Computer Aided Geometric Design最新文献

{"title":"On a nonlinear version of Lane-Riesenfeld's subdivision schemes converging to piecewise smooth functions preserving high regularity","authors":"Sergio Amat ,&nbsp;Sonia Busquier ,&nbsp;David Levin ,&nbsp;Juan Ruiz ,&nbsp;Dionisio F. Yáñez","doi":"10.1016/j.cagd.2025.102485","DOIUrl":"10.1016/j.cagd.2025.102485","url":null,"abstract":"<div><div>Lane-Riesenfeld's subdivision schemes provide a versatile tool for generating smooth and detailed curves and surfaces, making them valuable assets in computer graphics and geometric modeling. These schemes offer flexibility in controlling the regularity of the limit function by adjusting some parameters. In this paper, we propose a nonlinear modification of these algorithms for piecewise smooth functions. The new algorithm converges to piecewise smooth limit functions maintaining the high regularity of Lane-Riesenfeld's subdivision schemes in smooth zones. The practical results presented show a very good numerical behavior of the proposed algorithms.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"122 ","pages":"Article 102485"},"PeriodicalIF":1.7,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145109104","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":"The cubic de Casteljau construction and some classes of cubic curves on Riemannian manifolds","authors":"Erchuan Zhang ,&nbsp;Lyle Noakes","doi":"10.1016/j.cagd.2025.102478","DOIUrl":"10.1016/j.cagd.2025.102478","url":null,"abstract":"<div><div>The interpolation of data by curves in non-Euclidean spaces is important for trajectory planning, quantum computing and image registration. In particular, Riemannian cubics, Jupp and Kent cubics and Riemanninan cubics in tension are frequently used for Hermite interpolation. Except in very few cases, these curves cannot be given in closed form, which limits their applicability. The classical de Casteljau construction of cubic polynomials in Euclidean space has been generalized to Riemannian manifolds, where line segments are replaced by geodesic arcs on manifold. The authors (<span><span>Zhang and Noakes, 2019a</span></span>) showed that generalized cubic de Casteljau curves, can approximate Riemannian cubics quite closely, with error bounded by a 4th order curvature term. Motivated by that work, the present paper aims to analyze the quality of the generalized cubic de Casteljau curves approximating Jupp and Kent cubics, and Riemannian cubics in tension. We also modify the generalized de Casteljau algorithm to construct curves that are closer to Jupp and Kent cubics, and to Riemannian cubics in tension. We illustrate our theoretical results by numerical experiments on cubic curves in the 2-dimensional unit sphere <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and also in the special orthogonal group <span><math><mrow><mi>SO</mi></mrow><mo>(</mo><mn>3</mn><mo>)</mo></math></span>.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"121 ","pages":"Article 102478"},"PeriodicalIF":1.7,"publicationDate":"2025-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887037","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":"Euler's elastica and curvature based nonlinear mesh denoising method","authors":"Huayan Zhang ,&nbsp;Xingzhi Xie ,&nbsp;Yupeng Wang ,&nbsp;Xiaochao Wang","doi":"10.1016/j.cagd.2025.102477","DOIUrl":"10.1016/j.cagd.2025.102477","url":null,"abstract":"<div><div>In the paper, we extend a new nonlinear variational model based on the general Euler's elastica and curvature for triangulated surfaces. The new model intrinsically combines the gradient operator and the curvature operator in a multiplicative manner. By introducing the total variation norm restricted to triangles, we discretize the Euler's elastica and curvature model on triangulated surface into the triangle-based and edge-based formulations, respectively. A two-stage mesh denoising method is proposed using the general Euler's elastica and curvature model: first filtering the facet normals based on the Euler's elastica and curvature model and then updating the vertex positions. Through an efficient relaxation, the nonlinear and non-differentiable optimization problem is solved iteratively based on the operator splitting and alternating direction method of multipliers (ADMM). The proposed denoising method is evaluated in terms of parameters sensitivity, quantitative comparisons with several state-of-the-art techniques, and computational costs. Numerical experiments confirm that our approach produces competitive results when compared to several existing denoising algorithms at reasonable costs. It achieves promising results by preserving sharper features, restoring more details and structures, and alleviating the staircase effect (false edges). Moreover, the quantitative errors further verify that the proposed algorithm is robust numerically.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"121 ","pages":"Article 102477"},"PeriodicalIF":1.7,"publicationDate":"2025-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810230","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":"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}