Computer Aided Geometric Design最新文献

英文中文

Transferable and undefendable point cloud attacks via medial axis transform 通过中轴变换转移和不可防御的点云攻击

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2026-02-03 DOI: 10.1016/j.cagd.2026.102515

Keke Tang , Yuze Gao , Weilong Peng , Xiaofei Wang , Meie Fang , Peican Zhu

Studying adversarial attacks on point clouds is essential for evaluating and improving the robustness of 3D deep learning models. However, most existing attack methods are developed under ideal white-box settings and often suffer from limited transferability to unseen models and insufficient robustness against common defense mechanisms. In this paper, we propose MAT-Adv, a novel adversarial attack framework that enhances both transferability and undefendability by explicitly perturbing the medial axis transform (MAT) representations, in order to induce inherent adversarialness in the resulting point clouds. Specifically, we employ an autoencoder to project input point clouds into compact MAT representations that capture the intrinsic geometric structure of point clouds. By perturbing these intrinsic representations, MAT-Adv introduces structural-level adversarial characteristics that remain effective across diverse models and defense strategies. To mitigate overfitting and prevent perturbation collapse, we incorporate a dropout strategy into the optimization of MAT perturbations, further improving transferability and undefendability. Extensive experiments demonstrate that MAT-Adv significantly outperforms existing state-of-the-art methods in both transferability and undefendability.

研究点云的对抗性攻击对于评估和提高三维深度学习模型的鲁棒性至关重要。然而，大多数现有的攻击方法都是在理想的白盒设置下开发的，并且通常具有有限的可转移性和对常见防御机制的鲁棒性不足。在本文中，我们提出了一种新的对抗性攻击框架MAT- adv，它通过显式地扰动中间轴变换（MAT）表示来增强可转移性和不可防御性，从而在生成的点云中诱导固有的对抗性。具体来说，我们使用一个自动编码器将输入点云投影到紧凑的MAT表示中，以捕获点云的内在几何结构。通过干扰这些内在表征，MAT-Adv引入了结构级对抗特征，这些特征在不同的模型和防御策略中仍然有效。为了减轻过拟合和防止扰动崩溃，我们将退出策略纳入MAT扰动的优化中，进一步提高可转移性和不可防御性。大量的实验表明，MAT-Adv在可转移性和不可防御性方面明显优于现有的最先进的方法。

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引用次数: 0

UVConv: A UV grid-based convolutional neural network for classification and segmentation of 3D CAD models UVConv：一种基于UV网格的卷积神经网络，用于三维CAD模型的分类和分割

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2026-02-03 DOI: 10.1016/j.cagd.2026.102516

Zenghui Su , Jing Bai , Xiangyu Ma , Feiwei Qin

The widespread adoption of 3D CAD models in intelligent manufacturing and digital twin systems demands efficient and accurate classification and segmentation. While effective approaches typically model geometry and topology jointly using B-rep face-edge graphs, prevailing methods rely heavily on auxiliary information (e.g., supplemental geometry/semantics) to compensate for perceived shortcomings in raw B-rep data. This dependency incurs high preprocessing overhead, limits cross-platform generalization, and hinders industrial deployment. Furthermore, inherent redundancies within B-rep graphs can obscure essential semantics during encoding. To overcome these limitations, we propose UVConv, an end-to-end dual-path framework that operates exclusively on the original UV grid and face adjacency graph, eliminating auxiliary inputs. UVConv employs a serial geometry-topology processing: the geometric encoder utilizes bottleneck compression to amplify discriminative features, while the topological encoder integrates a Bidirectional Interaction Module (BIM) and an Attention Filtering Module (AFM) to extract critical structural semantics and suppress noise. Comprehensive experiments on multiple benchmark CAD datasets demonstrate that UVConv matches or surpasses state-of-the-art performance without auxiliary data, exhibiting superior representational capacity, robust generalization, and enhanced industrial deployability.

三维CAD模型在智能制造和数字孪生系统中的广泛应用要求高效、准确的分类和分割。虽然有效的方法通常是使用B-rep面边缘图联合建模几何和拓扑，但主流方法严重依赖辅助信息（例如，补充几何/语义）来弥补原始B-rep数据中的感知缺陷。这种依赖导致了很高的预处理开销，限制了跨平台的泛化，并阻碍了工业部署。此外，B-rep图中的固有冗余可能会在编码期间模糊基本语义。为了克服这些限制，我们提出了一种端到端双路径框架UVConv，它只在原始UV网格和人脸邻接图上运行，消除了辅助输入。UVConv采用串行几何-拓扑处理：几何编码器利用瓶颈压缩来放大区别特征，而拓扑编码器集成了双向交互模块（BIM）和注意过滤模块（AFM）来提取关键结构语义并抑制噪声。在多个基准CAD数据集上的综合实验表明，UVConv在没有辅助数据的情况下达到或超过了最先进的性能，表现出卓越的表征能力、稳健的泛化能力和增强的工业可部署性。

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引用次数: 0

A quaternion approach to G2 Hermite interpolation by quintic spatial Pythagorean-hodograph curves 用五次空间毕达哥拉斯曲线求G2 Hermite插值的四元数方法

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-12-05 DOI: 10.1016/j.cagd.2025.102505

Rida T. Farouki

The problem of constructing spatial Pythagorean–hodograph (PH) quintic curve segments that match prescribed

G^{2}

Hermite data—end points, Frenet frames, and curvatures—is considered. In terms of the quaternion representation, this problem entails four free parameters: the magnitudes of the two end derivatives, and the angular variables that arise in the standard

C^{1}

spatial PH quintic Hermite interpolation procedure. Equating two distinct expressions for the middle Bernstein coefficient of the quadratic quaternion pre-image polynomial, arising from matching the end points and curvature vectors, yields a system of four scalar algebraic/trigonometric equations, whose solutions identify the spatial PH quintic curves that interpolate the specified

G^{2}

Hermite data. Numerical methods for solving this system are formulated, and several computed examples illustrate the efficacy of the method.

构造空间毕达哥拉斯- hodograph （PH）五次曲线段的问题，该曲线段匹配规定的G2 Hermite数据——端点、Frenet帧和曲率。在四元数表示方面，这个问题需要四个自由参数：两个端导数的大小，以及在标准C1空间PH五次Hermite插值过程中出现的角变量。由匹配端点和曲率向量产生的二次四元数预像多项式的中间伯恩斯坦系数的两个不同表达式相等，产生一个由四个标量代数/三角方程组成的系统，其解确定插值指定的G2 Hermite数据的空间PH五次曲线。给出了求解该系统的数值方法，并通过算例说明了该方法的有效性。

引用次数: 0

Weighted transfinite interpolation for slightly unstructured curvilinear patches 略非结构化曲线斑块的加权超限插值

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-12-01 DOI: 10.1016/j.cagd.2025.102497

Christopher G. Provatidis

This paper presents an extension of the classical transfinite interpolation formula originally developed by Gordon and Hall, aimed at improving geometric modeling over slightly unstructured curvilinear patches. While traditional transfinite schemes rely on structured boundary data and cardinal blending functions, the proposed method introduces a weighted framework that accommodates irregularities in the layout of interpolation stations. By assigning suitable weights to both the blending and trial functions—such as Bernstein polynomials, B-splines, or NURBS—the interpolation scheme gains flexibility while preserving smoothness and continuity across the patch. The approach maintains the intuitive geometric structure of the original formulation, but significantly expands its applicability to more general domains encountered in computer-aided geometric design (CAGD), mesh generation, and isogeometric analysis. With the cylindrical patch serving as the primary benchmark and the spherical cap as the secondary, various combinations of blending and trial functions are investigated to illustrate the method’s capability to accurately represent mild irregularities in data distribution.

本文提出了由Gordon和Hall提出的经典超限插值公式的扩展，旨在改进稍微非结构化曲线块的几何建模。传统的超限方案依赖于结构化边界数据和基数混合函数，而该方法引入了一个加权框架，以适应插值站布局中的不规则性。通过分配适当的权重，以混合和试验函数，如伯恩斯坦多项式，b样条，或nurb -插值方案获得灵活性，同时保持整个补丁的平滑和连续性。该方法保持了原始公式的直观几何结构，但显着扩展了其在计算机辅助几何设计（CAGD），网格生成和等几何分析中遇到的更一般领域的适用性。以圆柱形贴片为主要基准，以球形帽为次要基准，研究了混合函数和试验函数的各种组合，以说明该方法能够准确地表示数据分布中的轻微不规则性。

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引用次数: 0

SceneFlow: Synthesizing indoor scenes via geometry-enhanced flow matching SceneFlow：通过几何增强流匹配合成室内场景

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-11-07 DOI: 10.1016/j.cagd.2025.102489

Wenming Wu , Akang Shen , Yanzhe Yin , Zixiang Chen , Gaofeng Zhang , Liping Zheng

Recent autoregressive and diffusion models are used to generate indoor scenes. However, they face challenges in maintaining geometric consistency and achieving real-time performance. Autoregressive models struggle with global dependencies, leading to functional inconsistencies, while diffusion-based methods suffer from slow sampling speeds. Motivated by simpler and smoother sampling trajectories, we propose SceneFlow, a novel indoor scene synthesis framework based on Flow Matching, which learns a flow to gradually move objects from an initial chaotic state to a structured layout. To further enhance geometric consistency, we introduce a geometry enhancement strategy comprising a non-overlap constraint to reduce object overlap and a geometry refinement to align objects with room boundaries. We evaluate our approach using the 3D-FRONT dataset. Extensive evaluations demonstrate that our method outperforms state-of-the-art methods in visual quality, geometric accuracy, and generation efficiency. Our method provides a practical solution for applications requiring high-quality indoor scene generation with real-time responsiveness.

最近的自回归和扩散模型用于生成室内场景。然而，它们在保持几何一致性和实现实时性能方面面临挑战。自回归模型与全局依赖关系作斗争，导致功能不一致，而基于扩散的方法则受到采样速度慢的影响。基于更简单、更平滑的采样轨迹，我们提出了一种基于流匹配的室内场景合成框架SceneFlow，该框架通过学习流将物体从初始混沌状态逐渐移动到结构化布局。为了进一步增强几何一致性，我们引入了一种几何增强策略，该策略包括非重叠约束以减少对象重叠和几何细化以使对象与房间边界对齐。我们使用3D-FRONT数据集评估我们的方法。广泛的评估表明，我们的方法在视觉质量，几何精度和生成效率方面优于最先进的方法。我们的方法为需要高质量的室内场景生成和实时响应的应用提供了一个实用的解决方案。

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引用次数: 0

Surface reconstruction of narrow-band guided Gray-Scott model 窄带制导Gray-Scott模型的表面重构

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-11-06 DOI: 10.1016/j.cagd.2025.102488

Jian Wang , Xuejuan Chen , Bowen Geng , Mengyu Luo , Shanshan Ge , Haozhe Wang , Jialin Chen , Junseok Kim

We propose a novel method that combines the modified Gray-Scott (GS) equation with a narrow-band model for efficient surface reconstruction of complex and irregular three-dimensional (3D) point cloud data. In the case of sparse or missing point cloud data, the method improves the point cloud using the Non-Uniform Rational B-Spline (NURBS) interpolation technique to improve its resolution and completeness. The initial implicit surface is generated in the narrow-band region of the point cloud, and the modified GS model is introduced to evolve the surface, which significantly improves the quality and computational efficiency of surface reconstruction. Computational results show that the proposed algorithm demonstrates good robustness and efficiency when handling different models and can provide accurate and smooth 3D surface reconstruction, which has high potential for applications and practical value.

本文提出了一种将改进的Gray-Scott （GS）方程与窄带模型相结合的方法，用于复杂和不规则三维点云数据的有效表面重建。在点云数据稀疏或缺失的情况下，该方法利用非均匀合理b样条（NURBS）插值技术对点云进行改进，提高点云的分辨率和完整性。在点云的窄带区域生成初始隐式曲面，并引入改进的GS模型对曲面进行演化，显著提高了曲面重建的质量和计算效率。计算结果表明，该算法在处理不同模型时具有良好的鲁棒性和效率，能够提供准确、流畅的三维表面重建，具有很高的应用潜力和实用价值。

引用次数: 0

Tooth mesh repair method based on side length-area constraint and dihedral angle driven subdivision 基于边长-面积约束和二面角驱动细分的齿网修复方法

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-11-01 DOI: 10.1016/j.cagd.2025.102487

Hongan Li , Kun Yang , Long Peng

Aiming at the problems of poor mesh quality and lack of details in hole repair in 3D tooth scanning model, this paper proposes a high-quality mesh repair algorithm combining multiple geometric constraints and local feature enhancement mechanism. This method first introduces the edge length-area joint constraint strategy, and standardizes the new triangle shape in the initial repair stage to avoid the generation of narrow or deformed grids. Then, according to the dihedral angle change between adjacent triangles, the high curvature region is adaptively selected for Sqrt3 subdivision operation, so as to enhance the detail expression ability of the repaired region. Finally, Laplacian smoothing is used to optimize the spatial distribution of new vertices, which improves the geometric consistency and visual continuity between the patched region and the original model. The experimental results show that the proposed algorithm shows high repair quality and detail fidelity on multiple tooth models. The shape regularity of the new triangular surface is better than that of the comparison method. The proportion of high-quality patches with quality factor q is more than 50%. Multi-metric evaluations demonstrate that this method outperforms the comparison method in terms of geometric accuracy and surface fidelity, making it suitable for high-precision dental modeling and digital restoration tasks.

针对三维牙齿扫描模型孔修复中存在的网格质量差、细节缺失等问题，提出了一种结合多个几何约束和局部特征增强机制的高质量网格修复算法。该方法首先引入边缘长度-面积联合约束策略，并在初始修复阶段对新三角形状进行标准化，避免网格产生狭窄或变形。然后，根据相邻三角形之间的二面角变化，自适应选择高曲率区域进行Sqrt3细分操作，增强修复区域的细节表达能力。最后，利用拉普拉斯平滑优化新顶点的空间分布，提高了修补区域与原模型之间的几何一致性和视觉连续性。实验结果表明，该算法对多个牙齿模型具有较高的修复质量和细节保真度。新三角曲面的形状规则性优于对比法。质量因子q的优质贴片比例大于50%。多度量评估表明，该方法在几何精度和表面保真度方面优于对比方法，适用于高精度牙科建模和数字修复任务。

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引用次数: 0

Corrigendum to “Isotopic equivalence by Bézier curve subdivision for application to high performance computing” [Computer Aided Geometric Design 31 (2013) 642–655] “应用于高性能计算的b2013.zier曲线细分的同位素等效”的勘误表[计算机辅助几何设计31 (2013)642-655]

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-11-01 DOI: 10.1016/j.cagd.2025.102486

K.E. Jordan, J. Li, T.J. Peters, J.A. Roulier

引用次数: 0

On a nonlinear version of Lane-Riesenfeld's subdivision schemes converging to piecewise smooth functions preserving high regularity Lane-Riesenfeld细分格式收敛于保持高正则性的分段光滑函数的一个非线性版本

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-09-16 DOI: 10.1016/j.cagd.2025.102485

Sergio Amat , Sonia Busquier , David Levin , Juan Ruiz , Dionisio F. Yáñez

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.

Lane-Riesenfeld的细分方案为生成光滑和详细的曲线和表面提供了一个通用的工具，使它们成为计算机图形学和几何建模的宝贵资产。这些方案通过调整一些参数来灵活地控制极限函数的正则性。在本文中，我们提出了这些算法的非线性修正，用于分段光滑函数。该算法收敛于分段光滑极限函数，保持了Lane-Riesenfeld细分格式在光滑区域内的高度正则性。实际计算结果表明，所提算法具有良好的数值性能。

引用次数: 0

The cubic de Casteljau construction and some classes of cubic curves on Riemannian manifolds 黎曼流形上的三次de Casteljau构造和几类三次曲线

IF 1.7 4区计算机科学 Q3 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer Aided Geometric Design

Pub Date : 2025-08-21 DOI: 10.1016/j.cagd.2025.102478

Erchuan Zhang , Lyle Noakes

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 (Zhang and Noakes, 2019a) 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

S^{2}

and also in the special orthogonal group

SO (3)

非欧几里得空间中的曲线插值对于轨迹规划、量子计算和图像配准具有重要意义。特别地，黎曼三次、Jupp和Kent三次以及张力的黎曼三次经常用于埃尔米特插值。除了在极少数情况下，这些曲线不能以封闭形式给出，这限制了它们的适用性。欧几里得空间中三次多项式的经典de Casteljau构造推广到黎曼流形中，其中线段被流形上的测地线弧代替。作者（Zhang和Noakes， 20119a）表明，广义三次de Casteljau曲线可以非常接近黎曼三次，误差由四阶曲率项限定。在此基础上，本文旨在分析在张力条件下近似于Jupp、Kent三次和riemann三次的广义三次de Casteljau曲线的质量。我们还修改了广义de Casteljau算法，以构造更接近于Jupp和Kent立方的曲线，以及更接近于张力的黎曼立方的曲线。我们通过在二维单位球S2和特殊正交群SO(3)中的三次曲线上的数值实验来说明我们的理论结果。

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