Computer Aided Geometric Design最新文献

英文中文

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 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

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

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.

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引用次数: 0

Infinity branches and asymptotic analysis of algebraic space curves: New techniques and applications

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

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

Let

C

represent an irreducible algebraic space curve defined by the real polynomials

f_{i} (x_{1}, x_{2}, x_{3})

for

i = 1, 2

. It is a recognized fact that a birational relationship invariably exists between the points on

C

and those on an associated irreducible plane curve, denoted as

C^{p}

. In this work, we leverage this established relationship to delineate the asymptotic behavior of

C

by examining the asymptotes of

C_{p}

. Building on this foundation, we introduce a novel and practical algorithm designed to efficiently compute the asymptotes of

C

, given that the asymptotes of

C_{p}

have been ascertained.

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引用次数: 0

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 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-02-01 DOI: 10.1016/j.cagd.2025.102413

Thomas Takacs

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 q over quadrilateral meshes. We then consider finite element discretizations which, over each ring, are mapped, piecewise polynomial functions of degree p. Such domains that are composed of self-similar rings may be created through a subdivision scheme or from a scaled boundary parameterization.

We study approximation properties over such recursively parameterized domains. The main finding is that, for generic isoparametric discretizations (i.e., where

p = q

), 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 p of the mapped elements. Especially, in general,

L^{\infty}

-errors converge at most with the rate

h^{2}

, where h is the mesh size, independent of the degree

p = q

. This has implications for subdivision based isogeometric analysis, which we will discuss in this paper.

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引用次数: 0

A C1 simplex-spline basis for the Alfeld split in Rs

IF 1.3 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-01-13 DOI: 10.1016/j.cagd.2025.102412

Tom Lyche , Jean-Louis Merrien , Hendrik Speleers

The Alfeld split is obtained by subdividing a simplex in

R^{s}

into

s + 1

subsimplices with the barycenter as one of their vertices. On this split, we consider the space of

C^{1}

splines of degree d (

d \geq s + 1

), for which we construct a basis of simplex-splines with knots at the barycenter and the vertices of the simplex. The basis consists of two types of simplex-splines: firstly Bernstein polynomials with domain points on the facets of the simplex and secondly certain simplex-splines with at least one knot at the barycenter. Partition of unity, Marsden-like identities, and domain points are shown. We also provide

C^{1}

smoothness conditions across a facet between two simplices.

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 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2024-11-13 DOI: 10.1016/j.cagd.2024.102402

Ciyang Zhou, Xingce Wang, Zhongke Wu

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.

自然界中的薄膜和外壳是异质的。它们被广泛应用于外科模拟、生物技术和计算机动画。相应的表面可变形模型可以对自然界中的薄膜和薄壳进行动态模拟，而大多数表面可变形模型都是各向同性的，不能准确地表现自然界中的薄膜和薄壳。因此，我们提出了一种基于物理的新型异质可变形表面模型。通过利用相同的 B 样条基函数或曲面几何表示的参数空间，我们实现了材料建模，并提出了用复合材料函数或连续材料函数表示具有材料变化的曲面。然后，我们提出了一种基于物理的新型弹性可变形曲面模型，该模型在参数空间中构建了无穷小元素，并利用弹性分析其变形。相应的弹性势能函数只与曲面的连续表示相关，我们的模型避免了因网格质量和点框架的大幅旋转造成的计算误差。我们采用等距分析法来求解由曲面模型导出的动态方程。为了证明我们模型的有效性和现实性，我们设计了几个对比实验。相应的结果符合预期，并与物理规律相一致。

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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 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2024-11-12 DOI: 10.1016/j.cagd.2024.102401

Ada Šadl Praprotnik , Aleš Vavpetič , Emil Žagar

The optimal one-sided parametric polynomial approximants of a circular arc are considered. More precisely, the approximant must be entirely in or out of the underlying circle of an arc. The natural restriction to an arc's approximants interpolating boundary points is assumed. However, the study of approximants, which additionally interpolate corresponding tangent directions and curvatures at the boundary of an arc, is also considered. Several low-degree polynomial approximants are studied in detail. When several solutions fulfilling the interpolation conditions exist, the optimal one is characterized, and a numerical algorithm for its construction is suggested. Theoretical results are demonstrated with several numerical examples and a comparison with general (i.e. non-one-sided) approximants are provided.

本文考虑了圆弧的最优单边参数多项式近似值。更确切地说，近似值必须完全在弧的底圆之内或之外。弧的近似值插值边界点的自然限制是假定的。然而，我们也考虑了对近似值的研究，这些近似值在弧的边界上插值相应的切线方向和曲率。本文详细研究了几种低度多项式近似值。当存在多个满足插值条件的解时，对最优解进行了表征，并提出了构建最优解的数值算法。通过几个数值实例证明了理论结果，并提供了与一般（即非单边）近似值的比较。

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 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

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

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.

快速成型制造（AM）技术可制造形状复杂的三维物体，已广泛应用于各行各业。AM 是一种分层制造工艺，影响制造性能和产品质量的因素很多。其中最重要的一个因素是热变形，它是由制造过程中的高温梯度引起的。热变形还受到打印对象支撑结构的影响，这种变形因所选的构建方向而异。此外，对于悬空区域，打印时需要额外的支撑，并将在后处理中去除。在三维打印过程中，热变形和支撑要求是相互关联的，并与构建方向有关。为了研究合适的构建方向，对热变形和支撑进行了量化，并提出了一种多目标构建方向优化方法，以获得具有代表性的方向。根据提出的方法，对 9 种典型的三维形状进行了评估。此外，还对单目标构建方向优化问题进行了研究和比较，并讨论了每阶段切片层数对模拟精度和效率的影响。该方法的有效性和适用性得到了验证，并可为不同的制造目的获得有代表性的方向。

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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 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2024-10-17 DOI: 10.1016/j.cagd.2024.102389

Maodong Pan , Ruijie Zou , Bert Jüttler

The simple mesh refinement algorithm of Groiss et al. (2023) 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

C^{s}

-smooth splines of degree

p = 2 s + 1

. 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.

Groiss 等人（2023 年）提出的简单网格细化算法可生成 T 型网格，允许具有局部线性独立特性的可达到最小支持（RM）B 样条，并形成非负的统一分割。该构造最初是针对双线性情况提出的，后来被扩展到 p=2s+1 度的 Cs 平滑样条曲线。本文主要介绍人民币样条曲线的算法和数据结构。我们证明了表示 T 形网格和相关人民币样条曲线的数据结构的内存消耗与网格大小呈线性关系，并描述了底层细化算法的细节。此外，我们还介绍了人民币样条曲线曲面的新型评估算法，该算法完全基于控制点的重复凸组合，从而推广了 de Boor 的张量乘积样条曲线算法。我们通过数值实验证明了所提出的数据结构和算法在效率方面的优势。我们发现，对于所考虑的网格，总计算时间（还包括误差估计和样条系数计算）与自由度数大致成线性关系。

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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 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

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

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 K-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.

本文探讨了从点云中识别多个物体和多个实例的问题。现有方法利用三维场描述符或点投票来实现这一任务，而我们的框架则同时利用基于描述符和基于投票的方案来实现更稳健、更高效的预测。具体来说，我们提出了一种名为 "方位增强快速点特征直方图"（OE-FPFH）的新型鲁棒描述符来描述物体模型和场景中的点，并进一步建立对应集。OE-FPFH 通过挖掘表面点局部结构的几何张量来整合方向向量，比原始 FPFH 描述符更具代表性。为了提高投票效率，我们设计了一种新颖的单点投票机制（SPVM），它利用方向向量在单点上构建唯一的局部参考框架（LRF）。SPVM 将对应点集作为输入，可为每个对应点生成一个姿势候选。这一过程通过匹配两个对应点的 LRF 来实现。随后，所有候选姿势都会被分成若干个簇，并使用 K-means 聚类算法进行聚合，从而推导出场景中不同物体或实例的姿势。在三个具有挑战性的数据集上进行的实验表明，我们的方法有效、高效，并且对遮挡和多实例具有鲁棒性。

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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 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2024-10-15 DOI: 10.1016/j.cagd.2024.102392

Kai Hormann , Claudio Mancinelli

Subdivision schemes are used to generate smooth curves by iteratively refining an initial control polygon. The simplest such schemes are corner cutting schemes, which specify two distinct points on each edge of the current polygon and connect them to get the refined polygon, thus cutting off the corners of the current polygon. While de Boor (1987) shows that this process always converges to a Lipschitz continuous limit curve, no matter how the points on each edge are chosen, Gregory and Qu (1996) discover that the limit curve is continuously differentiable under certain constraints. We extend these results and show that the limit curve can even be curvature continuous for specific sequences of cut ratios.

细分方案用于通过迭代细化初始控制多边形来生成平滑曲线。最简单的细分方案是切角方案，即在当前多边形的每条边上指定两个不同的点，然后将它们连接起来，得到细化多边形，从而切掉当前多边形的角。de Boor（1987 年）的研究表明，无论如何选择每条边上的点，这一过程总是收敛于一条 Lipschitz 连续的极限曲线，而 Gregory 和 Qu（1996 年）则发现，在某些约束条件下，极限曲线是连续可微的。我们扩展了这些结果，证明极限曲线甚至可以在特定的切割比序列中曲率连续。

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