Pub Date : 2026-01-01Epub Date: 2025-09-15DOI: 10.1016/j.cad.2025.103968
Alexander Belyaev , Pierre-Alain Fayolle
Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Two simple extensions of the heat method for distance computation are introduced and evaluated. The extensions are based on first- and second-order Taylor series extrapolations. Numerical experiments demonstrate that the extensions deliver more accurate and robust estimates of the distance function.
{"title":"Heat method extensions for distance function estimation in planar and space domains","authors":"Alexander Belyaev , Pierre-Alain Fayolle","doi":"10.1016/j.cad.2025.103968","DOIUrl":"10.1016/j.cad.2025.103968","url":null,"abstract":"<div><div>Given a bounded domain, we deal with the problem of estimating the distance function from the internal points of the domain to the boundary of the domain. Two simple extensions of the heat method for distance computation are introduced and evaluated. The extensions are based on first- and second-order Taylor series extrapolations. Numerical experiments demonstrate that the extensions deliver more accurate and robust estimates of the distance function.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103968"},"PeriodicalIF":3.1,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099142","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 : 2026-01-01Epub Date: 2025-09-13DOI: 10.1016/j.cad.2025.103953
Xiaopeng Zheng, Hao Wang, Na Lei, Zhongxuan Luo
Quadrilateral meshes derived from foliations and quadratic differentials possess a high structural regularity. However, for complex models, meshes directly generated by foliation and its induced holomorphic quadratic differentials face notable challenges regarding area distortion, corner preservation, and uniform cell size distribution. To overcome these limitations, we introduce a set of enhanced techniques grounded in surface foliation and meromorphic quadratic differentials. Specifically, we introduce pole-constrained foliations to compute meromorphic quadratic differentials, significantly reducing area distortion. Additionally, a modified double cover strategy is further introduced to preserve corner features by altering the model’s topology. Finally, adaptive metric graph optimization is utilized to ensure a uniform distribution of mesh elements. Experiments validate the effectiveness of the proposed approach.
{"title":"Quadrilateral mesh generation based on foliation and meromorphic quadratic differential","authors":"Xiaopeng Zheng, Hao Wang, Na Lei, Zhongxuan Luo","doi":"10.1016/j.cad.2025.103953","DOIUrl":"10.1016/j.cad.2025.103953","url":null,"abstract":"<div><div>Quadrilateral meshes derived from foliations and quadratic differentials possess a high structural regularity. However, for complex models, meshes directly generated by foliation and its induced holomorphic quadratic differentials face notable challenges regarding area distortion, corner preservation, and uniform cell size distribution. To overcome these limitations, we introduce a set of enhanced techniques grounded in surface foliation and meromorphic quadratic differentials. Specifically, we introduce pole-constrained foliations to compute meromorphic quadratic differentials, significantly reducing area distortion. Additionally, a modified double cover strategy is further introduced to preserve corner features by altering the model’s topology. Finally, adaptive metric graph optimization is utilized to ensure a uniform distribution of mesh elements. Experiments validate the effectiveness of the proposed approach.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103953"},"PeriodicalIF":3.1,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145099143","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 : 2025-12-01Epub Date: 2025-08-26DOI: 10.1016/j.cad.2025.103940
Qiang Zou, Lizhen Zhu
The recent rise of generative artificial intelligence (AI), powered by Transformer networks, has achieved remarkable success in natural language processing, computer vision, and graphics. However, the application of Transformers in computer-aided design (CAD), particularly for processing boundary representation (B-rep) models, remains largely unexplored. To bridge this gap, we propose a novel approach for adapting Transformers to B-rep learning, called the Boundary Representation Transformer (BRT). B-rep models pose unique challenges due to their irregular topology and continuous geometric definitions, which are fundamentally different from the structured and discrete data Transformers are designed for. To address this, BRT proposes a continuous geometric embedding method that encodes B-rep surfaces (trimmed and untrimmed) into Bézier triangles, preserving their shape and continuity without discretization. Additionally, BRT employs a topology-aware embedding method that organizes these geometric embeddings into a sequence of discrete tokens suitable for Transformers, capturing both geometric and topological characteristics within B-rep models. This enables the Transformer’s attention mechanism to effectively learn shape patterns and contextual semantics of boundary elements in a B-rep model. Extensive experiments demonstrate that BRT achieves state-of-the-art performance in part classification and feature recognition tasks.
{"title":"Bringing Attention to CAD: Boundary Representation Learning via Transformer","authors":"Qiang Zou, Lizhen Zhu","doi":"10.1016/j.cad.2025.103940","DOIUrl":"10.1016/j.cad.2025.103940","url":null,"abstract":"<div><div>The recent rise of generative artificial intelligence (AI), powered by Transformer networks, has achieved remarkable success in natural language processing, computer vision, and graphics. However, the application of Transformers in computer-aided design (CAD), particularly for processing boundary representation (B-rep) models, remains largely unexplored. To bridge this gap, we propose a novel approach for adapting Transformers to B-rep learning, called the Boundary Representation Transformer (BRT). B-rep models pose unique challenges due to their irregular topology and continuous geometric definitions, which are fundamentally different from the structured and discrete data Transformers are designed for. To address this, BRT proposes a continuous geometric embedding method that encodes B-rep surfaces (trimmed and untrimmed) into Bézier triangles, preserving their shape and continuity without discretization. Additionally, BRT employs a topology-aware embedding method that organizes these geometric embeddings into a sequence of discrete tokens suitable for Transformers, capturing both geometric and topological characteristics within B-rep models. This enables the Transformer’s attention mechanism to effectively learn shape patterns and contextual semantics of boundary elements in a B-rep model. Extensive experiments demonstrate that BRT achieves state-of-the-art performance in part classification and feature recognition tasks.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103940"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144912961","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 : 2025-12-01Epub 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":"2025-12-01","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 : 2025-12-01Epub Date: 2025-08-20DOI: 10.1016/j.cad.2025.103947
Jiantao Song , Rui Xu , Wensong Wang , Shiqing Xin , Shuangmin Chen , Jiaye Wang , Taku Komura , Wenping Wang , Changhe Tu
Querying the nearest distance from a point to line segments in 2D is a textbook problem in computational geometry. This paper presents P2Seg, a novel algorithmic strategy that transforms the intricate problem into an accessible linear traversal. Our method precomputes a KD tree and a Voronoi diagram for the site collection , where refers to the endpoints of all line segments. Obviously, for a query point , the nearest site provides a crucial clue for pinpointing the nearest line segment, i.e., the pairing effectively reduces the search from line segments to a limited number, represented as . The key idea of this paper is driven by an insightful observation: if the ray intersects with ’s Voronoi cell at a point, say , then is a subset of . This suggests that preprocessing efforts can be substantially minimized by focusing solely on scenarios where the query point lies on the Voronoi edges, which are fundamentally one-dimensional. We further prove that the challenge of locating the nearest line segment from can be distilled down to a simple linear traversal. Testing on datasets of varying complexities shows that P2Seg significantly outperforms state-of-the-art techniques. For example, in scenarios involving 10K segments with an average length of 0.5, our method runs 2.2 times faster than P2M and 60 times faster than AABB, as illustrated in the teaser figure.
{"title":"P2Seg: Distance query from point to segments","authors":"Jiantao Song , Rui Xu , Wensong Wang , Shiqing Xin , Shuangmin Chen , Jiaye Wang , Taku Komura , Wenping Wang , Changhe Tu","doi":"10.1016/j.cad.2025.103947","DOIUrl":"10.1016/j.cad.2025.103947","url":null,"abstract":"<div><div>Querying the nearest distance from a point to <span><math><mi>n</mi></math></span> line segments in 2D is a textbook problem in computational geometry. This paper presents P2Seg, a novel algorithmic strategy that transforms the intricate problem into an accessible linear traversal. Our method precomputes a KD tree and a Voronoi diagram for the site collection <span><math><mi>S</mi></math></span>, where <span><math><mi>S</mi></math></span> refers to the endpoints of all line segments. Obviously, for a query point <span><math><mi>q</mi></math></span>, the nearest site <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> provides a crucial clue for pinpointing the nearest line segment, i.e., the pairing <span><math><mrow><mo>(</mo><mi>q</mi><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow></math></span> effectively reduces the search from <span><math><mi>n</mi></math></span> line segments to a limited number, represented as <span><math><mrow><mi>L</mi><mrow><mo>(</mo><mi>q</mi><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span>. The key idea of this paper is driven by an insightful observation: if the ray <span><math><mrow><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><mi>q</mi></mrow></math></span> intersects with <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>’s Voronoi cell at a point, say <span><math><msup><mrow><mi>q</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span>, then <span><math><mrow><mi>L</mi><mrow><mo>(</mo><mi>q</mi><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> is a subset of <span><math><mrow><mi>L</mi><mrow><mo>(</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span>. This suggests that preprocessing efforts can be substantially minimized by focusing solely on scenarios where the query point lies on the Voronoi edges, which are fundamentally one-dimensional. We further prove that the challenge of locating the nearest line segment from <span><math><mrow><mi>L</mi><mrow><mo>(</mo><msup><mrow><mi>q</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>,</mo><msub><mrow><mi>s</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>)</mo></mrow></mrow></math></span> can be distilled down to a simple linear traversal. Testing on datasets of varying complexities shows that P2Seg significantly outperforms state-of-the-art techniques. For example, in scenarios involving 10K segments with an average length of 0.5, our method runs 2.2 times faster than P2M and 60 times faster than AABB, as illustrated in the teaser figure.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103947"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896242","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 : 2025-12-01Epub 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":"2025-12-01","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}
CAD assembly models are typically represented as a collection of components, each of which can share geometric interfaces with others. In the literature, geometric interfaces have been shown to play a fundamental role in assembly model analysis, component characterization, and classification. While these interfaces are not explicitly defined in CAD models, they can be inferred from the relative positioning of components. The resulting geometric interfaces can be categorized as either interference or contact. However, it is often unclear whether these interfaces stem from intentional design choices related to component shape and function, from consistently applied relative positioning, or from unintended errors.
In industrial practice, the design of complex products often involves models sourced from public catalogs for third-party components. These catalog models frequently include shape simplifications, which can lead to unintended intersections or clearances with surrounding components — deviations that do not exist in the final physical product. This study aims to provide a comprehensive analysis and formalization of geometric interfaces, based on the complementary roles of CAD assembly modules and digital component catalogs, both widely used in industry as foundational resources for generating assembly models. The results are directly applicable to industrial CAD assembly models and can serve as a reference for CAD developers seeking to improve and extend assembly processing, as well as for researchers conducting assembly analysis.
This work introduces a formalization of geometric interfaces, including contacts, interferences, and interface envelopes, which are essential for defining component mounting requirements. An analysis of geometric interface perturbations caused by repetition operators is performed, leading to the concept of an interface envelope to model specific interface repetitions. The nominal assembly representation, presented as a reference model, facilitates the formalization of interface consistency, supporting more robust reasoning processes.
{"title":"A structured analysis of CAD assembly model interfaces for their enhanced computerized processing","authors":"Jean-Claude Léon , Flavien Boussuge , Franca Giannini , Marina Monti , Katia Lupinetti , Brigida Bonino , Jean-Philippe Pernot , Roberto Raffaeli","doi":"10.1016/j.cad.2025.103911","DOIUrl":"10.1016/j.cad.2025.103911","url":null,"abstract":"<div><div>CAD assembly models are typically represented as a collection of components, each of which can share geometric interfaces with others. In the literature, geometric interfaces have been shown to play a fundamental role in assembly model analysis, component characterization, and classification. While these interfaces are not explicitly defined in CAD models, they can be inferred from the relative positioning of components. The resulting geometric interfaces can be categorized as either interference or contact. However, it is often unclear whether these interfaces stem from intentional design choices related to component shape and function, from consistently applied relative positioning, or from unintended errors.</div><div>In industrial practice, the design of complex products often involves models sourced from public catalogs for third-party components. These catalog models frequently include shape simplifications, which can lead to unintended intersections or clearances with surrounding components — deviations that do not exist in the final physical product. This study aims to provide a comprehensive analysis and formalization of geometric interfaces, based on the complementary roles of CAD assembly modules and digital component catalogs, both widely used in industry as foundational resources for generating assembly models. The results are directly applicable to industrial CAD assembly models and can serve as a reference for CAD developers seeking to improve and extend assembly processing, as well as for researchers conducting assembly analysis.</div><div>This work introduces a formalization of geometric interfaces, including contacts, interferences, and interface envelopes, which are essential for defining component mounting requirements. An analysis of geometric interface perturbations caused by repetition operators is performed, leading to the concept of an interface envelope to model specific interface repetitions. The nominal assembly representation, presented as a reference model, facilitates the formalization of interface consistency, supporting more robust reasoning processes.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103911"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896241","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 : 2025-12-01Epub Date: 2025-08-11DOI: 10.1016/j.cad.2025.103934
Yu Chen, Hongwei Lin
Reconstructing models from unorganized point clouds presents a significant challenge, especially when the models consist of multiple components represented by their surface point clouds. Such models often involve point clouds with noise that represent multiple closed surfaces with shared regions, making their automatic identification and separation inherently complex. In this paper, we propose an automatic method that uses the topological understanding provided by persistent homology, along with representative 2-cycles of persistent homology groups, to effectively distinguish and separate each closed surface. Furthermore, we employ Loop subdivision and least squares progressive iterative approximation (LSPIA) techniques to generate high-quality final surfaces and achieve complete model reconstruction. Our method is robust to noise in the point cloud, making it suitable for reconstructing models from such data. Experimental results demonstrate the effectiveness of our approach and highlight its potential for practical applications.
{"title":"Robust Model Reconstruction Based on the Topological Understanding of Point Clouds Using Persistent Homology","authors":"Yu Chen, Hongwei Lin","doi":"10.1016/j.cad.2025.103934","DOIUrl":"10.1016/j.cad.2025.103934","url":null,"abstract":"<div><div>Reconstructing models from unorganized point clouds presents a significant challenge, especially when the models consist of multiple components represented by their surface point clouds. Such models often involve point clouds with noise that represent multiple closed surfaces with shared regions, making their automatic identification and separation inherently complex. In this paper, we propose an automatic method that uses the topological understanding provided by persistent homology, along with representative 2-cycles of persistent homology groups, to effectively distinguish and separate each closed surface. Furthermore, we employ Loop subdivision and least squares progressive iterative approximation (LSPIA) techniques to generate high-quality final surfaces and achieve complete model reconstruction. Our method is robust to noise in the point cloud, making it suitable for reconstructing models from such data. Experimental results demonstrate the effectiveness of our approach and highlight its potential for practical applications.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103934"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144827089","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 : 2025-12-01Epub Date: 2025-08-06DOI: 10.1016/j.cad.2025.103943
Junfeng Gao, Zihao Yang, Yuan Liang, Yongcun Zhang, Kangjie Liu
Inspired by natural shell-infill systems with spatially adaptive coating thicknesses (e.g., human femur bones), this paper proposes a mixed-variable topology optimization method for collaboratively designing the base topology and the adaptive coating thickness distribution of shell-infill structures. The optimization framework consists of two coupled levels. At the first level, a discrete-variable topology optimization method is employed to generate a base structure (shell and infill) with uniform coating thickness, effectively eliminating intermediate density elements to ensure a clear material interface for coating identification. At the second level, the coating size optimization is realized through density-based topology optimization combined with a novel holeless coating constraint based on a virtual temperature field. Meanwhile, to ensure manufacturability, a minimum coating thickness constraint is introduced. A density field mapping strategy further couples the two optimization levels, enabling iterative updates of both the base topology and coating thickness distribution. Three numerical examples demonstrate the effectiveness of the proposed method. The shell-infill structure with adaptive coating thickness achieves over 10 % mass reduction. Additionally, the constraints successfully eliminate unmanufacturable holes while preserving thickness continuity. Moreover, a large-scale 3D case validates the capability of the method for handling complex three-dimensional coating problems. The results highlight the potential of the method in designing bio-inspired, high-performance shell-infill structures.
{"title":"Mixed-variable topology optimization for shell-infill structures with adaptive coating thickness","authors":"Junfeng Gao, Zihao Yang, Yuan Liang, Yongcun Zhang, Kangjie Liu","doi":"10.1016/j.cad.2025.103943","DOIUrl":"10.1016/j.cad.2025.103943","url":null,"abstract":"<div><div>Inspired by natural shell-infill systems with spatially adaptive coating thicknesses (e.g., human femur bones), this paper proposes a mixed-variable topology optimization method for collaboratively designing the base topology and the adaptive coating thickness distribution of shell-infill structures. The optimization framework consists of two coupled levels. At the first level, a discrete-variable topology optimization method is employed to generate a base structure (shell and infill) with uniform coating thickness, effectively eliminating intermediate density elements to ensure a clear material interface for coating identification. At the second level, the coating size optimization is realized through density-based topology optimization combined with a novel holeless coating constraint based on a virtual temperature field. Meanwhile, to ensure manufacturability, a minimum coating thickness constraint is introduced. A density field mapping strategy further couples the two optimization levels, enabling iterative updates of both the base topology and coating thickness distribution. Three numerical examples demonstrate the effectiveness of the proposed method. The shell-infill structure with adaptive coating thickness achieves over 10 % mass reduction. Additionally, the constraints successfully eliminate unmanufacturable holes while preserving thickness continuity. Moreover, a large-scale 3D case validates the capability of the method for handling complex three-dimensional coating problems. The results highlight the potential of the method in designing bio-inspired, high-performance shell-infill structures.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103943"},"PeriodicalIF":3.1,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810677","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 : 2025-12-01Epub 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.
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