Pub Date : 2025-11-08DOI: 10.1016/j.cad.2025.104007
Caleb B. Goates, Kendrick M. Shepherd
Harmonic maps are important in generating parameterizations for various domains, particularly in two and three dimensions. General extensions of two-dimensional harmonic parameterization methods to volumetric parameterizations are known to fail in a variety of contexts, though more specialized volumetric parameterizations have been proposed. This work provides and contextualizes a counterexample to various proposed proofs that employ harmonic maps to sweep a parameterization from a base surface, , to the entire domain of a geometry that is homeomorphic to or . The existence of a counterexample clarifies that these swept parameterizations come with no inherent guarantees of bijectivity, as they may in two dimensions.
{"title":"Harmonic-based sweeps need not yield volumetric parameterizations","authors":"Caleb B. Goates, Kendrick M. Shepherd","doi":"10.1016/j.cad.2025.104007","DOIUrl":"10.1016/j.cad.2025.104007","url":null,"abstract":"<div><div>Harmonic maps are important in generating parameterizations for various domains, particularly in two and three dimensions. General extensions of two-dimensional harmonic parameterization methods to volumetric parameterizations are known to fail in a variety of contexts, though more specialized volumetric parameterizations have been proposed. This work provides and contextualizes a counterexample to various proposed proofs that employ harmonic maps to sweep a parameterization from a base surface, <span><math><msub><mrow><mi>Γ</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span>, to the entire domain of a geometry that is homeomorphic to <span><math><mrow><msub><mrow><mi>Γ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>×</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span> or <span><math><mrow><msub><mrow><mi>Γ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup></mrow></math></span>. The existence of a counterexample clarifies that these swept parameterizations come with no inherent guarantees of bijectivity, as they may in two dimensions.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 104007"},"PeriodicalIF":3.1,"publicationDate":"2025-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145528381","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 : 2025-11-06DOI: 10.1016/j.cad.2025.104004
Olivier Coulaud
The present article studies the problem of approximating 3D surface models with meshes composed of curved triangles of arbitrary order. The considered process derives from a high-order solution-based mesh adaptation method called log-simplex method. In this case, it is locally applied on a specific 2D high-order solution, which is built from the features of the model and is defined on the tangent plane to the surface. This way, for a given mesh complexity, an optimal metric field is computed, which then drives the mesh adaptation procedure.
{"title":"High-order CAD-based surface mesh adaptation with the log-simplex method","authors":"Olivier Coulaud","doi":"10.1016/j.cad.2025.104004","DOIUrl":"10.1016/j.cad.2025.104004","url":null,"abstract":"<div><div>The present article studies the problem of approximating 3D surface models with meshes composed of curved triangles of arbitrary order. The considered process derives from a high-order solution-based mesh adaptation method called log-simplex method. In this case, it is locally applied on a specific 2D high-order solution, which is built from the features of the model and is defined on the tangent plane to the surface. This way, for a given mesh complexity, an optimal metric field is computed, which then drives the mesh adaptation procedure.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 104004"},"PeriodicalIF":3.1,"publicationDate":"2025-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474712","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 : 2025-11-03DOI: 10.1016/j.cad.2025.104005
Min Song, Chao Li, Xiao-Wei Guo, Qing-Yang Zhang, Jie Liu, Xiang Gao
This paper introduces a physics-driven approach to improve fluid dynamics simulations of multi-body geometries with non-matching interfaces. Conventional methods often suffer from inaccuracies due to the lack of robust physical models. Our solution integrates Computational Fluid Dynamics (CFD) techniques and proposes a conservative interpolation algorithm that resolves interface mismatches without mesh modification. By using a dual-weighting scheme based on overlapping face areas, the algorithm ensures flux consistency across subdomains while maintaining high computational efficiency. Applicable to both structured and unstructured meshes, this simple yet robust method has been implemented in general-purpose CFD software and validated through complex cases. Specifically, in Couette flow between concentric cylinders, it shows a maximum 1.556% relative error in velocity distribution against analytical solutions, outperforming continuous mesh methods in accuracy. In reactor pressure vessel simulations, it achieves a pressure distribution error of 0.586% and a maximum flow distribution error of 1.645% compared to continuous mesh solutions. These results validate the method’s high accuracy and reliability in simulating diverse flow regimes, thus facilitating precise analyses for complex engineering problems.
{"title":"A physics conservation-based mesh patching algorithm for multi-body modeling and simulation","authors":"Min Song, Chao Li, Xiao-Wei Guo, Qing-Yang Zhang, Jie Liu, Xiang Gao","doi":"10.1016/j.cad.2025.104005","DOIUrl":"10.1016/j.cad.2025.104005","url":null,"abstract":"<div><div>This paper introduces a physics-driven approach to improve fluid dynamics simulations of multi-body geometries with non-matching interfaces. Conventional methods often suffer from inaccuracies due to the lack of robust physical models. Our solution integrates Computational Fluid Dynamics (CFD) techniques and proposes a conservative interpolation algorithm that resolves interface mismatches without mesh modification. By using a dual-weighting scheme based on overlapping face areas, the algorithm ensures flux consistency across subdomains while maintaining high computational efficiency. Applicable to both structured and unstructured meshes, this simple yet robust method has been implemented in general-purpose CFD software and validated through complex cases. Specifically, in Couette flow between concentric cylinders, it shows a maximum 1.556% relative error in velocity distribution against analytical solutions, outperforming continuous mesh methods in accuracy. In reactor pressure vessel simulations, it achieves a pressure distribution error of 0.586% and a maximum flow distribution error of 1.645% compared to continuous mesh solutions. These results validate the method’s high accuracy and reliability in simulating diverse flow regimes, thus facilitating precise analyses for complex engineering problems.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 104005"},"PeriodicalIF":3.1,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474710","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 : 2025-10-30DOI: 10.1016/j.cad.2025.104003
Martin Roth , Jan Kopatsch , Kristina Wärmefjord , Rikard Söderberg , Stefan Goetz
Computer-Aided Tolerancing (CAT) software has become the standard for statistically analyzing the effects of geometrical part variations on product quality. Irrespective of CAT’s scope and technical depth, Finite Element Analysis (FEA) software, used to simulate the physical product behavior for ideal part geometry in the first place, is also often used for studies with geometrical shapes deviating from their nominal. However, this requires a manual translation of the tolerances specified in the design phase into geometrical variations represented by Finite Element (FE) meshes and their transfer to the FEA software. The method presented in this article exploits the potential of Model-Based Definition by establishing a link between Computer-Aided Design and FEA software to empower the latter for variation simulation based on semantic Geometric Dimensioning and Tolerancing (GD&T) information. To transfer this information exchanged via the Quality Information Framework (QIF) standard, a new mapping algorithm is presented that automatically decomposes FE meshes into geometrical face elements and creates a semantic link with the GD&T information carried in QIF. As a result, geometrical features are simultaneously described through meshes with nodes in the 3D Euclidean space and mathematical geometrical faces in the 2D parameter space. Exploiting this duality, mesh deviations are modeled indirectly by adjusting the mapped feature descriptions. An exemplary implementation in ANSYS® and its usage for non-intrusive structural simulations illustrates that sharing tolerancing information via QIF enables an automated, GD&T standards-compliant variation simulation within FEA software environments and is one step closer to a seamless digital thread for geometry assurance.
{"title":"Linking Model-Based Definition and Non-Intrusive Finite Element Analysis for Automated Variation Simulation","authors":"Martin Roth , Jan Kopatsch , Kristina Wärmefjord , Rikard Söderberg , Stefan Goetz","doi":"10.1016/j.cad.2025.104003","DOIUrl":"10.1016/j.cad.2025.104003","url":null,"abstract":"<div><div>Computer-Aided Tolerancing (CAT) software has become the standard for statistically analyzing the effects of geometrical part variations on product quality. Irrespective of CAT’s scope and technical depth, Finite Element Analysis (FEA) software, used to simulate the physical product behavior for ideal part geometry in the first place, is also often used for studies with geometrical shapes deviating from their nominal. However, this requires a manual translation of the tolerances specified in the design phase into geometrical variations represented by Finite Element (FE) meshes and their transfer to the FEA software. The method presented in this article exploits the potential of Model-Based Definition by establishing a link between Computer-Aided Design and FEA software to empower the latter for variation simulation based on semantic Geometric Dimensioning and Tolerancing (GD&T) information. To transfer this information exchanged via the Quality Information Framework (QIF) standard, a new mapping algorithm is presented that automatically decomposes FE meshes into geometrical face elements and creates a semantic link with the GD&T information carried in QIF. As a result, geometrical features are simultaneously described through meshes with nodes in the 3D Euclidean space and mathematical geometrical faces in the 2D parameter space. Exploiting this duality, mesh deviations are modeled indirectly by adjusting the mapped feature descriptions. An exemplary implementation in ANSYS® and its usage for non-intrusive structural simulations illustrates that sharing tolerancing information via QIF enables an automated, GD&T standards-compliant variation simulation within FEA software environments and is one step closer to a seamless digital thread for geometry assurance.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 104003"},"PeriodicalIF":3.1,"publicationDate":"2025-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145474711","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 : 2025-10-28DOI: 10.1016/j.cad.2025.104006
Jiwei Zhou , Jorge D. Camba , Pedro Company
Recent advances in generative Artificial Intelligence (AI)—particularly Large Language Models (LLMs)—offer a new paradigm for CAD interaction by enabling natural and intuitive input through texts, images, and context-aware selections. In this study, we present CADialogue, a multimodal LLM-powered conversational assistant to enable intuitive parametric CAD modeling through natural language, speech, image, and selection-based geometry interactions. Built on a general-purpose large language model, CADialogue translates user prompts into executable code to support geometry creation and context-aware editing. The system features a modular architecture that decouples prompt handling, refinement logic, and execution—allowing seamless model replacement as LLMs develop—and includes caching for rapid reuse of validated designs. We evaluate the system on 70 modeling and 10 editing tasks across varying difficulty levels, assessing performance in terms of accuracy, refinement behavior, and execution time. Results show an overall success rate of 95.71%, combining a 91.43% baseline under Text-Only input with additional recoveries enabled by Text + Image input, with robust recovery from failure via self-correction and human-in-the-loop refinement. Comparative analysis reveals that image input improves success in semantically complex prompts but introduces additional processing time. Furthermore, caching confirmed macros yields over 85.71% speedup in repeated executions. These findings highlight the potential of general-purpose LLMs for enabling accessible, iterative, and accurate CAD modeling workflows without domain-specific fine-tuning. The source code and dataset for CADialogue are available at https://github.com/Hiram31/CADialogue.
{"title":"CADialogue: A multimodal LLM-powered conversational assistant for intuitive parametric CAD modeling","authors":"Jiwei Zhou , Jorge D. Camba , Pedro Company","doi":"10.1016/j.cad.2025.104006","DOIUrl":"10.1016/j.cad.2025.104006","url":null,"abstract":"<div><div>Recent advances in generative Artificial Intelligence (AI)—particularly Large Language Models (LLMs)—offer a new paradigm for CAD interaction by enabling natural and intuitive input through texts, images, and context-aware selections. In this study, we present CADialogue, a multimodal LLM-powered conversational assistant to enable intuitive parametric CAD modeling through natural language, speech, image, and selection-based geometry interactions. Built on a general-purpose large language model, CADialogue translates user prompts into executable code to support geometry creation and context-aware editing. The system features a modular architecture that decouples prompt handling, refinement logic, and execution—allowing seamless model replacement as LLMs develop—and includes caching for rapid reuse of validated designs. We evaluate the system on 70 modeling and 10 editing tasks across varying difficulty levels, assessing performance in terms of accuracy, refinement behavior, and execution time. Results show an overall success rate of 95.71%, combining a 91.43% baseline under Text-Only input with additional recoveries enabled by Text + Image input, with robust recovery from failure via self-correction and human-in-the-loop refinement. Comparative analysis reveals that image input improves success in semantically complex prompts but introduces additional processing time. Furthermore, caching confirmed macros yields over 85.71% speedup in repeated executions. These findings highlight the potential of general-purpose LLMs for enabling accessible, iterative, and accurate CAD modeling workflows without domain-specific fine-tuning. The source code and dataset for CADialogue are available at <span><span>https://github.com/Hiram31/CADialogue</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 104006"},"PeriodicalIF":3.1,"publicationDate":"2025-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145425278","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 : 2025-10-16DOI: 10.1016/j.cad.2025.103972
Lu He, Na Lei, Ziliang Wang, Chen Wang, Xiaopeng Zheng, Zhongxuan Luo
Polycube-maps play a critical role in computer graphics, especially for generating high-quality hexahedral meshes. Existing polycube validity conditions, primarily based on Steinitz and Eppstein’s approach, are limited to 3-connected graphs. Extending polycube-maps to handle higher connectivity graphs is crucial for practical applications. In this work, we introduce Validity-Augmented Topological Conditions (VAT conditions) based on the Gauss–Bonnet theorem. These conditions offer both global and local topological criteria, enabling the solvability of k-connected graphs, non-manifold structures, and meshes with voids. Our VAT conditions allow models that do not meet traditional polycube validity criteria but are still valid polycube polyhedra in practice. Additionally, we propose an Immune Genetic Algorithm (ImGA) tailored to our VAT conditions to enhance the robustness of polycube-map generation. We evaluate our method using the Thingi10k and ABC datasets. Results demonstrate that our VAT conditions expands the solvable space of polycubes and achieves higher quality all-hexahedral meshing for higher-connectivity or more complex models. Furthermore, we discuss the limitations associated with our proposed method.
{"title":"High-connectivity polycube-maps: Solvable space expansion through validity-augmented topological conditions","authors":"Lu He, Na Lei, Ziliang Wang, Chen Wang, Xiaopeng Zheng, Zhongxuan Luo","doi":"10.1016/j.cad.2025.103972","DOIUrl":"10.1016/j.cad.2025.103972","url":null,"abstract":"<div><div>Polycube-maps play a critical role in computer graphics, especially for generating high-quality hexahedral meshes. Existing polycube validity conditions, primarily based on Steinitz and Eppstein’s approach, are limited to 3-connected graphs. Extending polycube-maps to handle higher connectivity graphs is crucial for practical applications. In this work, we introduce <em>Validity-Augmented Topological Conditions</em> (VAT conditions) based on the Gauss–Bonnet theorem. These conditions offer both global and local topological criteria, enabling the solvability of k-connected graphs, non-manifold structures, and meshes with voids. Our VAT conditions allow models that do not meet traditional polycube validity criteria but are still valid polycube polyhedra in practice. Additionally, we propose an Immune Genetic Algorithm (ImGA) tailored to our VAT conditions to enhance the robustness of polycube-map generation. We evaluate our method using the Thingi10k and ABC datasets. Results demonstrate that our VAT conditions expands the solvable space of polycubes and achieves higher quality all-hexahedral meshing for higher-connectivity or more complex models. Furthermore, we discuss the limitations associated with our proposed method.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 103972"},"PeriodicalIF":3.1,"publicationDate":"2025-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364941","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 : 2025-10-15DOI: 10.1016/j.cad.2025.103994
Kai Dai , Tianqi Song , Hangcheng Zhang , Yi-Jun Yang , Wei Zeng
Many computer graphics applications such as Boolean operation, visible surface determination, rendering, etc. require fast and robust computation of the relative positional relationships between points and shapes. The Line Segment Substitution (LSS) method presented in this paper is an improvement of the ray crossing method, which can effectively compute the positional relationship between a point and a closed planar shape. The boundary of the closed planar shape can be composed of line segments, conic curve segments, and spline curve segments. In the LSS method, complex curves will be directly replaced by line segments or replaced after iterative segmentation, depending on the type of curve and the positional relationship between the curve and target point. Then, the relationship between the point and the shape can be determined based on the parity of the number of intersections between a ray originating from the target point and the substitute line segments. Experiments have shown that, compared with other methods, the LSS method achieves the best efficiency and accuracy among methods that do not require preprocessing.
{"title":"An algorithm to compute the point inclusion of 2D planar shapes based on line segment substitution","authors":"Kai Dai , Tianqi Song , Hangcheng Zhang , Yi-Jun Yang , Wei Zeng","doi":"10.1016/j.cad.2025.103994","DOIUrl":"10.1016/j.cad.2025.103994","url":null,"abstract":"<div><div>Many computer graphics applications such as Boolean operation, visible surface determination, rendering, etc. require fast and robust computation of the relative positional relationships between points and shapes. The Line Segment Substitution (LSS) method presented in this paper is an improvement of the ray crossing method, which can effectively compute the positional relationship between a point and a closed planar shape. The boundary of the closed planar shape can be composed of line segments, conic curve segments, and spline curve segments. In the LSS method, complex curves will be directly replaced by line segments or replaced after iterative segmentation, depending on the type of curve and the positional relationship between the curve and target point. Then, the relationship between the point and the shape can be determined based on the parity of the number of intersections between a ray originating from the target point and the substitute line segments. Experiments have shown that, compared with other methods, the LSS method achieves the best efficiency and accuracy among methods that do not require preprocessing.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 103994"},"PeriodicalIF":3.1,"publicationDate":"2025-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145364942","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 : 2025-10-14DOI: 10.1016/j.cad.2025.103992
Zhuo Zhang , Sen Zhang , Yuan Zhao , Wei Wang , Hongzhou Wu , Xi Yang , Canqun Yang
Physics-Informed Neural Networks (PINNs) have shown great promise for solving partial differential equations (PDEs), but their application to multi-dimensional problems often suffers from the curse of dimensionality, leading to exponential growth in computational and memory requirements. Moreover, accurately capturing complex local features, such as those found in fluid flows, remains a significant challenge for existing approaches. To address these challenges, we propose the Dynamic Feature Separation Physics-Informed Neural Network (DFS-PINN), which introduces an innovative input-decoupling and dynamic interaction mechanism. This approach reduces computational complexity from to , enabling efficient training and improved accuracy for multi-dimensional problems, especially in real-time rendering and fluid simulations. When applied to the lid-driven cavity flow problem, DFS-PINN achieves a 6 reduction in runtime and a 62 reduction in memory usage with collocation points, compared to standard PINNs. For large-scale datasets with over points, DFS-PINN attains a mean squared error (MSE) of 0.000122, showcasing its superior computational efficiency and predictive accuracy. These results position DFS-PINN as a scalable and robust framework for solving multi-dimensional PDEs, demonstrating substantial improvements in both computational efficiency and modeling accuracy.
{"title":"DFS-PINN: A Dynamic Feature Separation Physics-Informed Neural Network","authors":"Zhuo Zhang , Sen Zhang , Yuan Zhao , Wei Wang , Hongzhou Wu , Xi Yang , Canqun Yang","doi":"10.1016/j.cad.2025.103992","DOIUrl":"10.1016/j.cad.2025.103992","url":null,"abstract":"<div><div>Physics-Informed Neural Networks (PINNs) have shown great promise for solving partial differential equations (PDEs), but their application to multi-dimensional problems often suffers from the curse of dimensionality, leading to exponential growth in computational and memory requirements. Moreover, accurately capturing complex local features, such as those found in fluid flows, remains a significant challenge for existing approaches. To address these challenges, we propose the Dynamic Feature Separation Physics-Informed Neural Network (DFS-PINN), which introduces an innovative input-decoupling and dynamic interaction mechanism. This approach reduces computational complexity from <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>N</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> to <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mi>N</mi><mo>×</mo><mi>d</mi><mo>)</mo></mrow></mrow></math></span>, enabling efficient training and improved accuracy for multi-dimensional problems, especially in real-time rendering and fluid simulations. When applied to the lid-driven cavity flow problem, DFS-PINN achieves a 6<span><math><mo>×</mo></math></span> reduction in runtime and a 62<span><math><mo>×</mo></math></span> reduction in memory usage with <span><math><msup><mrow><mn>2</mn></mrow><mrow><mn>15</mn></mrow></msup></math></span> collocation points, compared to standard PINNs. For large-scale datasets with over <span><math><msup><mrow><mn>2</mn></mrow><mrow><mn>20</mn></mrow></msup></math></span> points, DFS-PINN attains a mean squared error (MSE) of 0.000122, showcasing its superior computational efficiency and predictive accuracy. These results position DFS-PINN as a scalable and robust framework for solving multi-dimensional PDEs, demonstrating substantial improvements in both computational efficiency and modeling accuracy.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 103992"},"PeriodicalIF":3.1,"publicationDate":"2025-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145290010","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 : 2025-10-13DOI: 10.1016/j.cad.2025.103993
Yong Zhang , Yongfei Wang , Tao Wu , Ye Xu , Chen Li
A novel isoparametric tool path generation strategy incorporating spacing control was developed to overcome machining challenges in complex dental restoration fabrication, with particular emphasis on mitigating undercut formation and minimizing tool wear. To enhance machining efficiency and accuracy, a preprocessing strategy was introduced for prioritized reconstruction of offset surfaces, facilitating spiral trajectory parameterization. A segmented 3D-to-2D mapping algorithm was developed, achieving a 44.43 % reduction in computational time while maintaining machining precision. The formation mechanism of undercuts in dental restoration structures was systematically analyzed. Based on this analysis, a surface formation prediction algorithm was established to accurately identify undercut areas in cavity regions after machining. This enables the implementation of localized overcut strategies to replace conventional global undercut approaches, thereby improving the fitting accuracy and stability of dental restorations. The wear characteristics of ball-end grinding wheels were investigated, with particular focus on the relationship between spiral trajectory spacing and tool wear. In undercut regions, the machining allowance was observed to significantly affect cutting depth, leading to increased grinding forces and accelerated tool wear. To mitigate this effect, a localized spacing reduction strategy was proposed, which effectively minimizes tool wear while only slightly increasing machining time. The effectiveness of the proposed methodology was verified through precision grinding experiments on complex dental restoration structures. These methods have the potential to be applied to a wide range of complex 3D machining and manufacturing problems.
{"title":"Iso-parametric path planning to mitigate wheel wear in grinding of complex dental crowns","authors":"Yong Zhang , Yongfei Wang , Tao Wu , Ye Xu , Chen Li","doi":"10.1016/j.cad.2025.103993","DOIUrl":"10.1016/j.cad.2025.103993","url":null,"abstract":"<div><div>A novel isoparametric tool path generation strategy incorporating spacing control was developed to overcome machining challenges in complex dental restoration fabrication, with particular emphasis on mitigating undercut formation and minimizing tool wear. To enhance machining efficiency and accuracy, a preprocessing strategy was introduced for prioritized reconstruction of offset surfaces, facilitating spiral trajectory parameterization. A segmented 3D-to-2D mapping algorithm was developed, achieving a 44.43 % reduction in computational time while maintaining machining precision. The formation mechanism of undercuts in dental restoration structures was systematically analyzed. Based on this analysis, a surface formation prediction algorithm was established to accurately identify undercut areas in cavity regions after machining. This enables the implementation of localized overcut strategies to replace conventional global undercut approaches, thereby improving the fitting accuracy and stability of dental restorations. The wear characteristics of ball-end grinding wheels were investigated, with particular focus on the relationship between spiral trajectory spacing and tool wear. In undercut regions, the machining allowance was observed to significantly affect cutting depth, leading to increased grinding forces and accelerated tool wear. To mitigate this effect, a localized spacing reduction strategy was proposed, which effectively minimizes tool wear while only slightly increasing machining time. The effectiveness of the proposed methodology was verified through precision grinding experiments on complex dental restoration structures. These methods have the potential to be applied to a wide range of complex 3D machining and manufacturing problems.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 103993"},"PeriodicalIF":3.1,"publicationDate":"2025-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145334756","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 : 2025-10-13DOI: 10.1016/j.cad.2025.103990
Yu-Chou Chiang , Hui Wang , Xinye Li , Helmut Pottmann
A self-Airy membrane shell is a special type of shell structure whose shape coincides with the shell’s Airy stress surface. It provides the convenient property that any polyhedral discretization of such a surface will automatically generate a mesh in funicular equilibrium. A self-Airy shell designed for a uniform vertical load would simply have a constant isotropic Gaussian curvature. However, a challenge in implementing a self-Airy shell in architecture is the lack of a design method, especially in designing unreinforced boundaries. Those are singular planar curves, where the two principal curvatures approach 0 and individually. This paper presents methods for designing unreinforced boundaries of self-Airy shells, including both smooth and discrete methods. These methods work for both positively and negatively curved surfaces. The proposed methods work linearly without iteration. The preliminary results show that the seemingly very restrictive conditions admit a variety of non-trivial surfaces.
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