Pub Date : 2025-09-26DOI: 10.1016/j.cad.2025.103979
Shoichi Tsuchie
This paper proposes a novel measure based on curvature variation to evaluate the fairness of curves. It is demonstrated that, in the simplest case, controlling the curvature using the proposed measure results in the log-aesthetic curve (LAC). In other words, by utilizing the proposed measure as a novel shape parameter, a unified framework can be established for aesthetic curves that accommodates a broader range of curvature variations, encompassing the LAC as a special case. Several examples are presented to illustrate curve evaluation using the proposed measure, along with its application to the approximation of aesthetic curves. The findings of this study offer a new perspective for understanding and evaluating the geometric properties of curves, with potential applications in curve design, analysis, and fairing.
{"title":"A new measure of fairness for curves","authors":"Shoichi Tsuchie","doi":"10.1016/j.cad.2025.103979","DOIUrl":"10.1016/j.cad.2025.103979","url":null,"abstract":"<div><div>This paper proposes a novel measure based on curvature variation to evaluate the fairness of curves. It is demonstrated that, in the simplest case, controlling the curvature using the proposed measure results in the log-aesthetic curve (LAC). In other words, by utilizing the proposed measure as a novel shape parameter, a unified framework can be established for aesthetic curves that accommodates a broader range of curvature variations, encompassing the LAC as a special case. Several examples are presented to illustrate curve evaluation using the proposed measure, along with its application to the approximation of aesthetic curves. The findings of this study offer a new perspective for understanding and evaluating the geometric properties of curves, with potential applications in curve design, analysis, and fairing.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103979"},"PeriodicalIF":3.1,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-26DOI: 10.1016/j.cad.2025.103976
Jie Zhou , Yong Zhao , Fan Zhong
Few-shot point cloud segmentation aims to accurately decompose 3D point clouds into different semantic classes with few samples, and is crucial for subsequent tasks, such as analysis, modeling and editing. Despite the popularity of prototype-based approaches, prototypes often fail to adequately capture class-specific information. Therefore, for each class, a few points may exhibit significant differences from their prototype. And the lack of sufficient distinction between foreground and background prototypes presents a great challenge for precise segmentation. To address these issues, we propose a prototype optimization module to mitigate the interference among support prototypes, thereby generating prototypes of superior quality. These refined prototypes are capable of capturing the key characteristics of the data, which can prominently improve the generalization capability of our model. Then, we devise a self-training strategy that leverages pseudo query prototypes generated from high-confidence predicted labels. These prototypes are applied to query features to produce pseudo query labels and formulate a reconstruction constraint during training. By harnessing the contextual information embedded within query features, this approach significantly elevates segmentation performance. Extensive results on two popular benchmark datasets validate the superiority of our model, especially in the challenging 1-shot settings. Under the classic experimental setup, our method surpasses existing state-of-the-arts by 2.64% in 2-way 1-shot setting on the S3DIS dataset. On the ScanNet dataset, the improvements are 7.58% in 2-way 1-shot setting and 6.44% in 3-way 1-shot setting, respectively.
{"title":"Prototype optimization and self-training for few-shot 3D point cloud semantic segmentation","authors":"Jie Zhou , Yong Zhao , Fan Zhong","doi":"10.1016/j.cad.2025.103976","DOIUrl":"10.1016/j.cad.2025.103976","url":null,"abstract":"<div><div>Few-shot point cloud segmentation aims to accurately decompose 3D point clouds into different semantic classes with few samples, and is crucial for subsequent tasks, such as analysis, modeling and editing. Despite the popularity of prototype-based approaches, prototypes often fail to adequately capture class-specific information. Therefore, for each class, a few points may exhibit significant differences from their prototype. And the lack of sufficient distinction between foreground and background prototypes presents a great challenge for precise segmentation. To address these issues, we propose a prototype optimization module to mitigate the interference among support prototypes, thereby generating prototypes of superior quality. These refined prototypes are capable of capturing the key characteristics of the data, which can prominently improve the generalization capability of our model. Then, we devise a self-training strategy that leverages pseudo query prototypes generated from high-confidence predicted labels. These prototypes are applied to query features to produce pseudo query labels and formulate a reconstruction constraint during training. By harnessing the contextual information embedded within query features, this approach significantly elevates segmentation performance. Extensive results on two popular benchmark datasets validate the superiority of our model, especially in the challenging 1-shot settings. Under the classic experimental setup, our method surpasses existing state-of-the-arts by 2.64% in 2-way 1-shot setting on the S3DIS dataset. On the ScanNet dataset, the improvements are 7.58% in 2-way 1-shot setting and 6.44% in 3-way 1-shot setting, respectively.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103976"},"PeriodicalIF":3.1,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145269538","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}
Gaps are prevalent defects in triangular meshes, often arising from various sources such as surface scanning and CAD model generation. Despite their significance, the automatic repair of complex gaps has received limited attention compared to other mesh imperfections. This study presents a novel surface-based gap-closing method for triangular mesh repair, leveraging both local geometric and topological characteristics to robustly match and merge gap boundaries. The proposed approach first employs a global–local vertex merging procedure with adaptive tolerances to eliminate duplicate vertices and simplify complex gaps. Subsequently, gaps are identified and classified into connected and disconnected types based on their topological and geometric features. For each detected gap, a non-iterative closing procedure is applied, simultaneously matching and merging all boundary vertices. An adaptive scheme is introduced to determine the geometric tolerance for vertex matching, ensuring the effective preservation of the original geometric shape. Extensive numerical experiments on a large dataset of discrete models demonstrate the effectiveness and robustness of the proposed method in closing both connected and disconnected gaps.
{"title":"Adaptive gap closing for complex triangular mesh repair using geometric and topological characteristics","authors":"Shuwei Shen , Shuai Zhou , Zhoufang Xiao , Jingchen Gao , Chenhao Xu","doi":"10.1016/j.cad.2025.103981","DOIUrl":"10.1016/j.cad.2025.103981","url":null,"abstract":"<div><div>Gaps are prevalent defects in triangular meshes, often arising from various sources such as surface scanning and CAD model generation. Despite their significance, the automatic repair of complex gaps has received limited attention compared to other mesh imperfections. This study presents a novel surface-based gap-closing method for triangular mesh repair, leveraging both local geometric and topological characteristics to robustly match and merge gap boundaries. The proposed approach first employs a global–local vertex merging procedure with adaptive tolerances to eliminate duplicate vertices and simplify complex gaps. Subsequently, gaps are identified and classified into connected and disconnected types based on their topological and geometric features. For each detected gap, a non-iterative closing procedure is applied, simultaneously matching and merging all boundary vertices. An adaptive scheme is introduced to determine the geometric tolerance for vertex matching, ensuring the effective preservation of the original geometric shape. Extensive numerical experiments on a large dataset of discrete models demonstrate the effectiveness and robustness of the proposed method in closing both connected and disconnected gaps.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103981"},"PeriodicalIF":3.1,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-25DOI: 10.1016/j.cad.2025.103980
Chang Yu, Sanguo Zhang, Li-Yong Shen
Non-rigid point cloud registration is an important problem in computer vision and graphics, aiming to find the warping function between deformed point clouds. In this paper, we propose CORNet, a consistency-based outlier rejection network for non-rigid registration. By leveraging the local geometric structure and probability distribution of point clouds, we obtain local spatial consistency and Gaussian probabilistic consistency. We then employ the Transformer mechanism, combined with consistency information, to classify inliers and outliers in correspondences, ultimately obtaining high-quality correspondences for non-rigid registration. Ablation studies validate the effectiveness of our method, and extensive experiments demonstrate that our method achieves state-of-the-art performance.
{"title":"CORNet: A Consistency-based Outlier Rejection Network for non-rigid registration","authors":"Chang Yu, Sanguo Zhang, Li-Yong Shen","doi":"10.1016/j.cad.2025.103980","DOIUrl":"10.1016/j.cad.2025.103980","url":null,"abstract":"<div><div>Non-rigid point cloud registration is an important problem in computer vision and graphics, aiming to find the warping function between deformed point clouds. In this paper, we propose CORNet, a consistency-based outlier rejection network for non-rigid registration. By leveraging the local geometric structure and probability distribution of point clouds, we obtain local spatial consistency and Gaussian probabilistic consistency. We then employ the Transformer mechanism, combined with consistency information, to classify inliers and outliers in correspondences, ultimately obtaining high-quality correspondences for non-rigid registration. Ablation studies validate the effectiveness of our method, and extensive experiments demonstrate that our method achieves state-of-the-art performance.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103980"},"PeriodicalIF":3.1,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-22DOI: 10.1016/j.cad.2025.103982
Zhong Tian, Xu Xubing
This study presents a novel framework for real-time cloth wrinkle detection and optimisation, combining physics-based modelling with LSTM-Reinforcement Learning (LSTM-RL) and advanced computer vision techniques. A curated dataset of 45,876 annotated static garment images was used, featuring wrinkle attributes such as location, depth, width, and geometry. CNNs were employed for feature extraction, enhanced by Mask R-CNN to handle occlusions and RGBD data for depth-aware wrinkle modelling. A mass-spring system simulated fabric dynamics under environmental forces, while LSTM networks predicted the temporal evolution of wrinkles. Reinforcement learning dynamically adjusted fabric parameters, improving adaptability. The proposed RGBD model achieved a wrinkle detection accuracy of 96.4 %, outperforming the 2D model by over 9 %. Key metrics include an MSE of 0.0246, drift of 0.0187, and a reward value of -0.13543, with low policy and value loss confirming the RL agent’s learning stability. These results demonstrate high accuracy, real-time performance, and robustness, with strong implications for virtual fashion, robotics, and AR/VR applications.
{"title":"Research on dynamic simulation and optimization of garment wrinkles combining computer vision and image processing","authors":"Zhong Tian, Xu Xubing","doi":"10.1016/j.cad.2025.103982","DOIUrl":"10.1016/j.cad.2025.103982","url":null,"abstract":"<div><div>This study presents a novel framework for real-time cloth wrinkle detection and optimisation, combining physics-based modelling with LSTM-Reinforcement Learning (LSTM-RL) and advanced computer vision techniques. A curated dataset of 45,876 annotated static garment images was used, featuring wrinkle attributes such as location, depth, width, and geometry. CNNs were employed for feature extraction, enhanced by Mask R-CNN to handle occlusions and RGBD data for depth-aware wrinkle modelling. A mass-spring system simulated fabric dynamics under environmental forces, while LSTM networks predicted the temporal evolution of wrinkles. Reinforcement learning dynamically adjusted fabric parameters, improving adaptability. The proposed RGBD model achieved a wrinkle detection accuracy of 96.4 %, outperforming the 2D model by over 9 %. Key metrics include an MSE of 0.0246, drift of 0.0187, and a reward value of -0.13543, with low policy and value loss confirming the RL agent’s learning stability. These results demonstrate high accuracy, real-time performance, and robustness, with strong implications for virtual fashion, robotics, and AR/VR applications.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103982"},"PeriodicalIF":3.1,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145222448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-22DOI: 10.1016/j.cad.2025.103965
Li Ye , Xinhang Zhou , Peng Fan , Ruofeng Tong , Hailong Li , Peng Du , Min Tang
This paper addresses the challenge of efficiently abstracting mid-surfaces from complex variable thin-walled models, a critical task in computer-aided design (CAD) and finite element analysis (FEA) for simplifying thin-walled structures. Traditional methods often require manual specification of pairing faces, which can be time-consuming and error-prone. Alternatively, automatic face pairing methods fail to meet the actual needs of variable thin-walled models, resulting in the accumulation of topological errors. Additionally, existing algorithms struggle to extract mid-surfaces from models with varying wall thickness or produce mid-surfaces with poor accuracy, leading to geometric errors. Furthermore, the computational efficiency of these methods is often inadequate for large-scale models. To overcome these challenges, we propose an automated face-pairing mechanism that eliminates the need for manual intervention, enhancing the algorithm’s robustness and enabling it to handle cases that the commercial CAD modeling engine, Parasolid, cannot process. Our approach accurately processes variable thin-walled models, with results closely aligning with the ground truth, as demonstrated by the provided error distribution tables. Moreover, our algorithm achieves a times improvement in efficiency than previous methods over the geometry extraction stage and supports multi-threaded acceleration, significantly reducing computation time. Experimental results demonstrate that our algorithm surpasses existing methods in both accuracy and efficiency, offering a promising solution for mid-surface extraction in complex, variable thin-walled models.
{"title":"MidSurfer: Efficient Mid-Surface Abstraction from Variable Thin-Walled Models","authors":"Li Ye , Xinhang Zhou , Peng Fan , Ruofeng Tong , Hailong Li , Peng Du , Min Tang","doi":"10.1016/j.cad.2025.103965","DOIUrl":"10.1016/j.cad.2025.103965","url":null,"abstract":"<div><div>This paper addresses the challenge of efficiently abstracting mid-surfaces from complex variable thin-walled models, a critical task in computer-aided design (CAD) and finite element analysis (FEA) for simplifying thin-walled structures. Traditional methods often require manual specification of pairing faces, which can be time-consuming and error-prone. Alternatively, automatic face pairing methods fail to meet the actual needs of variable thin-walled models, resulting in the accumulation of topological errors. Additionally, existing algorithms struggle to extract mid-surfaces from models with varying wall thickness or produce mid-surfaces with poor accuracy, leading to geometric errors. Furthermore, the computational efficiency of these methods is often inadequate for large-scale models. To overcome these challenges, we propose an automated face-pairing mechanism that eliminates the need for manual intervention, enhancing the algorithm’s robustness and enabling it to handle cases that the commercial CAD modeling engine, Parasolid, cannot process. Our approach accurately processes variable thin-walled models, with results closely aligning with the ground truth, as demonstrated by the provided error distribution tables. Moreover, our algorithm achieves a <span><math><mrow><mn>4</mn><mo>−</mo><mn>12</mn></mrow></math></span> times improvement in efficiency than previous methods over the geometry extraction stage and supports multi-threaded acceleration, significantly reducing computation time. Experimental results demonstrate that our algorithm surpasses existing methods in both accuracy and efficiency, offering a promising solution for mid-surface extraction in complex, variable thin-walled models.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103965"},"PeriodicalIF":3.1,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159994","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-22DOI: 10.1016/j.cad.2025.103970
Chaoyun Wang , Jianlei Wang , Chengcheng Tang , Nanning Zheng , Caigui Jiang
This paper introduces an interactive design method for developable surfaces, centered on a data-driven approach to optimize surface patches for developability. Surface patches are the fundamental components of an entire surface, typically represented by triangular meshes. We propose a novel learning-based method that effectively transforms patches with arbitrary boundaries into their closest developable surfaces. Based on this method, our tools enable real-time, drag-and-drop design of developable surfaces and support piecewise developable approximation through interactive inputs. Experimental results demonstrate that this method provides a fast computational foundation for the interactive design of developable surfaces, enhancing design flexibility while exhibiting excellent robustness and generalization. The piecewise developable approximation of the model, guided by human–computer collaborative segmentation, achieved higher overall approximation accuracy, fewer patches, and lifelike papercraft outcomes. This offers greater flexibility to meet the application requirements of complex real-world scenarios and provides a new paradigm for integrating deep learning with interactive geometry design.
{"title":"Interactive design of developable surfaces by patch-based learning","authors":"Chaoyun Wang , Jianlei Wang , Chengcheng Tang , Nanning Zheng , Caigui Jiang","doi":"10.1016/j.cad.2025.103970","DOIUrl":"10.1016/j.cad.2025.103970","url":null,"abstract":"<div><div>This paper introduces an interactive design method for developable surfaces, centered on a data-driven approach to optimize surface patches for developability. Surface patches are the fundamental components of an entire surface, typically represented by triangular meshes. We propose a novel learning-based method that effectively transforms patches with arbitrary boundaries into their closest developable surfaces. Based on this method, our tools enable real-time, drag-and-drop design of developable surfaces and support piecewise developable approximation through interactive inputs. Experimental results demonstrate that this method provides a fast computational foundation for the interactive design of developable surfaces, enhancing design flexibility while exhibiting excellent robustness and generalization. The piecewise developable approximation of the model, guided by human–computer collaborative segmentation, achieved higher overall approximation accuracy, fewer patches, and lifelike papercraft outcomes. This offers greater flexibility to meet the application requirements of complex real-world scenarios and provides a new paradigm for integrating deep learning with interactive geometry design.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103970"},"PeriodicalIF":3.1,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-20DOI: 10.1016/j.cad.2025.103967
Pablo Antolin , Michael Bartoň , Georges-Pierre Bonneau , Annalisa Buffa , Amaia Calleja-Ochoa , Gershon Elber , Stefanie Elgeti , Gaizka Gómez Escudero , Alicia Gonzalez , Haizea González Barrio , Stefanie Hahmann , Thibaut Hirschler , Q Youn Hong , Konstantin Key , Myung-Soo Kim , Michael Kofler , Norberto Lopez de Lacalle , Silvia de la Maza , Kanika Rajain , Jacques Zwar
With the evolution of new manufacturing technologies such as multi-material 3D printing, one can think of new type of objects that consist of considerably less, yet heterogeneous, material, consequently being porous, lighter and cheaper, while having the very same functionality as the original object when manufactured from one single solid material. We aim at questioning five decades of traditional paradigms in geometric CAD and focus at new generation of CAD objects that are not solid, but contain heterogeneous free-form internal microstructures. We propose a unified manufacturing pipeline that involves all stages, namely design, optimization, manufacturing, and inspection of microstructured free-form geometries. We demonstrate our pipeline on an industrial test case of a blisk blade that sustains the desired pressure limits, yet requires significantly less material when compared to the solid counterpart.
{"title":"On design, analysis, and hybrid manufacturing of microstructured blade-like geometries","authors":"Pablo Antolin , Michael Bartoň , Georges-Pierre Bonneau , Annalisa Buffa , Amaia Calleja-Ochoa , Gershon Elber , Stefanie Elgeti , Gaizka Gómez Escudero , Alicia Gonzalez , Haizea González Barrio , Stefanie Hahmann , Thibaut Hirschler , Q Youn Hong , Konstantin Key , Myung-Soo Kim , Michael Kofler , Norberto Lopez de Lacalle , Silvia de la Maza , Kanika Rajain , Jacques Zwar","doi":"10.1016/j.cad.2025.103967","DOIUrl":"10.1016/j.cad.2025.103967","url":null,"abstract":"<div><div>With the evolution of new manufacturing technologies such as multi-material 3D printing, one can think of new type of objects that consist of considerably less, yet heterogeneous, material, consequently being porous, lighter and cheaper, while having the very same functionality as the original object when manufactured from one single solid material. We aim at questioning five decades of traditional paradigms in geometric CAD and focus at new generation of CAD objects that are not solid, but contain heterogeneous free-form internal microstructures. We propose a unified manufacturing pipeline that involves all stages, namely design, optimization, manufacturing, and inspection of microstructured free-form geometries. We demonstrate our pipeline on an industrial test case of a blisk blade that sustains the desired pressure limits, yet requires significantly less material when compared to the solid counterpart.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103967"},"PeriodicalIF":3.1,"publicationDate":"2025-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120121","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}
This paper proposes a novel approach for computing planar quadrilateral meshes complying with sizing prescriptions on boundary and feature curves. The method relies on computing integrable orthogonal frame fields, whose symmetries are implicitly represented using orthogonally decomposable (odeco) tensors. To formulate an integrability criterion, we express the frame field’s Lie bracket solely in terms of the tensor representation; this is made possible by studying the sensitivity of the frame with respect to perturbations in the tensor. We construct an energy formulation that computes smooth and integrable frame fields in both isotropic and anisotropic settings. The solver creates and places the singularities required to fit the sizing constraints with the correct topology. The computed frame field is integrated to a seamless parametrization that is aligned with the frame field, and we propose a mesh extraction method that relies on a greedy quantization of the parametrization.
{"title":"Size-controlled quadrilateral meshing using integrable odeco fields","authors":"Mattéo Couplet , Alexandre Chemin , Jean-François Remacle","doi":"10.1016/j.cad.2025.103974","DOIUrl":"10.1016/j.cad.2025.103974","url":null,"abstract":"<div><div>This paper proposes a novel approach for computing planar quadrilateral meshes complying with sizing prescriptions on boundary and feature curves. The method relies on computing <em>integrable</em> orthogonal frame fields, whose symmetries are implicitly represented using orthogonally decomposable (<em>odeco</em>) tensors. To formulate an integrability criterion, we express the frame field’s Lie bracket solely in terms of the tensor representation; this is made possible by studying the sensitivity of the frame with respect to perturbations in the tensor. We construct an energy formulation that computes smooth and integrable frame fields in both isotropic and anisotropic settings. The solver creates and places the singularities required to fit the sizing constraints with the correct topology. The computed frame field is integrated to a seamless parametrization that is aligned with the frame field, and we propose a mesh extraction method that relies on a greedy quantization of the parametrization.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103974"},"PeriodicalIF":3.1,"publicationDate":"2025-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145159993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-09-18DOI: 10.1016/j.cad.2025.103963
Taoran Liu , Hongfei Ye , Xiangqiao Meng , Zhiwei Liu , Jianjun Chen
Triangle meshes frequently exhibit defects such as self-intersections and low-quality elements. Existing intersection resolution methods either lack robustness due to floating-point inaccuracies or incur high computational costs by processing meshes globally. We propose a robust and efficient method for repairing meshes with intersecting triangles that combines localized processing with rational number computations. The core challenge we address is converting exact intersection repair results to stable floating-point representation without reintroducing intersections. Our solution embeds intersecting regions into tetrahedral meshes for constrained optimization, naturally preventing surface intersections during the conversion process. Our approach begins with a preprocessing step that refines the mesh and localizes intersection issues by separating intersecting and intersection-free regions. For each intersecting region, we ensure the robustness of intersection calculations by using rational numbers. Subsequently, the intersection repair results are stably converted from rational to floating-point representation using a constrained boundary tetrahedral mesh optimization method. The repaired local meshes are then stitched back into the intersection-free mesh, followed by a remeshing step to enhance overall mesh quality. Experimental results on complex models demonstrate that our method significantly reduces computational overhead while producing high-quality, intersection-free meshes suitable for downstream applications.
{"title":"Robust and fast local repair for intersecting triangle meshes","authors":"Taoran Liu , Hongfei Ye , Xiangqiao Meng , Zhiwei Liu , Jianjun Chen","doi":"10.1016/j.cad.2025.103963","DOIUrl":"10.1016/j.cad.2025.103963","url":null,"abstract":"<div><div>Triangle meshes frequently exhibit defects such as self-intersections and low-quality elements. Existing intersection resolution methods either lack robustness due to floating-point inaccuracies or incur high computational costs by processing meshes globally. We propose a robust and efficient method for repairing meshes with intersecting triangles that combines localized processing with rational number computations. The core challenge we address is converting exact intersection repair results to stable floating-point representation without reintroducing intersections. Our solution embeds intersecting regions into tetrahedral meshes for constrained optimization, naturally preventing surface intersections during the conversion process. Our approach begins with a preprocessing step that refines the mesh and localizes intersection issues by separating intersecting and intersection-free regions. For each intersecting region, we ensure the robustness of intersection calculations by using rational numbers. Subsequently, the intersection repair results are stably converted from rational to floating-point representation using a constrained boundary tetrahedral mesh optimization method. The repaired local meshes are then stitched back into the intersection-free mesh, followed by a remeshing step to enhance overall mesh quality. Experimental results on complex models demonstrate that our method significantly reduces computational overhead while producing high-quality, intersection-free meshes suitable for downstream applications.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"190 ","pages":"Article 103963"},"PeriodicalIF":3.1,"publicationDate":"2025-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160125","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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