-party meshes","authors":"Kaloyan S. Kirilov , Jingtian Zhou , Joaquim Peiró , David Moxey","doi":"10.1016/j.cad.2025.103962","DOIUrl":"10.1016/j.cad.2025.103962","url":null,"abstract":"<div><div>Established <em>a posteriori</em> mesh generation, high-order mesh curving and some mesh optimisation approaches often rely on an accurate CAD parametrisation of the boundary of the computational domain. This information, however, is not always available, especially when composite multi-software workflows are employed. To deal with such cases, we propose a method for reconstructing the missing connectivity information between the mesh and the CAD geometry when importing an arbitrarily sourced mesh. The reconstruction is followed by curving methods for order elevation, projections or subsequently optimisations with boundary-conforming node sliding. Lastly, mesh modification techniques are used to achieve the desired mesh resolution and quality for meshes incorporating boundary layers. We illustrate the steps of the proposed end-to-end workflow through two simple geometries coming from different sources and an end-to-end complex automotive mesh generation test case.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 103962"},"PeriodicalIF":3.1,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145290011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-02DOI: 10.1016/j.cad.2025.103950
Guoyue Luo, Qiang Zou
Lattice structures, distinguished by their customizable geometries at the microscale and outstanding mechanical performance, have found widespread application across various industries. One fundamental process in their design and manufacturing is constructing boundary representation (B-rep) models, which are essential for running advanced applications like simulation, optimization, and process planning. However, this construction process presents significant challenges due to the high complexity of lattice structures, particularly in generating nodal shapes where robustness and smoothness issues can arise from the complex intersections between struts. To address these challenges, this paper proposes a novel approach for lattice structure construction by cutting struts and filling void regions with subdivisional nodal shapes. Inspired by soap films, the method generates smooth, shape-preserving control meshes using Laplacian fairing and subdivides them through the point-normal Loop (PN-Loop) subdivision scheme to obtain subdivisional nodal shapes. The proposed method ensures robust model construction with reduced shape deviations, enhanced surface fairness, and smooth transitions between subdivisional nodal shapes and retained struts. The effectiveness of the method has been demonstrated by a series of examples and comparisons. The code and associated data have been made available at: https://github.com/Qiang-Zou/Subdiv-Lattice.
{"title":"Soap Film-Inspired Subdivisional Lattice Structure Construction","authors":"Guoyue Luo, Qiang Zou","doi":"10.1016/j.cad.2025.103950","DOIUrl":"10.1016/j.cad.2025.103950","url":null,"abstract":"<div><div>Lattice structures, distinguished by their customizable geometries at the microscale and outstanding mechanical performance, have found widespread application across various industries. One fundamental process in their design and manufacturing is constructing boundary representation (B-rep) models, which are essential for running advanced applications like simulation, optimization, and process planning. However, this construction process presents significant challenges due to the high complexity of lattice structures, particularly in generating nodal shapes where robustness and smoothness issues can arise from the complex intersections between struts. To address these challenges, this paper proposes a novel approach for lattice structure construction by cutting struts and filling void regions with subdivisional nodal shapes. Inspired by soap films, the method generates smooth, shape-preserving control meshes using Laplacian fairing and subdivides them through the point-normal Loop (PN-Loop) subdivision scheme to obtain subdivisional nodal shapes. The proposed method ensures robust model construction with reduced shape deviations, enhanced surface fairness, and smooth transitions between subdivisional nodal shapes and retained struts. The effectiveness of the method has been demonstrated by a series of examples and comparisons. The code and associated data have been made available at: <span><span>https://github.com/Qiang-Zou/Subdiv-Lattice</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103950"},"PeriodicalIF":3.1,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-02DOI: 10.1016/j.cad.2025.103949
Jingqi Zhang , Zihao Zhou , Lixin Ren , Junyuan Liu , Ying Li , Xiaowei He
Signed Distance Fields (SDFs) are essential in various applications, particularly in level set problems, where computing the SDF is equivalent to solving the Eikonal equation. Common approaches to solving these equations include the Fast Marching Method (FMM), the Fast Sweeping Method (FSM), and the Fast Iterative Method (FIM). However, FMM and FSM face significant challenges in parallelization, increasing interest in developing FIM for GPU architectures. In this paper, we extend the innovative FIM algorithm (Huang, 2021), which is GPU-friendly but relies on a single uniform grid, by incorporating multiscale techniques to accelerate wavefront propagation from source points to infinity. Unlike the traditional Fast Iterative Method, which operates on a single uniform grid and propagates the wavefront at a constant speed of one grid spacing per iteration, our multiscale approach applies a hierarchy of varying propagation speeds to accelerate the convergence. Once all source and infinite points are properly initialized, only a few FIM iterations are required to refine the values of points near the source. A coarser-grained scale, with twice the spacing of the finer grid, is then used to propagate values from accepted and tentative points to the outer regions. This process is repeated until the top-level scale is reached. Subsequently, we reverse this process by performing FIM calculations from the coarsest scale until reaching the finest grid, thereby completing a V-cycle. With multiscale V-cycles, the solution progressively converges across the entire computational domain. Comparative experimental results show that our algorithm improves computational efficiency by approximately 128% over the GPU-based Fast Marching Method and by a factor of 23 compared to the improved FIM algorithm (Huang, 2021) at scale of . This optimized approach applies to numerical simulations of multi-body systems, including fluid–structure interactions, as well as numerical analyses of flooding and earthquake scenarios.
{"title":"A parallel multiscale FIM approach in solving the Eikonal equation on GPU","authors":"Jingqi Zhang , Zihao Zhou , Lixin Ren , Junyuan Liu , Ying Li , Xiaowei He","doi":"10.1016/j.cad.2025.103949","DOIUrl":"10.1016/j.cad.2025.103949","url":null,"abstract":"<div><div>Signed Distance Fields (SDFs) are essential in various applications, particularly in level set problems, where computing the SDF is equivalent to solving the Eikonal equation. Common approaches to solving these equations include the Fast Marching Method (FMM), the Fast Sweeping Method (FSM), and the Fast Iterative Method (FIM). However, FMM and FSM face significant challenges in parallelization, increasing interest in developing FIM for GPU architectures. In this paper, we extend the innovative FIM algorithm (Huang, 2021), which is GPU-friendly but relies on a single uniform grid, by incorporating multiscale techniques to accelerate wavefront propagation from source points to infinity. Unlike the traditional Fast Iterative Method, which operates on a single uniform grid and propagates the wavefront at a constant speed of one grid spacing per iteration, our multiscale approach applies a hierarchy of varying propagation speeds to accelerate the convergence. Once all source and infinite points are properly initialized, only a few FIM iterations are required to refine the values of points near the source. A coarser-grained scale, with twice the spacing of the finer grid, is then used to propagate values from accepted and tentative points to the outer regions. This process is repeated until the top-level scale is reached. Subsequently, we reverse this process by performing FIM calculations from the coarsest scale until reaching the finest grid, thereby completing a V-cycle. With multiscale V-cycles, the solution progressively converges across the entire computational domain. Comparative experimental results show that our algorithm improves computational efficiency by approximately 128% over the GPU-based Fast Marching Method and by a factor of 23 compared to the improved FIM algorithm (Huang, 2021) at scale of <span><math><mrow><mi>N</mi><mo>=</mo><mn>2</mn><mi>E</mi><mn>8</mn></mrow></math></span>. This optimized approach applies to numerical simulations of multi-body systems, including fluid–structure interactions, as well as numerical analyses of flooding and earthquake scenarios.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103949"},"PeriodicalIF":3.1,"publicationDate":"2025-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-01DOI: 10.1016/j.cad.2025.103948
Jiayu Wu , Zhengwen Feng , Qiang Zou
B-spline modeling is fundamental to CAD systems, and its evaluation and manipulation algorithms currently in use were developed decades ago, specifically for CPU architectures. While remaining effective for many applications, these algorithms become increasingly inadequate as CAD models grow more complex, such as large-scale assemblies and microstructures. GPU acceleration offers a promising solution, but most existing GPU B-spline algorithms simply adapt CPU counterparts without accounting for the mismatch between the unstructured, recursive nature of B-splines and the structured nature of GPU kernels, ultimately failing to fully leverage GPU capabilities. This paper presents a novel approach that transforms B-spline representations into regular matrix structures, reducing all evaluation and manipulation computations to matrix addition and multiplication, thus better aligning with GPU architecture. By combining this matrix representation with GPU-optimized task scheduling and memory access patterns, the paper demonstrates significant performance improvements in the key B-spline operations of inversion and projection. Experimental results show an improvement of about two orders of magnitude in computational speed compared to existing methods.
{"title":"Matrix representation and GPU-optimized parallel B-spline computing","authors":"Jiayu Wu , Zhengwen Feng , Qiang Zou","doi":"10.1016/j.cad.2025.103948","DOIUrl":"10.1016/j.cad.2025.103948","url":null,"abstract":"<div><div>B-spline modeling is fundamental to CAD systems, and its evaluation and manipulation algorithms currently in use were developed decades ago, specifically for CPU architectures. While remaining effective for many applications, these algorithms become increasingly inadequate as CAD models grow more complex, such as large-scale assemblies and microstructures. GPU acceleration offers a promising solution, but most existing GPU B-spline algorithms simply adapt CPU counterparts without accounting for the mismatch between the unstructured, recursive nature of B-splines and the structured nature of GPU kernels, ultimately failing to fully leverage GPU capabilities. This paper presents a novel approach that transforms B-spline representations into regular matrix structures, reducing all evaluation and manipulation computations to matrix addition and multiplication, thus better aligning with GPU architecture. By combining this matrix representation with GPU-optimized task scheduling and memory access patterns, the paper demonstrates significant performance improvements in the key B-spline operations of inversion and projection. Experimental results show an improvement of about two orders of magnitude in computational speed compared to existing methods.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103948"},"PeriodicalIF":3.1,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144933023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-29DOI: 10.1016/j.cad.2025.103952
Kinga Kruppa , Juan Zaragoza Chichell , Michal Bizzarri , Michael Bartoň
We propose a computational framework for motion planning for 5-axis CNC machining of free-form surfaces. Given a reference surface, a set of contact paths on it, and a shape of a toroidal cutting tool as input, the proposed algorithm designs the tool motions that are by construction locally and globally collision-free, and offers a trade-off between approximation quality and tool wear using an optimization-based framework. The proposed algorithm first quickly constructs 2D time-tilt configuration spaces along each contact path, detecting regions that are collision-free. The configuration spaces are then merged into a single time-tilt configuration space to find a global tilt function to control the overall motion of the tool. An initial collision-free tilt function in B-spline form is first estimated and then optimized to minimize the machining error while distributing the tool wear as uniformly as possible along the entire cutting edge of the tool while staying in the collision-free region. Our algorithm is validated on both synthetic free-form surfaces and industrial benchmarks, showing that one can considerably reduce the tool wear without degrading the machining accuracy.
{"title":"On tool wear optimized motion planning for 5-axis CNC machining of free-form surfaces using toroidal cutting tools","authors":"Kinga Kruppa , Juan Zaragoza Chichell , Michal Bizzarri , Michael Bartoň","doi":"10.1016/j.cad.2025.103952","DOIUrl":"10.1016/j.cad.2025.103952","url":null,"abstract":"<div><div>We propose a computational framework for motion planning for 5-axis CNC machining of free-form surfaces. Given a reference surface, a set of contact paths on it, and a shape of a toroidal cutting tool as input, the proposed algorithm designs the tool motions that are by construction locally and globally collision-free, and offers a trade-off between approximation quality and tool wear using an optimization-based framework. The proposed algorithm first quickly constructs 2D time-tilt configuration spaces along each contact path, detecting regions that are collision-free. The configuration spaces are then merged into a single time-tilt configuration space to find a global tilt function to control the overall motion of the tool. An initial collision-free tilt function in B-spline form is first estimated and then optimized to minimize the machining error while distributing the tool wear as uniformly as possible along the entire cutting edge of the tool while staying in the collision-free region. Our algorithm is validated on both synthetic free-form surfaces and industrial benchmarks, showing that one can considerably reduce the tool wear without degrading the machining accuracy.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103952"},"PeriodicalIF":3.1,"publicationDate":"2025-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145010590","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-28DOI: 10.1016/j.cad.2025.103945
Alessandro Maissen , Aleksandra Anna Apolinarska , Sophia V. Kuhn , Luis Salamanca , Michael A. Kraus , Konstantinos Tatsis , Gonzalo Casas , Rafael Bischof , Romana Rust , Walter Kaufmann , Fernando Pérez-Cruz , Matthias Kohler
Design processes, in many disciplines like architecture, civil engineering or mechanical engineering, involve navigating large, high-dimensional and heterogeneous data. While AI-driven approaches like inverse design and surrogate modeling can enhance design exploration, their adoption is hindered by complex workflows and the need for coding and machine learning expertise. To address this, we introduce AI-eXtended Design (AIXD): a low-code, open-source toolbox that integrates AI into computational design. AIXD simplifies handling of mixed data types, as well as the analysis, training, and deployment of machine learning models for inverse design, surrogate modeling, and sensitivity analysis, enabling domain experts to rapidly explore diverse solutions with minimal coding. In this paper, we show the functionalities of the toolbox, and we demonstrate AIXD’s capabilities in architectural and engineering design applications, showing how it accelerates performance evaluation, generates high-performing alternatives, and improves design understanding by delivering new insights. By bridging AI and design practice, AIXD lowers the entry barrier to data-driven methods, making AI-extended design more accessible and efficient.
{"title":"AIXD: AI-eXtended Design Toolbox for data-driven and inverse design","authors":"Alessandro Maissen , Aleksandra Anna Apolinarska , Sophia V. Kuhn , Luis Salamanca , Michael A. Kraus , Konstantinos Tatsis , Gonzalo Casas , Rafael Bischof , Romana Rust , Walter Kaufmann , Fernando Pérez-Cruz , Matthias Kohler","doi":"10.1016/j.cad.2025.103945","DOIUrl":"10.1016/j.cad.2025.103945","url":null,"abstract":"<div><div>Design processes, in many disciplines like architecture, civil engineering or mechanical engineering, involve navigating large, high-dimensional and heterogeneous data. While AI-driven approaches like inverse design and surrogate modeling can enhance design exploration, their adoption is hindered by complex workflows and the need for coding and machine learning expertise. To address this, we introduce AI-eXtended Design (AIXD): a low-code, open-source toolbox that integrates AI into computational design. AIXD simplifies handling of mixed data types, as well as the analysis, training, and deployment of machine learning models for inverse design, surrogate modeling, and sensitivity analysis, enabling domain experts to rapidly explore diverse solutions with minimal coding. In this paper, we show the functionalities of the toolbox, and we demonstrate AIXD’s capabilities in architectural and engineering design applications, showing how it accelerates performance evaluation, generates high-performing alternatives, and improves design understanding by delivering new insights. By bridging AI and design practice, AIXD lowers the entry barrier to data-driven methods, making AI-extended design more accessible and efficient.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103945"},"PeriodicalIF":3.1,"publicationDate":"2025-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145003999","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-27DOI: 10.1016/j.cad.2025.103942
Jingyu Zhang , Qiuyang Song , Pengbo Bo , Jianrui Ding , Caiming Zhang
B-spline curve interpolation to sequential data points is a fundamental problem in various applications and has been extensively studied. However, little attention has been given to optimizing the shape quality of the interpolation curve for each specific dataset. In this paper, we propose a novel approach to B-spline curve interpolation that directly enhances shape quality by minimizing a curve-quality evaluation function, jointly optimizing the control points, location parameters, and knot vectors. The key challenge lies in satisfying the necessary constraints to ensure the existence of a B-spline interpolation curve. To address this, we reformulate the problem as an unconstrained optimization, which inherently enforces these constraints. The interpolation curve is derived by perturbing an approximation curve to eliminate its distance error while preserving its optimized shape quality. To theoretically justify this process, we establish a formal connection between the approximation and interpolation curves, proving that the distance error between them is bounded by a factor of the approximation error with respect to the data points. Experimental results and comparisons with existing methods demonstrate the effectiveness and robustness of our approach in producing high-quality interpolation curves.
{"title":"B-spline curve interpolation to ordered points through shape quality optimization","authors":"Jingyu Zhang , Qiuyang Song , Pengbo Bo , Jianrui Ding , Caiming Zhang","doi":"10.1016/j.cad.2025.103942","DOIUrl":"10.1016/j.cad.2025.103942","url":null,"abstract":"<div><div>B-spline curve interpolation to sequential data points is a fundamental problem in various applications and has been extensively studied. However, little attention has been given to optimizing the shape quality of the interpolation curve for each specific dataset. In this paper, we propose a novel approach to B-spline curve interpolation that directly enhances shape quality by minimizing a curve-quality evaluation function, jointly optimizing the control points, location parameters, and knot vectors. The key challenge lies in satisfying the necessary constraints to ensure the existence of a B-spline interpolation curve. To address this, we reformulate the problem as an unconstrained optimization, which inherently enforces these constraints. The interpolation curve is derived by perturbing an approximation curve to eliminate its distance error while preserving its optimized shape quality. To theoretically justify this process, we establish a formal connection between the approximation and interpolation curves, proving that the distance error between them is bounded by a factor of the approximation error with respect to the data points. Experimental results and comparisons with existing methods demonstrate the effectiveness and robustness of our approach in producing high-quality interpolation curves.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103942"},"PeriodicalIF":3.1,"publicationDate":"2025-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144908388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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