Computer Aided Geometric Design最新文献

Approximation properties over self-similar meshes of curved finite elements and applications to subdivision based isogeometric analysis

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2025-02-01 DOI: 10.1016/j.cagd.2025.102413

Thomas Takacs

{"title":"Approximation properties over self-similar meshes of curved finite elements and applications to subdivision based isogeometric analysis","authors":"Thomas Takacs","doi":"10.1016/j.cagd.2025.102413","DOIUrl":"10.1016/j.cagd.2025.102413","url":null,"abstract":"<div><div>In this study we consider domains that are composed of an infinite sequence of self-similar rings and corresponding finite element spaces over those domains. The rings are parameterized using piecewise polynomial or tensor-product B-spline mappings of degree <em>q</em> over quadrilateral meshes. We then consider finite element discretizations which, over each ring, are mapped, piecewise polynomial functions of degree <em>p</em>. Such domains that are composed of self-similar rings may be created through a subdivision scheme or from a scaled boundary parameterization.</div><div>We study approximation properties over such recursively parameterized domains. The main finding is that, for generic isoparametric discretizations (i.e., where <span><math><mi>p</mi><mo>=</mo><mi>q</mi></math></span>), the approximation properties always depend only on the degree of polynomials that can be reproduced exactly in the physical domain and not on the degree <em>p</em> of the mapped elements. Especially, in general, <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-errors converge at most with the rate <span><math><msup><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, where <em>h</em> is the mesh size, independent of the degree <span><math><mi>p</mi><mo>=</mo><mi>q</mi></math></span>. This has implications for subdivision based isogeometric analysis, which we will discuss in this paper.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"116 ","pages":"Article 102413"},"PeriodicalIF":1.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143402940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A novel heterogeneous deformable surface model based on elasticity 基于弹性的新型异质可变形表面模型

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-11-13 DOI: 10.1016/j.cagd.2024.102402

Ciyang Zhou, Xingce Wang, Zhongke Wu

{"title":"A novel heterogeneous deformable surface model based on elasticity","authors":"Ciyang Zhou, Xingce Wang, Zhongke Wu","doi":"10.1016/j.cagd.2024.102402","DOIUrl":"10.1016/j.cagd.2024.102402","url":null,"abstract":"<div><div>The thin membranes and shells in nature are heterogeneous. They are widely used in surgical simulation, biological techniques, and computer animation. The corresponding surface deformable models can implement dynamic simulations of thin membranes and shells in nature, while most surface deformable models are isotropic and cannot represent thin membranes and shells in nature accurately. Therefore, we propose a novel physically-based heterogeneous deformable surface model. By utilizing the same B-spline basis functions or the parameter space of surfaces' geometric representations, we implement material modeling and propose the representations of surfaces with material variations with composite or continuous material functions. Then, we propose a novel physically-based elastic deformable surface model that constructs infinitesimal elements in the parameter space and employs elasticity to analyze their deformation. The corresponding elastic potential energy function is only related to surfaces' continuous representations, and our model avoids the computation error caused by meshes' quality and large rotation of points' frames. We employ isogeometric analysis to solve the dynamic equations derived from our surface model. To demonstrate the validity and reality of our model, several comparison experiments are designed. The corresponding results are in line with expectations and consistent with physical laws.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"115 ","pages":"Article 102402"},"PeriodicalIF":1.3,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704183","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}

引用次数: 0

Optimal one-sided approximants of circular arc 圆弧的最佳单边近似值

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-11-12 DOI: 10.1016/j.cagd.2024.102401

Ada Šadl Praprotnik , Aleš Vavpetič , Emil Žagar

引用次数: 0

Build orientation optimization considering thermal distortion in additive manufacturing 在考虑热变形的情况下优化增材制造的构建方向

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-10-18 DOI: 10.1016/j.cagd.2024.102393

Weiming Wang , Shan Li , Li Yang , Jiepeng Liu , Yi Xia , Ligang Liu

{"title":"Build orientation optimization considering thermal distortion in additive manufacturing","authors":"Weiming Wang , Shan Li , Li Yang , Jiepeng Liu , Yi Xia , Ligang Liu","doi":"10.1016/j.cagd.2024.102393","DOIUrl":"10.1016/j.cagd.2024.102393","url":null,"abstract":"<div><div>Additive manufacturing (AM) technology enables the fabrication of three-dimensional objects with complex shapes and has been extensively applied in various industries. AM is a layer-wise fabrication process where a variety of factors affect manufacturing performance and product quality. One of the most important factor is the thermal distortion, which is caused by the high temperature gradients in the fabrication process. The thermal distortion is also influenced by the support structure of the printing object, and this distortion varies depending on the chosen build orientation. Additionally, for the overhang regions, extra supports are required for printing and will be removed in the post-processing. For the 3D printing process, the thermal distortion and support requirements are interconnected and linked to build orientation. To investigate suitable build orientation, the thermal distortion and support are quantified, and a multi-objective build orientation optimization method is proposed to obtain representative orientations. Based on the proposed method, 9 typical 3D shapes are evaluated. In addition, the single-objective build orientation optimization problem is studied and compared, and the influence of slicing layers per stage on the simulation accuracy and efficiency is discussed. The effectiveness and applicability of the method are verified, and representative directions can be obtained for different fabrication purposes.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"114 ","pages":"Article 102393"},"PeriodicalIF":1.3,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527859","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}

引用次数: 0

Algorithms and data structures for Cs-smooth RMB-splines of degree 2s + 1 阶数为 2s + 1 的 Cs 平滑人民币样条函数的算法和数据结构

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-10-17 DOI: 10.1016/j.cagd.2024.102389

Maodong Pan , Ruijie Zou , Bert Jüttler

{"title":"Algorithms and data structures for Cs-smooth RMB-splines of degree 2s + 1","authors":"Maodong Pan , Ruijie Zou , Bert Jüttler","doi":"10.1016/j.cagd.2024.102389","DOIUrl":"10.1016/j.cagd.2024.102389","url":null,"abstract":"<div><div>The simple mesh refinement algorithm of <span><span>Groiss et al. (2023)</span></span> generates T-meshes admitting Reachable Minimally supported (RM) B-splines that possess the property of local linear independence and form a non-negative partition of unity. The construction was first presented for the bilinear case and has later been extended to <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>s</mi></mrow></msup></math></span>-smooth splines of degree <span><math><mi>p</mi><mo>=</mo><mn>2</mn><mi>s</mi><mo>+</mo><mn>1</mn></math></span>. The present paper is devoted to algorithms and data structures for RMB-splines. We prove that the memory consumption of the data structures for representing a T-mesh and the associated RMB-splines is linear with respect to the mesh size, and we describe the details of the underlying refinement algorithm. Moreover, we introduce a novel evaluation algorithm for RMB-spline surfaces, which is based solely on repeated convex combinations of the control points, thereby generalizing de Boor's algorithm for tensor-product splines. Numerical experiments are included to demonstrate the advantageous behavior of the proposed data structures and algorithms with respect to their efficiency. We observe that the total computational time (which includes also error estimation and spline coefficient computation) scales roughly linearly with the number of degrees of freedom for the meshes considered.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"114 ","pages":"Article 102389"},"PeriodicalIF":1.3,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142527955","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}

引用次数: 0

Efficient object recognition under cluttered scenes via descriptor-based matching and single point voting 通过基于描述符的匹配和单点表决实现杂乱场景下的高效物体识别

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-10-16 DOI: 10.1016/j.cagd.2024.102394

Xiaoge He , Yuanpeng Liu , Jun Zhou , Yuqi Zhang , Jun Wang

{"title":"Efficient object recognition under cluttered scenes via descriptor-based matching and single point voting","authors":"Xiaoge He , Yuanpeng Liu , Jun Zhou , Yuqi Zhang , Jun Wang","doi":"10.1016/j.cagd.2024.102394","DOIUrl":"10.1016/j.cagd.2024.102394","url":null,"abstract":"<div><div>This paper addresses the problem of recognizing multiple objects and multiple instances from point clouds. Whereas existing methods utilize descriptors on 3D fields or pointwise voting to achieve this task, our framework takes advantage of both descriptor-based and voting-based schemes to realize more robust and efficient prediction. Specifically, we propose a novel and robust descriptor called an orientation-enhanced fast point feature histogram (OE-FPFH) to describe points in both the object model and scene, and further to build the correspondence set. The OE-FPFH integrates an orientation vector through mining the geometric tensor of the local structure of a surface point, which is more representative than the original FPFH descriptor. To improve voting efficiency, we devise a novel single-point voting mechanism (SPVM), which constructs a unique local reference frame (LRF) on a single point using the orientation vector. The SPVM takes as input the corresponding point set and can generate a pose candidate for each correspondence. The process is realized by matching LRFs from two corresponding points. All pose candidates are subsequently divided into clusters and aggregated using the <em>K</em>-means clustering algorithm to deduce the poses for different objects or instances in the scene. Experiments on three challenging datasets demonstrate that our method is effective, efficient, and robust to occlusions and multiple instances.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"114 ","pages":"Article 102394"},"PeriodicalIF":1.3,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442502","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}

引用次数: 0

Curvature continuous corner cutting 曲率连续切角

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-10-15 DOI: 10.1016/j.cagd.2024.102392

Kai Hormann , Claudio Mancinelli

引用次数: 0

GeoHi-GNN: Geometry-aware hierarchical graph representation learning for normal estimation GeoHi-GNN：用于正态估计的几何感知分层图表示学习

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-10-09 DOI: 10.1016/j.cagd.2024.102390

Nannan Li , Xinyuan Li , Jun Zhou , Dong Jiang , Jian Liu , Hong Qin

{"title":"GeoHi-GNN: Geometry-aware hierarchical graph representation learning for normal estimation","authors":"Nannan Li , Xinyuan Li , Jun Zhou , Dong Jiang , Jian Liu , Hong Qin","doi":"10.1016/j.cagd.2024.102390","DOIUrl":"10.1016/j.cagd.2024.102390","url":null,"abstract":"<div><div>Normal estimation has been one of the key tasks in point cloud analysis, while it is challenging when facing with severe noises or complex regions. The challenges mainly come from the selection of supporting points for estimation, that is, improper selections of points and points' scale will lead to insufficient information, loss of details, etc. To this end, this paper proposes one feature-centric fitting scheme, GeoHi-GNN, by learning geometry-aware hierarchical graph representation for fitting weights estimation. The main functional module is the continuously conducted Hierarchically Geometric-aware (HG) module, consisting of two core operations, namely, the graph node construction (GNC) and the geometric-aware dynamic graph convolution (GDGC). GNC aims to aggregate the feature information onto a smaller number of nodes, providing global-to-local information while avoiding the interferences from noises in larger scales. With these nodes distributed in different scales, GDGC dynamically updates the node features regarding to both intrinsic feature and extrinsic geometric information. Finally, the hierarchical graphical features are cascaded to estimate the weights for supporting points in the surface fitting. Through the extensive experiments and comprehensive comparisons with the state-of-the-arts, our scheme has exhibited many attractive advantages such as being geometry-aware and robust, empowering further applications like more accurate surface reconstruction.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"114 ","pages":"Article 102390"},"PeriodicalIF":1.3,"publicationDate":"2024-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142432316","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}

引用次数: 0

Computing properties of subdivision schemes using small real Fourier indexed matrices 利用小实数傅里叶索引矩阵计算细分方案的特性

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-09-24 DOI: 10.1016/j.cagd.2024.102391

Cédric Gérot , Loïc Barthe , Neil A. Dodgson , Malcolm A. Sabin

{"title":"Computing properties of subdivision schemes using small real Fourier indexed matrices","authors":"Cédric Gérot , Loïc Barthe , Neil A. Dodgson , Malcolm A. Sabin","doi":"10.1016/j.cagd.2024.102391","DOIUrl":"10.1016/j.cagd.2024.102391","url":null,"abstract":"<div><div>The quality of a subdivision scheme in the vicinity of a vertex or a face-centre is related to the eigenstructure of the subdivision matrix. When the scheme has the appropriate symmetries, a common technique, based on discrete Fourier transform, builds small complex matrices that ease the numerical analysis of the eigenelements using in particular their Fourier index. But the numerical analysis of the eigenelements remains difficult when matrix entries involve complex numbers and unknowns, for example, in cases where we are tuning a scheme. We present techniques to build similar small matrices, still associated with a Fourier index and whose eigenstructure is simply related to the full matrix, but which are real. They extend the known techniques to schemes which rotate the lattice and with vertices which do not lie topologically on symmetry axes of the studied vicinity of vertex or face centre. Our techniques make it easier to tune these subdivision schemes. We illustrate it with the analysis of the so-called Simplest Scheme at the centre of an <em>n</em>-sided face.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"114 ","pages":"Article 102391"},"PeriodicalIF":1.3,"publicationDate":"2024-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142426603","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}

引用次数: 0

Computing the cut locus, Voronoi diagram, and signed distance function of polygons 计算多边形的切割位置、沃罗诺图和符号距离函数

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2024-09-18 DOI: 10.1016/j.cagd.2024.102388

Csaba Bálint, Róbert Bán, Gábor Valasek

引用次数: 0