Computer Aided Geometric Design最新文献

英文中文

Euler's elastica and curvature based nonlinear mesh denoising method 基于欧拉弹性和曲率的非线性网格去噪方法

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

Computer Aided Geometric Design

Pub Date : 2025-08-07 DOI: 10.1016/j.cagd.2025.102477

Huayan Zhang , Xingzhi Xie , Yupeng Wang , Xiaochao Wang

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.

在本文中，我们推广了一个新的非线性变分模型，该模型是基于一般欧拉弹性和曲率的三角曲面。该模型将梯度算子和曲率算子以乘法的方式结合在一起。通过引入限制于三角形的总变分范数，将三角曲面上的欧拉弹性模型和曲率模型分别离散为基于三角形和基于边的公式。提出了一种基于通用欧拉弹性和曲率模型的两阶段网格去噪方法：首先基于欧拉弹性和曲率模型对面法线进行滤波，然后更新顶点位置。通过一种有效的松弛，基于算子分裂和乘法器交替方向法（ADMM）迭代求解非线性不可微优化问题。从参数敏感性、与几种最新技术的定量比较和计算成本等方面对所提出的去噪方法进行了评估。数值实验证实，与现有的几种降噪算法相比，我们的方法在合理的成本下产生了具有竞争力的结果。它通过保留更清晰的特征，恢复更多的细节和结构，减轻楼梯效应（假边缘），取得了令人满意的效果。定量误差进一步验证了算法的数值鲁棒性。

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引用次数: 0

Discrete Gaussian free field methods for random curve shape generation 随机曲线形状生成的离散高斯自由场方法

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

Computer Aided Geometric Design

Pub Date : 2025-07-09 DOI: 10.1016/j.cagd.2025.102469

Wenzhong Zhang

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.

研究了一维离散高斯自由场（DGFF）和基于DGFF的二维固定端随机曲线采样方法，包括一种优先考虑形状变化且不需要现有数据的直接采样方法，以及一种数据驱动的扩散模型，用于从曲线形状的经验分布中采样。我们在形状优化问题中测试了所提出的方法，包括一个二维随机翼型形状采样问题，假设已知最小的物理知识。

引用次数: 0

Sibson's formula for higher order Voronoi diagrams Sibson高阶Voronoi图的公式

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

Computer Aided Geometric Design

Pub Date : 2025-07-08 DOI: 10.1016/j.cagd.2025.102470

Mercè Claverol , Andrea de las Heras-Parrilla , Clemens Huemer , Dolores Lara

Let S be a set of n points in general position in

R^{d}

. The order-k Voronoi diagram of S,

V_{k} (S)

, is a subdivision of

R^{d}

into cells whose points have the same k nearest points of S. Sibson, in his seminal paper from 1980 (A vector identity for the Dirichlet tessellation), gives a formula to express a point Q of S as a convex combination of other points of S using ratios of volumes of the intersection of cells of

V_{2} (S)

and the cell of Q in

V_{1} (S)

. The natural neighbour interpolation method is based on Sibson's formula. We generalize his result to express Q as a convex combination of other points of S by using ratios of volumes from Voronoi diagrams of any given order.

让年代是一组n个点通常在Rd位置。k阶泰森多边形法图的年代,Vk (S),是一个细分的Rd进入细胞的点相同的事务部门主管美国Sibson k最近的点在他的论文从1980年(狄利克雷镶嵌一个向量的身份),让一个公式来表达点Q的凸组合其他点的年代使用的比率卷V2的十字路口的细胞(S)和细胞问的V1 (S)。自然邻域插值法基于Sibson公式。我们利用任意阶的Voronoi图的体积比，推广了他的结果，将Q表示为S的其他点的凸组合。

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引用次数: 0

Log-aesthetic curves and generalized Archimedean spirals 对数美曲线与广义阿基米德螺旋

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

Computer Aided Geometric Design

Pub Date : 2025-07-03 DOI: 10.1016/j.cagd.2025.102468

Péter Salvi

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.

我们证明了对数曲线的径向是广义阿基米德螺旋。检查对数曲率直方图显示，这些径向与相关的对数美学曲线具有固有的相似性，并且也可以用作计算廉价的近似值。提出了不同的拟合形式，并通过实例进行了讨论。本文还探讨了基于广义阿基米德螺旋的对数美学曲线的一种可能的推广。

引用次数: 0

Paul de Faget de Casteljau, a pioneer in CAGD Paul de Faget de Casteljau, CAGD的先驱

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

Computer Aided Geometric Design

Pub Date : 2025-06-01 DOI: 10.1016/j.cagd.2025.102431

Carolina Vittoria Beccari , Kai Hormann , Christophe Rabut , Wenping Wang

引用次数: 0

A multilevel feature-based method for mapping sparse point clouds to CAD models 一种基于多层特征的稀疏点云到CAD模型映射方法

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

Computer Aided Geometric Design

Pub Date : 2025-05-28 DOI: 10.1016/j.cagd.2025.102457

Youlong Zeng , Haiyan Sun , Xiaobin Li , Zhuoyi Chen

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.

稀疏点云到CAD模型的精确映射在数字孪生、三维重建和工程设计等领域变得越来越重要。然而，通过激光雷达扫描获得的点云数据的稀疏性和不规则性给特征映射精度和与CAD模型的无缝集成带来了重大挑战。传统的方法很难保持精确的映射，特别是在处理复杂的点云场景或稀疏数据时。这些方法在将稀疏点云精确映射到实体模型方面存在明显的局限性。为了解决这些挑战，本文引入了一种多层特征映射方法，该方法对CAD模型和点云数据的几何特征进行了深入分析，显著提高了特征匹配的精度。在CAD模型处理中，利用几何特征签名（Geometric Feature Signature， GFS）映射函数，通过对几何特征量的综合提取，实现高精度的几何形态描述。对于点云数据处理，采用密集域滤波（DDF）优化空间分布，最大限度地减少噪声和冗余数据的影响。该方法结合密度控制几何一致特征提取（DC-GCFE），通过对稀疏点云的几何特征量进行综合分析，实现了关键特征点的精确提取。该方法通过将CAD模型的几何特征与点云的局部和全局特征有效匹配，保证了在稀疏和复杂点云环境下的精确映射，为虚拟仿真和设计优化提供了有力的支持。与传统方法相比，该方法在捕获复杂细节和处理缺失特征方面表现出色。最后，实验验证了该方法在复杂场景下具有较高的匹配精度和鲁棒性，验证了该方法在稀疏点云到CAD模型精确映射中的有效性。

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引用次数: 0

Geodesic distance approximation using a surface finite element method for the p-Laplacian 用表面有限元法求测地线距离近似的p-拉普拉斯

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

Computer Aided Geometric Design

Pub Date : 2025-05-22 DOI: 10.1016/j.cagd.2025.102458

Hannah Potgieter, Razvan C. Fetecau, Steven J. Ruuth

We use the p-Laplacian with large p-values in order to approximate geodesic distances to features on surfaces. This differs from Fayolle and Belyaev's (2018) computational results using the p-Laplacian for the distance-to-surface 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 Crane et al. (2017) and the classical polyhedral method from Mitchell et al. (1987).

我们使用具有大p值的p-拉普拉斯算子来近似地表特征的测地线距离。这与Fayolle和Belyaev（2018）使用p-拉普拉斯算子求解距离表面问题的计算结果不同。与其他流行的基于pde的距离函数近似方法相比，我们的方法似乎提供了一些明显的优势。我们采用了一种曲面有限元格式，并证明了对真测地线距离函数的数值收敛性。我们检查我们的数值结果是否符合三角不等式，并检查对几何噪声（如顶点扰动）的鲁棒性。我们还将我们的方法与Crane等人（2017）的热法和Mitchell等人（1987）的经典多面体法进行了比较。

引用次数: 0

ParaValve: An open source framework for parametric design and fluid–structure interaction simulation of bioprosthetic heart valves in patient-specific aortic geometries ParaValve：一个开源框架，用于患者特定主动脉几何形状的生物人工心脏瓣膜的参数化设计和流-结构相互作用模拟

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

Computer Aided Geometric Design

Pub Date : 2025-05-20 DOI: 10.1016/j.cagd.2025.102455

Mehdi Saraeian, Ashton M. Corpuz, Ming-Chen Hsu, Adarsh Krishnamurthy

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.

心脏瓣膜病（HVD）是一种重要的心血管并发症，是全球发病率和死亡率的主要原因之一。HVD的治疗通常涉及生物假体瓣膜等医疗设备。然而，这些装置的设计和优化需要彻底了解其生物力学和血流动力学与患者特定解剖结构的相互作用。参数化程序几何已成为提高此类器件设计优化效率和准确性的有力工具，使研究人员能够系统地探索各种可能的配置。在这项工作中，我们提出了一个强大的框架，用于支架生物人工心脏瓣膜和患者特定主动脉几何形状的参数化和程序化建模。该框架采用非均匀有理b样条（NURBS）为基础的几何参数化，能够精确控制关键的解剖和设计变量。通过实现模块化和可扩展的工作流程，该框架支持阀门设计的迭代优化，以实现更好的血流动力学性能和耐用性。我们通过模拟生物假体主动脉瓣来证明其适用性，强调几何参数对瓣膜功能的影响及其个性化设备设计的潜力。通过将参数几何与计算工具相结合，该框架为研究人员和工程师提供了一条通向创新和患者特定心血管解决方案的流线型途径。

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引用次数: 0

Detail-preserving shape completion of point cloud models with articulated structure 具有关节结构的点云模型的保细节形状补全

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

Computer Aided Geometric Design

Pub Date : 2025-05-20 DOI: 10.1016/j.cagd.2025.102456

Yi Quan , Chen Li , Yang Li , Changbo Wang , Hong Qin

This paper advocates a novel deep-learning-based method for point cloud completion of multi-categorical articulated objects sharing the same topology. One popular approach for point cloud completion is to rely on a generic encoder-decoder architecture, where the feature maps of input are extracted with the critical set, which essentially consists of a set of points that play critical roles in the max-pooled features. But this pipeline has difficulties in retaining the local details, especially for arbitrary deformable, articulated objects of various categories, bringing category confused completion. In this paper, we propose a detail-preserving point cloud completion method for the complex articulated models by extracting features guided by their articulation topology with a fixed-order scheme, so as to accommodate both fine-grained categorical appearance and non-rigid deformation. First, we construct key subsets, which preserve both local, category-aware and global, non-rigid deformation features simultaneously for input sharing similar point densities, guided by a set of regressed key points approximating articulations. Second, we organize the key subsets with a fixed-order scheme during feature extraction to combat the possible interference due to diverse data component permutations during feature extraction, while upholding the algorithmic efficiency. Finally, we confirm in our evaluations that the new method completes general articulated point clouds with detailed categorical characteristics in high quality. We also show that after training on synthetic data, our method can be applied to real scan or web downloaded point clouds with similar point densities. Meanwhile, we built an Quadruped Point Cloud Completion (QPCC) dataset upon which new research topics could be further explored in geometry modeling and computer graphics.

本文提出了一种基于深度学习的点云补全新方法，该方法适用于具有相同拓扑结构的多分类铰接对象。点云补全的一种流行方法是依赖于通用的编码器-解码器架构，其中输入的特征映射是用关键集提取的，关键集本质上由一组在最大池特征中起关键作用的点组成。但是，这种管道在保留局部细节方面存在困难，特别是对于任意可变形的、铰接的各种类别的对象，导致类别完成混乱。在本文中，我们提出了一种保留细节的点云补全方法，该方法通过固定顺序的格式提取复杂铰接模型的铰接拓扑引导下的特征，以适应细粒度的分类外观和非刚性变形。首先，在一组近似关节的回归关键点的指导下，我们构建了键子集，该子集同时保留了具有相似点密度的输入的局部、类别感知和全局非刚性变形特征。其次，在特征提取过程中对关键子集进行定序组织，在保证算法效率的前提下，克服了特征提取过程中由于数据成分排列不同而可能产生的干扰。最后，我们在评估中证实，新方法高质量地完成了具有详细分类特征的一般铰接点云。我们还表明，经过对合成数据的训练，我们的方法可以应用于具有相似点密度的真实扫描或网络下载点云。同时，我们建立了一个四足点云补全（QPCC）数据集，在此基础上进一步探索几何建模和计算机图形学的新研究课题。

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3D shape analysis via multi-modal contrastive learning 基于多模态对比学习的三维形状分析

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

Computer Aided Geometric Design

Pub Date : 2025-05-02 DOI: 10.1016/j.cagd.2025.102454

Zhenyu Shu , Xufei Sun , Chaoyi Pang

In recent years, 3D shape analysis has emerged as a crucial field with applications in various domains, such as multimedia processing, computer graphics, computer vision, and robotics. The ability to understand and interpret 3D shapes is fundamental for tasks like 3D shape segmentation, points of interest detection, shape retrieval, recognition, and generation. However, the complexity of 3D mesh models is a significant barrier that stops the topic from enhancing. Thus, we propose a novel 3D shape analysis framework in this paper by multi-modal contrastive learning techniques. Our framework makes use of the original mesh data and the projected images from various points of view of the mesh model. Those two modals contribute to providing more precise features with the help of our within-modal and cross-modal losses, which respectively calculate the distances of feature vectors within the mesh model and between feature vectors of mesh and image. Our framework is tested on downstream tasks, including 3D shape segmentation and points of interest detection, and outperforms most state-of-the-art methods on public datasets.

近年来，三维形状分析已成为多媒体处理、计算机图形学、计算机视觉和机器人技术等各个领域的重要应用领域。理解和解释3D形状的能力是诸如3D形状分割、兴趣点检测、形状检索、识别和生成等任务的基础。然而，三维网格模型的复杂性是阻碍该主题增强的重要障碍。因此，本文提出了一种基于多模态对比学习技术的三维形状分析框架。我们的框架利用了原始网格数据和从网格模型的各个角度投影的图像。这两种模态有助于提供更精确的特征，我们的模态内损失和跨模态损失分别计算网格模型内特征向量的距离和网格与图像特征向量之间的距离。我们的框架在下游任务上进行了测试，包括3D形状分割和兴趣点检测，并且在公共数据集上优于大多数最先进的方法。

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