Pub Date : 2026-02-01Epub 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":"2026-02-01","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 : 2026-02-01Epub 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":"2026-02-01","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 : 2026-02-01Epub 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":"2026-02-01","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 : 2026-02-01Epub 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":"2026-02-01","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 : 2026-02-01Epub 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":"2026-02-01","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 : 2026-02-01Epub 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":"2026-02-01","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 : 2026-02-01Epub 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":"2026-02-01","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 : 2026-02-01Epub Date: 2025-11-20DOI: 10.1016/j.cad.2025.104008
Yan Zhao , Qingyue Liu , Yinglei Wei
Origami patterns enable the transformation of two-dimensional flat sheet materials into three-dimensional target surfaces through folding. However, existing origami patterns exhibit limitations in both diversity and performance when applied to inverse design problems. In this paper, we focus on a novel Kresling variant pattern and demonstrate its flexibility in approximating target surfaces with freeform shapes and varying curvatures. Given a standard Kresling pattern, the upper and lower edges of each unit are expanded into four small triangles to obtain the Kresling variant pattern. This variant pattern inherits the developability and flat-foldability of the original Kresling pattern while providing more flexibility for inverse design. We then tile the partially folded Kresling variant pattern onto the target surface and solve the inverse-origami-design problem through optimization. In the optimization process, unknown variables can be selected and residuals of origami geometric constraints can be eliminated without relaxation. In addition, we demonstrate that origami approximations are capable of fitting between two target surfaces with or without developability. To improve mesh quality, we incorporate additional constraints on the aspect ratio and area of each triangular facet. These constraints supplement the origami geometric constraints for improving the regularity and stability of the final approximations. Paper fabrications and folding simulations confirm the validity and flexibility of our approach. Our work reveals the potential of the Kresling variant pattern for inverse origami design and opens up novel avenues for applications across diverse fields, including architecture, aerospace, and robotics.
{"title":"Novel Kresling variant patterns for inverse origami design","authors":"Yan Zhao , Qingyue Liu , Yinglei Wei","doi":"10.1016/j.cad.2025.104008","DOIUrl":"10.1016/j.cad.2025.104008","url":null,"abstract":"<div><div>Origami patterns enable the transformation of two-dimensional flat sheet materials into three-dimensional target surfaces through folding. However, existing origami patterns exhibit limitations in both diversity and performance when applied to inverse design problems. In this paper, we focus on a novel Kresling variant pattern and demonstrate its flexibility in approximating target surfaces with freeform shapes and varying curvatures. Given a standard Kresling pattern, the upper and lower edges of each unit are expanded into four small triangles to obtain the Kresling variant pattern. This variant pattern inherits the developability and flat-foldability of the original Kresling pattern while providing more flexibility for inverse design. We then tile the partially folded Kresling variant pattern onto the target surface and solve the inverse-origami-design problem through optimization. In the optimization process, unknown variables can be selected and residuals of origami geometric constraints can be eliminated without relaxation. In addition, we demonstrate that origami approximations are capable of fitting between two target surfaces with or without developability. To improve mesh quality, we incorporate additional constraints on the aspect ratio and area of each triangular facet. These constraints supplement the origami geometric constraints for improving the regularity and stability of the final approximations. Paper fabrications and folding simulations confirm the validity and flexibility of our approach. Our work reveals the potential of the Kresling variant pattern for inverse origami design and opens up novel avenues for applications across diverse fields, including architecture, aerospace, and robotics.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 104008"},"PeriodicalIF":3.1,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579685","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 : 2026-02-01Epub 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.
{"title":"Designing self-Airy shells with unreinforced boundaries","authors":"Yu-Chou Chiang , Hui Wang , Xinye Li , Helmut Pottmann","doi":"10.1016/j.cad.2025.103990","DOIUrl":"10.1016/j.cad.2025.103990","url":null,"abstract":"<div><div>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 <em>isotropic</em> 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 <span><math><mi>∞</mi></math></span> 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.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 103990"},"PeriodicalIF":3.1,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145290009","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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