Computer Aided Geometric Design最新文献_第3页

Transfinite barycentric coordinates for arbitrary planar domains 任意平面域的超有限质心坐标

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2025-04-23 DOI: 10.1016/j.cagd.2025.102433

Qingjun Chang, Kai Hormann

{"title":"Transfinite barycentric coordinates for arbitrary planar domains","authors":"Qingjun Chang, Kai Hormann","doi":"10.1016/j.cagd.2025.102433","DOIUrl":"10.1016/j.cagd.2025.102433","url":null,"abstract":"<div><div>Generalized barycentric coordinates provide a simple way of interpolating data given at the vertices of a polygon or polyhedron, with widespread applications in computer graphics, geometry processing, and other fields. Transfinite barycentric coordinates, also known as barycentric kernels, extend this idea to curved domains and can be used to interpolate continuous data given on the boundary of such domains. We present a novel framework for defining non-negative barycentric kernels over arbitrary bounded planar domains. This framework is inspired by the construction of a transfinite version of maximum likelihood coordinates and can be used to define a variety of barycentric kernels, including a simple pseudo-harmonic kernel and a non-negative variant of the mean value kernel. Moreover, we propose a novel barycentric kernel which yields transfinite interpolants that are similar to harmonic interpolants. We tested our new kernel for domains and boundary data described by closed uniform quadratic splines and in particular for image deformation. The results indicate that our method has several advantages over alternative approaches.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"119 ","pages":"Article 102433"},"PeriodicalIF":1.3,"publicationDate":"2025-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868337","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

MTSegNet: Manifold Transformer for 3D shape segmentation MTSegNet：用于3D形状分割的歧管变压器

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2025-04-22 DOI: 10.1016/j.cagd.2025.102440

Zhenyu Shu , Zhichao Zhang , Yiming Zhao , Teng Wu

{"title":"MTSegNet: Manifold Transformer for 3D shape segmentation","authors":"Zhenyu Shu , Zhichao Zhang , Yiming Zhao , Teng Wu","doi":"10.1016/j.cagd.2025.102440","DOIUrl":"10.1016/j.cagd.2025.102440","url":null,"abstract":"<div><div>The semantic segmentation of 3D meshes is a critical component of 3D shape analysis, which involves assigning semantic labels to each face of a 3D mesh. Despite its significance, current methods often struggle to capture manifold information in 3D meshes, a fundamental characteristic distinguishing them from other representation forms of 3D data, like 3D point clouds or 3D voxels, resulting in suboptimal segmentation outcomes. In this paper, we propose a novel Transformer-based approach, Manifold Transformer (MTSegNet), for 3D mesh semantic segmentation, which effectively learns manifold information. By using hierarchical Transformers, MTSegNet can capture both local and global features of 3D meshes, while reducing the computational complexity and memory consumption. To further improve the performance of our method, we design an effective input-generating algorithm that serializes input data into multiple sequences of tokens that represent the geometry and topology of 3D meshes. This algorithm preserves the structural information and spatial relations of 3D meshes, while enabling the use of standard Transformer architectures. The proposed method is evaluated on four benchmark datasets: PSB, COSEG, ShapeNetCore, and HumanBody, and it achieves state-of-the-art results on all datasets, outperforming the previous methods.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"119 ","pages":"Article 102440"},"PeriodicalIF":1.3,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143894411","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 worst-case topology optimization of self-supporting structures for additive manufacturing 增材制造自支撑结构的高效最坏情况拓扑优化

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2025-04-22 DOI: 10.1016/j.cagd.2025.102441

Nan Zheng, Xiaoya Zhai, Falai Chen

{"title":"Efficient worst-case topology optimization of self-supporting structures for additive manufacturing","authors":"Nan Zheng, Xiaoya Zhai, Falai Chen","doi":"10.1016/j.cagd.2025.102441","DOIUrl":"10.1016/j.cagd.2025.102441","url":null,"abstract":"<div><div>In worst-case topology optimization, uncertain loads can result in complex internal structures and intricate printed details that challenge manufacturability. However, the impact of these features on manufacturing performance is often overlooked, potentially compromising the printability and quality of the final product in additive manufacturing (AM). This paper introduces a novel approach for generating 3D self-supporting structures under worst-case topology optimization. The proposed framework utilizes an implicit tensor-product B-spline (ITPBS) representation, directly adopting its coefficients as design variables to minimize compliance while enforcing self-supporting constraints and minimal length scale. By reformulating AM constraints, we analytically derive a single geometric fabrication constraint that simultaneously addresses both overhang regions and the dripping effect. The solid-void boundary representation provided by ITPBS enables seamless integration of fabrication constraints into the worst-case optimization process. Worst-case compliance is evaluated by solving an eigenvalue problem, and sensitivity analysis is conducted using the adjoint variable method. Numerical experiments demonstrate that the proposed approach effectively produces self-supporting structures across various models.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"119 ","pages":"Article 102441"},"PeriodicalIF":1.3,"publicationDate":"2025-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143868338","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

On the triple-parameter least squares progressive iterative approximation and its convergence analysis 三参数最小二乘渐进迭代逼近及其收敛性分析

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2025-04-17 DOI: 10.1016/j.cagd.2025.102439

Nian-Ci Wu , Chengzhi Liu , Juncheng Li

{"title":"On the triple-parameter least squares progressive iterative approximation and its convergence analysis","authors":"Nian-Ci Wu , Chengzhi Liu , Juncheng Li","doi":"10.1016/j.cagd.2025.102439","DOIUrl":"10.1016/j.cagd.2025.102439","url":null,"abstract":"<div><div>In the domain of large-scale data fitting, the least squares progressive iterative approximation (LSPIA) method, introduced by <span><span>Deng and Lin (2014)</span></span>, stands as a prominent figure in geometric iterative techniques due to its simplicity and effectiveness. Herein, we incorporate a triple-parameter modification to fine-tune the control points, hereby denoted as the TLSPIA method. Opting for a suitable parameter within the TLSPIA framework reverts it to the traditional LSPIA and its variant, such as PmLSPIA proposed by <span><span>Liu et al. (2024)</span></span>. Through singular value decomposition of the collocation matrix, we derive closed forms for the error sequences generated by the LSPIA, PmLSPIA, and TLSPIA methods, demonstrating that these sequences exhibit linear decrease and diverge in their convergence rates across different subspaces corresponding to any right singular vector of the collocation matrix. Empirical numerical examples are provided to substantiate our theoretical claims, highlighting the practical viability and efficacy of the proposed algorithm.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"119 ","pages":"Article 102439"},"PeriodicalIF":1.3,"publicationDate":"2025-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143860258","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

ESA-GS: Elongation splitting and assimilation in Gaussian splatting for accurate surface reconstruction ESA-GS：用于精确表面重建的高斯溅射中的伸长分裂和同化

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2025-04-17 DOI: 10.1016/j.cagd.2025.102434

Yuyang Chen, Wenming Wu, Yusheng Peng, Yue Fei, Liping Zheng

引用次数: 0

Topology guaranteed and error controlled curve tracing for parametric surface-surface intersection 参数曲面相交的拓扑保证和误差控制曲线跟踪

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2025-04-11 DOI: 10.1016/j.cagd.2025.102432

Bingwei Zhang , Jin-San Cheng , Yu-Shen Liu , Zhaoqi Zhang

引用次数: 0

A shift-invariant C12-subdivision algorithm which rotates the lattice 一个平移不变的c12细分算法，它旋转晶格

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2025-03-18 DOI: 10.1016/j.cagd.2025.102430

Cédric Gérot , Malcolm A. Sabin

引用次数: 0

RBF-MAT: Computing medial axis transform from point clouds by optimizing radial basis functions RBF-MAT：通过优化径向基函数计算点云的中轴变换

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2025-03-04 DOI: 10.1016/j.cagd.2025.102421

Mengyuan Ge , Junfeng Yao , Baorong Yang , Ningna Wang , Zhonggui Chen , Xiaohu Guo

{"title":"RBF-MAT: Computing medial axis transform from point clouds by optimizing radial basis functions","authors":"Mengyuan Ge , Junfeng Yao , Baorong Yang , Ningna Wang , Zhonggui Chen , Xiaohu Guo","doi":"10.1016/j.cagd.2025.102421","DOIUrl":"10.1016/j.cagd.2025.102421","url":null,"abstract":"<div><div>In this paper, we present a simple yet effective method RBF-MAT, for computing medial axis transform (MAT) from point cloud using radial basis functions (RBFs), where the surface is represented as the zero-level set of an interpolating function composed of a linear combination of RBFs. Firstly, we propose a new strategy for selecting the initial medial spheres based on the Voronoi vertices computed from the input points while preserving necessary geometric characteristics. Then the centers and radii of the generated medial spheres are iteratively optimized by minimizing the RBF-based surface reconstruction error. Additionally, the connectivity of the refined medial spheres is constructed as the dual of the restricted power diagram for these spheres. Experimental results across diverse 3D shapes demonstrate our method's efficacy in capturing global structural attributes and local geometric intricacies, with our connectivity approach surpassing existing methods. Besides, the experimental results show that the MATs computed with our method better approximate the point cloud surface than state-of-the-art methods.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"118 ","pages":"Article 102421"},"PeriodicalIF":1.3,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143563232","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

Infinity branches and asymptotic analysis of algebraic space curves: New techniques and applications 代数空间曲线的无穷分支与渐近分析：新技术与应用

IF 1.3 4区计算机科学

Computer Aided Geometric Design Pub Date : 2025-03-01 DOI: 10.1016/j.cagd.2025.102422

Sonia Pérez-Díaz , Li-Yong Shen , Xin-Yu Wang , R. Magdalena-Benedicto

{"title":"Infinity branches and asymptotic analysis of algebraic space curves: New techniques and applications","authors":"Sonia Pérez-Díaz , Li-Yong Shen , Xin-Yu Wang , R. Magdalena-Benedicto","doi":"10.1016/j.cagd.2025.102422","DOIUrl":"10.1016/j.cagd.2025.102422","url":null,"abstract":"<div><div>Let <span><math><mi>C</mi></math></span> represent an irreducible algebraic space curve defined by the real polynomials <span><math><msub><mrow><mi>f</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span> for <span><math><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span>. It is a recognized fact that a birational relationship invariably exists between the points on <span><math><mi>C</mi></math></span> and those on an associated irreducible plane curve, denoted as <span><math><msup><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>. In this work, we leverage this established relationship to delineate the asymptotic behavior of <span><math><mi>C</mi></math></span> by examining the asymptotes of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>. Building on this foundation, we introduce a novel and practical algorithm designed to efficiently compute the asymptotes of <span><math><mi>C</mi></math></span>, given that the asymptotes of <span><math><msub><mrow><mi>C</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span> have been ascertained.</div></div>","PeriodicalId":55226,"journal":{"name":"Computer Aided Geometric Design","volume":"117 ","pages":"Article 102422"},"PeriodicalIF":1.3,"publicationDate":"2025-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143547933","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

Approximation properties over self-similar meshes of curved finite elements and applications to subdivision based isogeometric analysis 曲面有限元自相似网格的近似性质及其在细分等几何分析中的应用

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