Pub Date : 2025-08-07DOI: 10.1016/j.cad.2025.103932
Zhihe Wu , Yaomin Wang , Zhenzhong Kuang , Jiajun Ding , Min Tan , Xuefei Yin , Yanming Zhu
Point clouds are widely used across various domains, yet their unordered and unstructured nature presents challenges for lightweight models and real-time inference. This paper introduces ViewCloud, a novel multi-view point-cloud-like representation that integrates the advantages of 2D renderings and 3D point clouds while maintaining a compact and efficient structure. Unlike conventional 3D representations, ViewCloud explicitly preserves viewpoint-specific geometric and semantic features, ensuring high information density with minimal redundancy. To construct ViewCloud, we propose an adaptive sampling strategy that extracts contour and interior pixels from multi-view 2D renderings, capturing essential shape characteristics while reducing storage overhead. We further design a ViewCloud-based multi-view feature aggregation Network, incorporating a contrastive learning-based semantic alignment Loss to enhance cross-view consistency and improve 3D recognition. Additionally, we extend ViewCloud to cross-domain retrieval, leveraging it as an intermediate representation to bridge 2D images and 3D point clouds within a shared feature space. Experiments on three benchmark datasets demonstrate that ViewCloud surpasses state-of-the-art methods in 3D recognition and cross-domain retrieval while significantly reducing storage and computational costs. These results establish ViewCloud as a scalable, efficient, and generalizable 3D representation.
{"title":"ViewCloud: A lightweight multi-view point cloud representation for efficient 3D recognition and cross-domain retrieval","authors":"Zhihe Wu , Yaomin Wang , Zhenzhong Kuang , Jiajun Ding , Min Tan , Xuefei Yin , Yanming Zhu","doi":"10.1016/j.cad.2025.103932","DOIUrl":"10.1016/j.cad.2025.103932","url":null,"abstract":"<div><div>Point clouds are widely used across various domains, yet their unordered and unstructured nature presents challenges for lightweight models and real-time inference. This paper introduces ViewCloud, a novel multi-view point-cloud-like representation that integrates the advantages of 2D renderings and 3D point clouds while maintaining a compact and efficient structure. Unlike conventional 3D representations, ViewCloud explicitly preserves viewpoint-specific geometric and semantic features, ensuring high information density with minimal redundancy. To construct ViewCloud, we propose an adaptive sampling strategy that extracts contour and interior pixels from multi-view 2D renderings, capturing essential shape characteristics while reducing storage overhead. We further design a ViewCloud-based multi-view feature aggregation Network, incorporating a contrastive learning-based semantic alignment Loss to enhance cross-view consistency and improve 3D recognition. Additionally, we extend ViewCloud to cross-domain retrieval, leveraging it as an intermediate representation to bridge 2D images and 3D point clouds within a shared feature space. Experiments on three benchmark datasets demonstrate that ViewCloud surpasses state-of-the-art methods in 3D recognition and cross-domain retrieval while significantly reducing storage and computational costs. These results establish ViewCloud as a scalable, efficient, and generalizable 3D representation.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103932"},"PeriodicalIF":3.1,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144860792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
CAD assembly models are typically represented as a collection of components, each of which can share geometric interfaces with others. In the literature, geometric interfaces have been shown to play a fundamental role in assembly model analysis, component characterization, and classification. While these interfaces are not explicitly defined in CAD models, they can be inferred from the relative positioning of components. The resulting geometric interfaces can be categorized as either interference or contact. However, it is often unclear whether these interfaces stem from intentional design choices related to component shape and function, from consistently applied relative positioning, or from unintended errors.
In industrial practice, the design of complex products often involves models sourced from public catalogs for third-party components. These catalog models frequently include shape simplifications, which can lead to unintended intersections or clearances with surrounding components — deviations that do not exist in the final physical product. This study aims to provide a comprehensive analysis and formalization of geometric interfaces, based on the complementary roles of CAD assembly modules and digital component catalogs, both widely used in industry as foundational resources for generating assembly models. The results are directly applicable to industrial CAD assembly models and can serve as a reference for CAD developers seeking to improve and extend assembly processing, as well as for researchers conducting assembly analysis.
This work introduces a formalization of geometric interfaces, including contacts, interferences, and interface envelopes, which are essential for defining component mounting requirements. An analysis of geometric interface perturbations caused by repetition operators is performed, leading to the concept of an interface envelope to model specific interface repetitions. The nominal assembly representation, presented as a reference model, facilitates the formalization of interface consistency, supporting more robust reasoning processes.
{"title":"A structured analysis of CAD assembly model interfaces for their enhanced computerized processing","authors":"Jean-Claude Léon , Flavien Boussuge , Franca Giannini , Marina Monti , Katia Lupinetti , Brigida Bonino , Jean-Philippe Pernot , Roberto Raffaeli","doi":"10.1016/j.cad.2025.103911","DOIUrl":"10.1016/j.cad.2025.103911","url":null,"abstract":"<div><div>CAD assembly models are typically represented as a collection of components, each of which can share geometric interfaces with others. In the literature, geometric interfaces have been shown to play a fundamental role in assembly model analysis, component characterization, and classification. While these interfaces are not explicitly defined in CAD models, they can be inferred from the relative positioning of components. The resulting geometric interfaces can be categorized as either interference or contact. However, it is often unclear whether these interfaces stem from intentional design choices related to component shape and function, from consistently applied relative positioning, or from unintended errors.</div><div>In industrial practice, the design of complex products often involves models sourced from public catalogs for third-party components. These catalog models frequently include shape simplifications, which can lead to unintended intersections or clearances with surrounding components — deviations that do not exist in the final physical product. This study aims to provide a comprehensive analysis and formalization of geometric interfaces, based on the complementary roles of CAD assembly modules and digital component catalogs, both widely used in industry as foundational resources for generating assembly models. The results are directly applicable to industrial CAD assembly models and can serve as a reference for CAD developers seeking to improve and extend assembly processing, as well as for researchers conducting assembly analysis.</div><div>This work introduces a formalization of geometric interfaces, including contacts, interferences, and interface envelopes, which are essential for defining component mounting requirements. An analysis of geometric interface perturbations caused by repetition operators is performed, leading to the concept of an interface envelope to model specific interface repetitions. The nominal assembly representation, presented as a reference model, facilitates the formalization of interface consistency, supporting more robust reasoning processes.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103911"},"PeriodicalIF":3.1,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144896241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-06DOI: 10.1016/j.cad.2025.103943
Junfeng Gao, Zihao Yang, Yuan Liang, Yongcun Zhang, Kangjie Liu
Inspired by natural shell-infill systems with spatially adaptive coating thicknesses (e.g., human femur bones), this paper proposes a mixed-variable topology optimization method for collaboratively designing the base topology and the adaptive coating thickness distribution of shell-infill structures. The optimization framework consists of two coupled levels. At the first level, a discrete-variable topology optimization method is employed to generate a base structure (shell and infill) with uniform coating thickness, effectively eliminating intermediate density elements to ensure a clear material interface for coating identification. At the second level, the coating size optimization is realized through density-based topology optimization combined with a novel holeless coating constraint based on a virtual temperature field. Meanwhile, to ensure manufacturability, a minimum coating thickness constraint is introduced. A density field mapping strategy further couples the two optimization levels, enabling iterative updates of both the base topology and coating thickness distribution. Three numerical examples demonstrate the effectiveness of the proposed method. The shell-infill structure with adaptive coating thickness achieves over 10 % mass reduction. Additionally, the constraints successfully eliminate unmanufacturable holes while preserving thickness continuity. Moreover, a large-scale 3D case validates the capability of the method for handling complex three-dimensional coating problems. The results highlight the potential of the method in designing bio-inspired, high-performance shell-infill structures.
{"title":"Mixed-variable topology optimization for shell-infill structures with adaptive coating thickness","authors":"Junfeng Gao, Zihao Yang, Yuan Liang, Yongcun Zhang, Kangjie Liu","doi":"10.1016/j.cad.2025.103943","DOIUrl":"10.1016/j.cad.2025.103943","url":null,"abstract":"<div><div>Inspired by natural shell-infill systems with spatially adaptive coating thicknesses (e.g., human femur bones), this paper proposes a mixed-variable topology optimization method for collaboratively designing the base topology and the adaptive coating thickness distribution of shell-infill structures. The optimization framework consists of two coupled levels. At the first level, a discrete-variable topology optimization method is employed to generate a base structure (shell and infill) with uniform coating thickness, effectively eliminating intermediate density elements to ensure a clear material interface for coating identification. At the second level, the coating size optimization is realized through density-based topology optimization combined with a novel holeless coating constraint based on a virtual temperature field. Meanwhile, to ensure manufacturability, a minimum coating thickness constraint is introduced. A density field mapping strategy further couples the two optimization levels, enabling iterative updates of both the base topology and coating thickness distribution. Three numerical examples demonstrate the effectiveness of the proposed method. The shell-infill structure with adaptive coating thickness achieves over 10 % mass reduction. Additionally, the constraints successfully eliminate unmanufacturable holes while preserving thickness continuity. Moreover, a large-scale 3D case validates the capability of the method for handling complex three-dimensional coating problems. The results highlight the potential of the method in designing bio-inspired, high-performance shell-infill structures.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103943"},"PeriodicalIF":3.1,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-06DOI: 10.1016/j.cad.2025.103944
Min Wu , Yinghui Wang , Liangyi Huang , Jinlong Yang , Wei Li , Jiaxing Shen , Xiaojuan Ning
Normal estimation for point clouds is fundamental to 3D geometric processing and applications. Despite recent advances by deep learning-based methods, effectively representing geometric structures in regions with sharp features and complex geometries remains challenging. This limitation primarily arises from the use of general architectures (e.g., CNNs, PointNet) or conventional graph convolutions, which limits the ability to capture fine geometric details in local point cloud patches. Moreover, the persistent issue of scale ambiguity in selecting optimal neighborhoods further hinders precise encoding of local structures. To address these challenges, we propose EPR-Net, a novel framework that enhances local patch representation learning for normal estimation in point clouds. Specifically, we introduce the GraphFormer module, which builds on the PoolFormer architecture to improve feature learning and incorporates graph convolution with adaptive kernels to capture geometric details across different semantic regions, thereby enabling more discriminative feature encodings. Additionally, we design the pyramid dynamic graph update (PDGU) strategy, which guides multi-scale feature aggregation through geometric weights to alleviate the scale ambiguity in neighborhood selection. PDGU also dynamically updates the local k-nearest neighbor (kNN) graph to expand the receptive field, thereby enhancing the ability of the model to extract long-range semantic information from point cloud patches. Extensive experiments are conducted on both synthetic and real-world datasets, and the qualitative and quantitative evaluations demonstrate the superiority of our method in point cloud normal estimation.
{"title":"EPR-Net: Enhanced patch representation network for point cloud normal estimation","authors":"Min Wu , Yinghui Wang , Liangyi Huang , Jinlong Yang , Wei Li , Jiaxing Shen , Xiaojuan Ning","doi":"10.1016/j.cad.2025.103944","DOIUrl":"10.1016/j.cad.2025.103944","url":null,"abstract":"<div><div>Normal estimation for point clouds is fundamental to 3D geometric processing and applications. Despite recent advances by deep learning-based methods, effectively representing geometric structures in regions with sharp features and complex geometries remains challenging. This limitation primarily arises from the use of general architectures (e.g., CNNs, PointNet) or conventional graph convolutions, which limits the ability to capture fine geometric details in local point cloud patches. Moreover, the persistent issue of scale ambiguity in selecting optimal neighborhoods further hinders precise encoding of local structures. To address these challenges, we propose EPR-Net, a novel framework that enhances local patch representation learning for normal estimation in point clouds. Specifically, we introduce the GraphFormer module, which builds on the PoolFormer architecture to improve feature learning and incorporates graph convolution with adaptive kernels to capture geometric details across different semantic regions, thereby enabling more discriminative feature encodings. Additionally, we design the pyramid dynamic graph update (PDGU) strategy, which guides multi-scale feature aggregation through geometric weights to alleviate the scale ambiguity in neighborhood selection. PDGU also dynamically updates the local k-nearest neighbor (kNN) graph to expand the receptive field, thereby enhancing the ability of the model to extract long-range semantic information from point cloud patches. Extensive experiments are conducted on both synthetic and real-world datasets, and the qualitative and quantitative evaluations demonstrate the superiority of our method in point cloud normal estimation.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103944"},"PeriodicalIF":3.1,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144842237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-06DOI: 10.1016/j.cad.2025.103928
Jun Min , Xin Li , Li-yong Shen
This paper extends the generalized NURBS representation to support local refinement via truncation hierarchical mechanism. The new representation is called truncated hierarchical GNURBS (TH-GNURBS), which provides adaptive refinement on arbitrary topological unstructured quadrilateral control mesh with non-uniform knot intervals. To construct TH-GNURBS, this paper builds the hierarchical structure and applies the truncation mechanism for highly localized refinement. During the construction, we modify TH-GNURBS basis functions to maintains the continuity around the extraordinary points (EPs). The TH-GNURBS basis functions satisfy partition of unity, everywhere except at the local region surrounding EPs. Finally, we provide a fitting algorithm to approximate an arbitrary triangle mesh with TH-GNURBS. Experimental results show that higher fitting accuracy with fewer control points via adaptive spline surface fitting.
{"title":"Truncated hierarchical GNURBS for adaptive spline surface fitting","authors":"Jun Min , Xin Li , Li-yong Shen","doi":"10.1016/j.cad.2025.103928","DOIUrl":"10.1016/j.cad.2025.103928","url":null,"abstract":"<div><div>This paper extends the generalized NURBS representation to support local refinement via truncation hierarchical mechanism. The new representation is called truncated hierarchical GNURBS (TH-GNURBS), which provides adaptive refinement on arbitrary topological unstructured quadrilateral control mesh with non-uniform knot intervals. To construct TH-GNURBS, this paper builds the hierarchical structure and applies the truncation mechanism for highly localized refinement. During the construction, we modify TH-GNURBS basis functions to maintains the continuity around the extraordinary points (EPs). The TH-GNURBS basis functions satisfy partition of unity, <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> everywhere except <span><math><msup><mrow><mi>G</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> at the local region surrounding EPs. Finally, we provide a fitting algorithm to approximate an arbitrary triangle mesh with TH-GNURBS. Experimental results show that higher fitting accuracy with fewer control points via adaptive spline surface fitting.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103928"},"PeriodicalIF":3.1,"publicationDate":"2025-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144827088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-08-05DOI: 10.1016/j.cad.2025.103941
Xiangyu Li , Dong He , Jiancheng Hao , Zhaoyu Li , Xifan Zhang , Takyu Lau , Ziyuan Zhao , Xuehan Wang , Junxue Ren , Kai Tang
Conical toroidal-end cutters are being increasingly adopted for multi-axis milling of free-form surfaces in industrial manufacturing, benefiting from their higher cutting speed and stiffness than the conventional cylindrical ball-end cutters with the same radius. Calculating the feasible space of tool axis (FSTA) for such cutters in complex environments containing free-form surface obstacles, for any given cutting contact position with its associated normal vector, is an extremely time-consuming task. The computational challenge arises because the conventional brute-force approach needs to check collision for a huge number of sampled tool axes. To address this challenge, this paper developed the state-of-the-art boundary-focused computational framework for constructing FSTA, which is featured by direct identification of characteristic points corresponding to the critical tool axes located on the check surfaces, applicable to conical toroidal-end cutters. The essential breakthrough is the derivation of geometric properties of the characteristic points for toroidal-end cutter whose head center is non-fixed and varies with tool axis. Based on these theoretical insights, a tracking-based numerical algorithm for efficiently constructing FSTA is then described. Simulation tests validate that our algorithm significantly enhances the computational efficiency while simultaneously improving the accuracy of FSTA boundary.
{"title":"A three-dimensional tracking algorithm for efficient construction of the feasible space of tool axis for a conical toroidal-end cutter in five-axis machining","authors":"Xiangyu Li , Dong He , Jiancheng Hao , Zhaoyu Li , Xifan Zhang , Takyu Lau , Ziyuan Zhao , Xuehan Wang , Junxue Ren , Kai Tang","doi":"10.1016/j.cad.2025.103941","DOIUrl":"10.1016/j.cad.2025.103941","url":null,"abstract":"<div><div>Conical toroidal-end cutters are being increasingly adopted for multi-axis milling of free-form surfaces in industrial manufacturing, benefiting from their higher cutting speed and stiffness than the conventional cylindrical ball-end cutters with the same radius. Calculating the feasible space of tool axis (FSTA) for such cutters in complex environments containing free-form surface obstacles, for any given cutting contact position with its associated normal vector, is an extremely time-consuming task. The computational challenge arises because the conventional brute-force approach needs to check collision for a huge number of sampled tool axes. To address this challenge, this paper developed the state-of-the-art boundary-focused computational framework for constructing FSTA, which is featured by direct identification of characteristic points corresponding to the critical tool axes located on the check surfaces, applicable to conical toroidal-end cutters. The essential breakthrough is the derivation of geometric properties of the characteristic points for toroidal-end cutter whose head center is non-fixed and varies with tool axis. Based on these theoretical insights, a tracking-based numerical algorithm for efficiently constructing FSTA is then described. Simulation tests validate that our algorithm significantly enhances the computational efficiency while simultaneously improving the accuracy of FSTA boundary.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"189 ","pages":"Article 103941"},"PeriodicalIF":3.1,"publicationDate":"2025-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810676","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 : 2025-07-31DOI: 10.1016/j.cad.2025.103930
Dong Xiao , Yueji Ma , Zuoqiang Shi , Shiqing Xin , Wenping Wang , Bailin Deng , Bin Wang
We propose to explore the properties of raw point clouds through the winding clearness, a concept we first introduce for measuring the clarity of the interior/exterior relationships represented by the winding number field of the point cloud. In geometric modeling, the winding number is a powerful tool for distinguishing the interior and exterior of a given surface , and it has been previously used for point normal orientation and surface reconstruction. In this work, we introduce a novel approach to evaluate and optimize the quality of point clouds based on the winding clearness. We observe that point clouds with less noise generally exhibit better winding clearness. Accordingly, we propose an objective function that quantifies the error in winding clearness, solely utilizing the coordinates of the point clouds. Moreover, we demonstrate that the winding clearness error is differentiable and can serve as a loss function in point cloud processing. We present this observation from two aspects: (1) We update the coordinates of the points by back-propagating the loss function for individual point clouds, resulting in an overall improvement without involving a neural network. (2) We incorporate winding clearness as a geometric constraint in the diffusion-based 3D generative model and update the network parameters to generate point clouds with less noise. Experimental results demonstrate the effectiveness of optimizing the winding clearness in enhancing the point cloud quality. Notably, our method exhibits superior performance in handling noisy point clouds with thin structures, highlighting the benefits of the global perspective enabled by the winding number. The source code is available at https://github.com/Submanifold/WindingClearness.
{"title":"Winding clearness for differentiable point cloud optimization","authors":"Dong Xiao , Yueji Ma , Zuoqiang Shi , Shiqing Xin , Wenping Wang , Bailin Deng , Bin Wang","doi":"10.1016/j.cad.2025.103930","DOIUrl":"10.1016/j.cad.2025.103930","url":null,"abstract":"<div><div>We propose to explore the properties of raw point clouds through the <em>winding clearness</em>, a concept we first introduce for measuring the clarity of the interior/exterior relationships represented by the winding number field of the point cloud. In geometric modeling, the winding number is a powerful tool for distinguishing the interior and exterior of a given surface <span><math><mrow><mi>∂</mi><mi>Ω</mi></mrow></math></span>, and it has been previously used for point normal orientation and surface reconstruction. In this work, we introduce a novel approach to evaluate and optimize the quality of point clouds based on the winding clearness. We observe that point clouds with less noise generally exhibit better winding clearness. Accordingly, we propose an objective function that quantifies the error in winding clearness, solely utilizing the coordinates of the point clouds. Moreover, we demonstrate that the winding clearness error is differentiable and can serve as a loss function in point cloud processing. We present this observation from two aspects: (1) We update the coordinates of the points by back-propagating the loss function for individual point clouds, resulting in an overall improvement without involving a neural network. (2) We incorporate winding clearness as a geometric constraint in the diffusion-based 3D generative model and update the network parameters to generate point clouds with less noise. Experimental results demonstrate the effectiveness of optimizing the winding clearness in enhancing the point cloud quality. Notably, our method exhibits superior performance in handling noisy point clouds with thin structures, highlighting the benefits of the global perspective enabled by the winding number. The source code is available at <span><span>https://github.com/Submanifold/WindingClearness</span><svg><path></path></svg></span>.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"188 ","pages":"Article 103930"},"PeriodicalIF":3.1,"publicationDate":"2025-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144750124","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 : 2025-07-28DOI: 10.1016/j.cad.2025.103931
Payam Khanteimouri , Marcel Campen
We describe a first method for the generation of higher-order triangle meshes in 2D with the following properties: Polynomial as well as rational elements of arbitrary order are supported, the resulting mesh is guaranteed to conform to the curved domain boundary, its elements are guaranteed to be regular, i.e. free of degeneracies and inversions, and are guaranteed to respect an adjustable lower bound on quality in terms of the scaled Jacobian metric. Previous methods support only subsets of these desirable properties. We achieve this by carefully generalizing a method proposed for the polynomial case to the more challenging rational case and analyzing its correctness.
{"title":"Guaranteed-Quality Rational Bézier Guarding","authors":"Payam Khanteimouri , Marcel Campen","doi":"10.1016/j.cad.2025.103931","DOIUrl":"10.1016/j.cad.2025.103931","url":null,"abstract":"<div><div>We describe a first method for the generation of higher-order triangle meshes in 2D with the following properties: Polynomial as well as rational elements of arbitrary order are supported, the resulting mesh is guaranteed to conform to the curved domain boundary, its elements are guaranteed to be regular, i.e. free of degeneracies and inversions, and are guaranteed to respect an adjustable lower bound on quality in terms of the scaled Jacobian metric. Previous methods support only subsets of these desirable properties. We achieve this by carefully generalizing a method proposed for the polynomial case to the more challenging rational case and analyzing its correctness.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"188 ","pages":"Article 103931"},"PeriodicalIF":3.1,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144721126","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 : 2025-07-26DOI: 10.1016/j.cad.2025.103929
Jiao Huang , Chongjun Li , Yingshi Li , Ke Liu , Jinting Xu
In CNC machining research, there is an important method to generate streamlined toolpaths based on the streamfunction and the corresponding vector field. Typically, the tensor-product B-spline method has been used to reconstruct the streamfunction, ensuring smooth continuity and global control over the generated streamlined toolpaths. However, this approach introduces redundant degrees of freedom or parameters to satisfy the topological constraints of rectangular meshes due to the lack of a local refinement algorithm, thereby reducing computational efficiency. To address this limitation, this paper proposes a method to reconstruct streamfunctions using cubic spline interpolation basis functions defined on hierarchical quadrilateral meshes with an adaptive local refinement algorithm. Meanwhile, we consider the optimization model by balancing alignment with the consistent preferred feed vector field and the fairing of toolpaths, thus obtaining streamlined toolpaths that achieve global optimization of total length, uniform scallop height distribution, and fairing. This method is significantly effective in generating toolpaths for parametric surfaces defined on polygonal parameter domains with vector fields containing local variations. The effectiveness of the proposed method is validated through three numerical examples compared with traditional approaches, including the Iso-parametric and B-spline methods.
{"title":"Streamlined toolpath planning based on adaptively hierarchical quadrilateral meshes for polygonal parametric surfaces","authors":"Jiao Huang , Chongjun Li , Yingshi Li , Ke Liu , Jinting Xu","doi":"10.1016/j.cad.2025.103929","DOIUrl":"10.1016/j.cad.2025.103929","url":null,"abstract":"<div><div>In CNC machining research, there is an important method to generate streamlined toolpaths based on the streamfunction and the corresponding vector field. Typically, the tensor-product B-spline method has been used to reconstruct the streamfunction, ensuring smooth continuity and global control over the generated streamlined toolpaths. However, this approach introduces redundant degrees of freedom or parameters to satisfy the topological constraints of rectangular meshes due to the lack of a local refinement algorithm, thereby reducing computational efficiency. To address this limitation, this paper proposes a method to reconstruct streamfunctions using cubic spline interpolation basis functions defined on hierarchical quadrilateral meshes with an adaptive local refinement algorithm. Meanwhile, we consider the optimization model by balancing alignment with the consistent preferred feed vector field and the fairing of toolpaths, thus obtaining streamlined toolpaths that achieve global optimization of total length, uniform scallop height distribution, and fairing. This method is significantly effective in generating toolpaths for parametric surfaces defined on polygonal parameter domains with vector fields containing local variations. The effectiveness of the proposed method is validated through three numerical examples compared with traditional approaches, including the Iso-parametric and B-spline methods.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"188 ","pages":"Article 103929"},"PeriodicalIF":3.0,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144713074","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 : 2025-07-23DOI: 10.1016/j.cad.2025.103927
Romain Mesnil , Kazuki Hayashi
Spectral geometry is a mathematical field that links geometrical properties to eigenvalues of differential operators on surfaces. Although it is a well-established tool in geometry processing and has been used in many contexts, the structural engineering and architectural geometry communities have not yet adopted this framework for shape modeling. This paper aims to explore spectral methods for applications in architectural geometries. A novel methodology for generating anisotropic Laplacian operators based on regions of interest defined by the user is proposed. The potential of spectral methods in structural design is illustrated through design problems expressed on meshes and graphs.
{"title":"Spectral architectural geometry","authors":"Romain Mesnil , Kazuki Hayashi","doi":"10.1016/j.cad.2025.103927","DOIUrl":"10.1016/j.cad.2025.103927","url":null,"abstract":"<div><div>Spectral geometry is a mathematical field that links geometrical properties to eigenvalues of differential operators on surfaces. Although it is a well-established tool in geometry processing and has been used in many contexts, the structural engineering and architectural geometry communities have not yet adopted this framework for shape modeling. This paper aims to explore spectral methods for applications in architectural geometries. A novel methodology for generating anisotropic Laplacian operators based on regions of interest defined by the user is proposed. The potential of spectral methods in structural design is illustrated through design problems expressed on meshes and graphs.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"188 ","pages":"Article 103927"},"PeriodicalIF":3.0,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144703399","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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