Computer Aided Geometric Design最新文献

{"title":"Discrete Gaussian free field methods for random curve shape generation","authors":"Wenzhong Zhang","doi":"10.1016/j.cagd.2025.102469","DOIUrl":"10.1016/j.cagd.2025.102469","url":null,"abstract":"<div><div>We study the one-dimensional discrete Gaussian free field (DGFF) and DGFF based methods for sampling random 2-dimensional curves with fixed ends, including a direct sampling method that prioritizes shape variety and does not require existing data, and a data-driven diffusion model for sampling from an empirical distribution of curve shapes. We test the proposed methods in shape optimization problems, including a 2-dimensional random airfoil shape sampling problem, assuming minimal physical knowledge is known.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"121 ","pages":"Article 102469"},"PeriodicalIF":1.3,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sibson's formula for higher order Voronoi diagrams","authors":"Mercè Claverol ,&nbsp;Andrea de las Heras-Parrilla ,&nbsp;Clemens Huemer ,&nbsp;Dolores Lara","doi":"10.1016/j.cagd.2025.102470","DOIUrl":"10.1016/j.cagd.2025.102470","url":null,"abstract":"<div><div>Let <em>S</em> be a set of <em>n</em> points in general position in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>. The order-<em>k</em> Voronoi diagram of <em>S</em>, <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo></math></span>, is a subdivision of <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> into cells whose points have the same <em>k</em> nearest points of <em>S</em>. Sibson, in his seminal paper from 1980 (A vector identity for the Dirichlet tessellation), gives a formula to express a point <em>Q</em> of <em>S</em> as a convex combination of other points of <em>S</em> using ratios of volumes of the intersection of cells of <span><math><msub><mrow><mi>V</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo></math></span> and the cell of <em>Q</em> in <span><math><msub><mrow><mi>V</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>S</mi><mo>)</mo></math></span>. The natural neighbour interpolation method is based on Sibson's formula. We generalize his result to express <em>Q</em> as a convex combination of other points of <em>S</em> by using ratios of volumes from Voronoi diagrams of any given order.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"121 ","pages":"Article 102470"},"PeriodicalIF":1.3,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144653234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Log-aesthetic curves and generalized Archimedean spirals","authors":"Péter Salvi","doi":"10.1016/j.cagd.2025.102468","DOIUrl":"10.1016/j.cagd.2025.102468","url":null,"abstract":"<div><div>We show that the radials of log-aesthetic curves are generalized Archimedean spirals. Examining the logarithmic curvature histogram reveals that these radials have an inherent similarity to the associated log-aesthetic curves, and can also be used as computationally inexpensive approximants. Different kinds of fits are proposed and discussed through examples. A possible generalization of log-aesthetic curves based on generalized Archimedean spirals is also explored.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"121 ","pages":"Article 102468"},"PeriodicalIF":1.3,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144534813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Paul de Faget de Casteljau, a pioneer in CAGD","authors":"Carolina Vittoria Beccari ,&nbsp;Kai Hormann ,&nbsp;Christophe Rabut ,&nbsp;Wenping Wang","doi":"10.1016/j.cagd.2025.102431","DOIUrl":"10.1016/j.cagd.2025.102431","url":null,"abstract":"","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"119 ","pages":"Article 102431"},"PeriodicalIF":1.3,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144221348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A multilevel feature-based method for mapping sparse point clouds to CAD models","authors":"Youlong Zeng ,&nbsp;Haiyan Sun ,&nbsp;Xiaobin Li ,&nbsp;Zhuoyi Chen","doi":"10.1016/j.cagd.2025.102457","DOIUrl":"10.1016/j.cagd.2025.102457","url":null,"abstract":"<div><div>Accurate mapping of sparse point clouds to CAD models is becoming increasingly crucial in fields such as digital twinning, 3D reconstruction, and engineering design. However, the sparsity and irregularity of point cloud data obtained through LiDAR scanning pose significant challenges to feature mapping precision and seamless integration with CAD models. Traditional methods struggle to maintain accurate mapping, especially when dealing with complex point cloud scenes or sparse data. These methods have significant limitations in accurately mapping sparse point clouds to solid models. To address these challenges, this paper introduces a multilevel feature mapping method that thoroughly analyzes the geometric features of both CAD models and point cloud data, significantly improving feature matching accuracy. In CAD model processing, the Geometric Feature Signature (GFS) mapping function is used to achieve high-precision geometric morphology descriptions through comprehensive extraction of geometric feature quantities. For point cloud data processing, Dense Domain Filtering (DDF) is employed to optimize the spatial distribution, minimizing the impact of noise and redundant data. Combined with Density-Controlled Geometric Consistent Feature Extraction (DC-GCFE), this method achieves accurate key feature point extraction from sparse point clouds by analyzing geometric feature quantities comprehensively. By efficiently matching the CAD model's geometric features with the point cloud's local and global features, the proposed multilevel feature mapping method ensures precise mapping even in sparse and complex point cloud environments, offering strong support for virtual simulation and design optimization. In comparison with traditional methods, this approach excels at capturing complex details and handling missing features. Finally, experimental validation confirms the method's high matching accuracy and robustness in complex scenes, verifying its effectiveness in precisely mapping sparse point clouds to CAD models.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"120 ","pages":"Article 102457"},"PeriodicalIF":1.3,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144169290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geodesic distance approximation using a surface finite element method for the p-Laplacian","authors":"Hannah Potgieter,&nbsp;Razvan C. Fetecau,&nbsp;Steven J. Ruuth","doi":"10.1016/j.cagd.2025.102458","DOIUrl":"10.1016/j.cagd.2025.102458","url":null,"abstract":"<div><div>We use the <em>p</em>-Laplacian with large <em>p</em>-values in order to approximate geodesic distances to features on surfaces. This differs from Fayolle and Belyaev's (<span><span>2018</span></span>) computational results using the <em>p</em>-Laplacian for the <em>distance-to-surface</em> problem. Our approach appears to offer some distinct advantages over other popular PDE-based distance function approximation methods. We employ a surface finite element scheme and demonstrate numerical convergence to the true geodesic distance functions. We check that our numerical results adhere to the triangle inequality and examine robustness against geometric noise such as vertex perturbations. We also present comparisons of our method with the heat method from <span><span>Crane et al. (2017)</span></span> and the classical polyhedral method from <span><span>Mitchell et al. (1987)</span></span>.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"120 ","pages":"Article 102458"},"PeriodicalIF":1.3,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144138330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ParaValve: An open source framework for parametric design and fluid–structure interaction simulation of bioprosthetic heart valves in patient-specific aortic geometries","authors":"Mehdi Saraeian,&nbsp;Ashton M. Corpuz,&nbsp;Ming-Chen Hsu,&nbsp;Adarsh Krishnamurthy","doi":"10.1016/j.cagd.2025.102455","DOIUrl":"10.1016/j.cagd.2025.102455","url":null,"abstract":"<div><div>Heart valve disease (HVD), a significant cardiovascular complication, is one of the leading global causes of morbidity and mortality. Treatment for HVD often involves medical devices such as bioprosthetic valves. However, the design and optimization of these devices require a thorough understanding of their biomechanical and hemodynamic interactions with patient-specific anatomical structures. Parametric procedural geometry has become a powerful tool in enhancing the efficiency and accuracy of design optimization for such devices, allowing researchers to systematically explore a wide range of possible configurations. In this work, we present a robust framework for parametric and procedural modeling of stented bioprosthetic heart valves and patient-specific aortic geometries. The framework employs non-uniform rational B-splines (NURBS)-based geometric parameterization, enabling precise control over key anatomical and design variables. By enabling a modular and expandable workflow, the framework supports iterative optimization of valve designs to achieve improved hemodynamic performance and durability. We demonstrate its applicability through simulations on bioprosthetic aortic valves, highlighting the impact of geometric parameters on valve function and their potential for personalized device design. By coupling parametric geometry with computational tools, this framework offers researchers and engineers a streamlined pathway toward innovative and patient-specific cardiovascular solutions.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"120 ","pages":"Article 102455"},"PeriodicalIF":1.3,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Detail-preserving shape completion of point cloud models with articulated structure","authors":"Yi Quan ,&nbsp;Chen Li ,&nbsp;Yang Li ,&nbsp;Changbo Wang ,&nbsp;Hong Qin","doi":"10.1016/j.cagd.2025.102456","DOIUrl":"10.1016/j.cagd.2025.102456","url":null,"abstract":"<div><div>This paper advocates a novel deep-learning-based method for point cloud completion of multi-categorical articulated objects sharing the same topology. One popular approach for point cloud completion is to rely on a generic encoder-decoder architecture, where the feature maps of input are extracted with the critical set, which essentially consists of a set of points that play critical roles in the max-pooled features. But this pipeline has difficulties in retaining the local details, especially for arbitrary deformable, articulated objects of various categories, bringing category confused completion. In this paper, we propose a detail-preserving point cloud completion method for the complex articulated models by extracting features guided by their articulation topology with a fixed-order scheme, so as to accommodate both fine-grained categorical appearance and non-rigid deformation. First, we construct key subsets, which preserve both local, category-aware and global, non-rigid deformation features simultaneously for input sharing similar point densities, guided by a set of regressed key points approximating articulations. Second, we organize the key subsets with a fixed-order scheme during feature extraction to combat the possible interference due to diverse data component permutations during feature extraction, while upholding the algorithmic efficiency. Finally, we confirm in our evaluations that the new method completes general articulated point clouds with detailed categorical characteristics in high quality. We also show that after training on synthetic data, our method can be applied to real scan or web downloaded point clouds with similar point densities. Meanwhile, we built an Quadruped Point Cloud Completion (QPCC) dataset upon which new research topics could be further explored in geometry modeling and computer graphics.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"120 ","pages":"Article 102456"},"PeriodicalIF":1.3,"publicationDate":"2025-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144116509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"3D shape analysis via multi-modal contrastive learning","authors":"Zhenyu Shu ,&nbsp;Xufei Sun ,&nbsp;Chaoyi Pang","doi":"10.1016/j.cagd.2025.102454","DOIUrl":"10.1016/j.cagd.2025.102454","url":null,"abstract":"<div><div>In recent years, 3D shape analysis has emerged as a crucial field with applications in various domains, such as multimedia processing, computer graphics, computer vision, and robotics. The ability to understand and interpret 3D shapes is fundamental for tasks like 3D shape segmentation, points of interest detection, shape retrieval, recognition, and generation. However, the complexity of 3D mesh models is a significant barrier that stops the topic from enhancing. Thus, we propose a novel 3D shape analysis framework in this paper by multi-modal contrastive learning techniques. Our framework makes use of the original mesh data and the projected images from various points of view of the mesh model. Those two modals contribute to providing more precise features with the help of our within-modal and cross-modal losses, which respectively calculate the distances of feature vectors within the mesh model and between feature vectors of mesh and image. Our framework is tested on downstream tasks, including 3D shape segmentation and points of interest detection, and outperforms most state-of-the-art methods on public datasets.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"119 ","pages":"Article 102454"},"PeriodicalIF":1.3,"publicationDate":"2025-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143904466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A dynamic arrangement framework for automatic tooth alignment based on orthodontic rules","authors":"Yeying Fan ,&nbsp;Guangshun Wei ,&nbsp;Weijie Liu ,&nbsp;Chuanxiang Yang ,&nbsp;Chuanyun Fu ,&nbsp;Wenping Wang ,&nbsp;Yuanfeng Zhou","doi":"10.1016/j.cagd.2025.102436","DOIUrl":"10.1016/j.cagd.2025.102436","url":null,"abstract":"<div><div>Automatically achieving functionally and aesthetically aligned teeth is a critical task in computer-aided orthodontic treatment. However, existing expert rule-based approaches still require manual intervention and focus solely on occlusion functionality. Meanwhile, data-driven methods rely on large paired datasets of pre- and post-treatment cases, making it challenging to address issues such as missing teeth or collisions effectively. To alleviate these problems, this paper proposes a novel framework <em>DyOrthoAlign</em> that translates the automatic tooth alignment into a dynamic arrangement process based on orthodontic rules. Our <em>DyOrthoAlign</em> consists of two stages. We first construct the ideal dental occlusion curve based on tooth anatomical features. Then, we arrange each tooth along the ideal occlusion curve in a specific order and a series of decisions. The dynamic arrangement process continues until all the teeth are arranged, resulting in the final ideal tooth arrangement. Extensive qualitative and quantitative experiments validate our framework can produce ideal tooth alignment and offer significant practical value for personalized and efficient orthodontic treatment.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"119 ","pages":"Article 102436"},"PeriodicalIF":1.3,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143899298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}