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Momentum-accelerated randomized geometric iterative methods for curve and surface approximation 曲线和曲面逼近的动量加速随机几何迭代方法
IF 3.1 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2025-11-26 DOI: 10.1016/j.cad.2025.104011
Nian-Ci Wu , Hong-Hong Cao , Chengzhi Liu
Geometric iterative methods form a distinct family of data-fitting techniques, distinguished by their progressive, iterative nature and endowed with clear geometric interpretations. Least-squares progressive iterative approximation (LSPIA), a prominent member of this family, enables efficient handling of large-scale point sets. In this work, we accelerate LSPIA by incorporating Polyak and Nesterov momentum together with random-sampling strategies. The resulting algorithms adaptively update control points via randomized index selection while exploiting historical information on both the control points and the gradients. We prove that the resulting algorithms converge in expectation to the least-squares fitting result of the given data points. We also derive explicit formulas for the momentum parameters. Numerical experiments demonstrate the improved efficiency and accuracy of the proposed methods compared to conventional approaches.
几何迭代方法形成了一个独特的数据拟合技术家族,其特点是递进迭代,并具有明确的几何解释。最小二乘渐进迭代逼近(LSPIA)是该家族的杰出成员,它能够有效地处理大规模点集。在这项工作中,我们通过将Polyak和Nesterov动量与随机抽样策略结合在一起来加速LSPIA。所得算法通过随机索引选择自适应更新控制点,同时利用控制点和梯度的历史信息。我们证明了所得到的算法在期望上收敛于给定数据点的最小二乘拟合结果。我们还推导了动量参数的显式公式。数值实验表明,与传统方法相比,该方法提高了效率和精度。
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引用次数: 0
An STL-free method for concurrent optimization and fabrication of morphing strut-based lattice structures 基于变形杆的晶格结构并行优化与制造的无stl方法
IF 3.1 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2025-11-21 DOI: 10.1016/j.cad.2025.104012
Chao Feng, Liang Gao, Hao Li
The enhanced geometric freedom in additive manufacturing has renewed interest in multiscale topology optimization. Nevertheless, multiscale design and additive manufacturing have yet to be sufficiently integrated to achieve multiple population, multiscale, lattice structures. In this study, we propose an STL-free method that unifies the design and manufacturing of spatially varying lattice structures via a novel functional representation of morphing strut-like microstructures with curved profiles. Specifically, a new morphing strut microstructure (MSM) is proposed and represented by a cluster of quadratic and planar half-spaces. Benefiting from the superior mechanical properties, the MSMs are integrated into the concurrent multiscale design for an optimized layout of a continuously smooth transition. To avoid prohibitively expensive surface representations and time-consuming intermediate conversion, we develop a direct slicing algorithm based on implicit representation, which is locally evaluated in an interval calculation manner. The resultant slices are directly embedded into the 3D printer without requiring intermediate data conversions such as triangulation, greatly improving additive manufacturing efficiency. The presented paradigm has been validated by some representative examples filled with different types of MSMs and demonstrated via digital light processing (DLP) 3D printing. The ideas are expected to provide a unified model data stream for solving the scalability and efficiency challenges of optimized design and additive manufacturing in engineering-scale applications.
增材制造中几何自由度的增强重新引起了人们对多尺度拓扑优化的兴趣。然而,多尺度设计和增材制造尚未充分集成,以实现多人口,多尺度,点阵结构。在这项研究中,我们提出了一种无stl的方法,通过一种新颖的具有弯曲轮廓的变形杆状微结构的功能表示,将空间变化晶格结构的设计和制造统一起来。具体来说,提出了一种新的变形支撑结构(MSM),并将其表示为一组二次半空间和平面半空间。得益于优越的力学性能,msm被集成到并行多尺度设计中,以优化连续平滑过渡的布局。为了避免过于昂贵的表面表示和耗时的中间转换,我们开发了一种基于隐式表示的直接切片算法,该算法以区间计算的方式局部求值。生成的切片直接嵌入到3D打印机中,无需中间数据转换,如三角测量,大大提高了增材制造效率。所提出的范式已经通过一些具有代表性的例子进行了验证,这些例子充满了不同类型的msm,并通过数字光处理(DLP) 3D打印进行了演示。这些想法有望为解决工程规模应用中优化设计和增材制造的可扩展性和效率挑战提供统一的模型数据流。
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引用次数: 0
Novel Kresling variant patterns for inverse origami design 反折纸设计的新型Kresling变体图案
IF 3.1 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2025-11-20 DOI: 10.1016/j.cad.2025.104008
Yan Zhao , Qingyue Liu , Yinglei Wei
Origami patterns enable the transformation of two-dimensional flat sheet materials into three-dimensional target surfaces through folding. However, existing origami patterns exhibit limitations in both diversity and performance when applied to inverse design problems. In this paper, we focus on a novel Kresling variant pattern and demonstrate its flexibility in approximating target surfaces with freeform shapes and varying curvatures. Given a standard Kresling pattern, the upper and lower edges of each unit are expanded into four small triangles to obtain the Kresling variant pattern. This variant pattern inherits the developability and flat-foldability of the original Kresling pattern while providing more flexibility for inverse design. We then tile the partially folded Kresling variant pattern onto the target surface and solve the inverse-origami-design problem through optimization. In the optimization process, unknown variables can be selected and residuals of origami geometric constraints can be eliminated without relaxation. In addition, we demonstrate that origami approximations are capable of fitting between two target surfaces with or without developability. To improve mesh quality, we incorporate additional constraints on the aspect ratio and area of each triangular facet. These constraints supplement the origami geometric constraints for improving the regularity and stability of the final approximations. Paper fabrications and folding simulations confirm the validity and flexibility of our approach. Our work reveals the potential of the Kresling variant pattern for inverse origami design and opens up novel avenues for applications across diverse fields, including architecture, aerospace, and robotics.
折纸图案使二维平面材料通过折叠转化为三维目标表面。然而,现有的折纸模式在应用于反设计问题时,在多样性和性能上都存在局限性。本文重点研究了一种新的Kresling变图,并证明了它在逼近具有自由形状和变曲率的目标表面时的灵活性。给定一个标准的Kresling图案,将每个单元的上下边扩展成四个小三角形,得到Kresling变体图案。这种变体模式继承了原始Kresling模式的可展开性和可平折性,同时为逆向设计提供了更大的灵活性。然后,我们将部分折叠的Kresling变体图案平铺到目标表面上,并通过优化解决反折纸设计问题。在优化过程中,可以选择未知变量,不松弛地消除折纸几何约束的残差。此外,我们证明了折纸近似能够在具有或不具有可展性的两个目标表面之间进行拟合。为了提高网格质量,我们在每个三角形面的纵横比和面积上加入了额外的约束。这些约束补充了折纸几何约束,以提高最终逼近的规律性和稳定性。纸张制造和折叠模拟验证了我们方法的有效性和灵活性。我们的工作揭示了Kresling变体模式在反折纸设计中的潜力,并为包括建筑、航空航天和机器人在内的不同领域的应用开辟了新的途径。
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引用次数: 0
Guest Editorial: Proceedings of SPM 2025 Symposium 嘉宾评论:SPM 2025研讨会论文集
IF 3.1 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2025-11-18 DOI: 10.1016/j.cad.2025.104009
Xiaohu Guo, Lucia Romani, Yunbo Zhang
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引用次数: 0
Feature-aware manifold meshing and remeshing of point clouds and polyhedral surfaces with guaranteed smallest edge length 特征感知的点云和多面体表面的流形网格划分和重划分,保证最小的边缘长度
IF 3.1 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2025-11-17 DOI: 10.1016/j.cad.2025.104010
Henriette Lipschütz , Ulrich Reitebuch , Konrad Polthier , Martin Skrodzki
Point clouds and polygonal meshes are widely used when modeling real-world scenarios. Here, point clouds arise, for instance, from acquisition processes applied in various surroundings, such as reverse engineering, rapid prototyping, or cultural preservation. Based on these raw data, polygonal meshes are created to, for example, run various simulations. For such applications, the utilized meshes must be of high quality. This paper presents an algorithm to derive triangle meshes from unstructured point clouds. The occurring edges have a close to uniform length and their lengths are bounded from below. Theoretical results guarantee the output to be manifold, provided suitable input and parameter choices. Further, the paper presents several experiments establishing that the algorithms can compete with widely used competitors in terms of quality of the output and timing and the output is stable under moderate levels of noise. Additionally, we expand the algorithm to detect and respect features on point clouds as well as to remesh polyhedral surfaces, possibly with features.
Supplementary material, an extended preprint, a link to a previously published version of the article, utilized models, and implementation details are made available online.
点云和多边形网格在建模现实场景时被广泛使用。例如,点云产生于应用于各种环境的获取过程中,例如逆向工程、快速原型或文化保护。基于这些原始数据,创建多边形网格,例如,运行各种模拟。对于这样的应用,使用的网格必须是高质量的。提出了一种从非结构化点云中导出三角形网格的算法。出现的边具有接近均匀的长度,并且它们的长度从下面有界。理论结果保证了输出是多种多样的,提供了合适的输入和参数选择。此外,本文提出了几个实验,证明该算法在输出质量和时序方面可以与广泛使用的竞争对手竞争,并且在中等噪声水平下输出稳定。此外,我们扩展了算法来检测和尊重点云上的特征,以及对多面体表面进行网格划分,可能会有特征。补充材料、扩展的预印本、到文章先前发布版本的链接、使用的模型和实现细节都可以在线获得。
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引用次数: 0
Harmonic-based sweeps need not yield volumetric parameterizations 基于谐波的扫描不需要产生体积参数化
IF 3.1 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2025-11-08 DOI: 10.1016/j.cad.2025.104007
Caleb B. Goates, Kendrick M. Shepherd
Harmonic maps are important in generating parameterizations for various domains, particularly in two and three dimensions. General extensions of two-dimensional harmonic parameterization methods to volumetric parameterizations are known to fail in a variety of contexts, though more specialized volumetric parameterizations have been proposed. This work provides and contextualizes a counterexample to various proposed proofs that employ harmonic maps to sweep a parameterization from a base surface, Γ0, to the entire domain of a geometry that is homeomorphic to Γ0×[0,1] or Γ0×S1. The existence of a counterexample clarifies that these swept parameterizations come with no inherent guarantees of bijectivity, as they may in two dimensions.
谐波映射对于生成各种领域的参数化非常重要,特别是在二维和三维领域。二维谐波参数化方法对体积参数化的一般扩展在各种情况下都是失败的,尽管已经提出了更专门的体积参数化。这项工作提供了一个反例,并将其背景化为各种提出的证明,这些证明使用调和映射将参数化从基面Γ0扫描到与Γ0×[0,1]或Γ0×S1同纯的整个几何域。反例的存在澄清了这些扫描参数化没有固有的双向性保证,就像在二维中一样。
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引用次数: 0
High-order CAD-based surface mesh adaptation with the log-simplex method 基于对数单纯形法的高阶cad曲面网格自适应
IF 3.1 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2025-11-06 DOI: 10.1016/j.cad.2025.104004
Olivier Coulaud
The present article studies the problem of approximating 3D surface models with meshes composed of curved triangles of arbitrary order. The considered process derives from a high-order solution-based mesh adaptation method called log-simplex method. In this case, it is locally applied on a specific 2D high-order solution, which is built from the features of the model and is defined on the tangent plane to the surface. This way, for a given mesh complexity, an optimal metric field is computed, which then drives the mesh adaptation procedure.
本文研究了用任意顺序的曲面三角形组成的网格逼近三维曲面模型的问题。所考虑的过程源于一种基于高阶解的网格自适应方法,称为对数单纯形法。在这种情况下,它局部应用于特定的2D高阶解,该解由模型的特征构建,并在与表面的切平面上定义。这样,对于给定的网格复杂度,计算一个最优度量域,然后驱动网格自适应过程。
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引用次数: 0
A physics conservation-based mesh patching algorithm for multi-body modeling and simulation 一种基于物理守恒的多体建模与仿真网格修补算法
IF 3.1 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2025-11-03 DOI: 10.1016/j.cad.2025.104005
Min Song, Chao Li, Xiao-Wei Guo, Qing-Yang Zhang, Jie Liu, Xiang Gao
This paper introduces a physics-driven approach to improve fluid dynamics simulations of multi-body geometries with non-matching interfaces. Conventional methods often suffer from inaccuracies due to the lack of robust physical models. Our solution integrates Computational Fluid Dynamics (CFD) techniques and proposes a conservative interpolation algorithm that resolves interface mismatches without mesh modification. By using a dual-weighting scheme based on overlapping face areas, the algorithm ensures flux consistency across subdomains while maintaining high computational efficiency. Applicable to both structured and unstructured meshes, this simple yet robust method has been implemented in general-purpose CFD software and validated through complex cases. Specifically, in Couette flow between concentric cylinders, it shows a maximum 1.556% relative error in velocity distribution against analytical solutions, outperforming continuous mesh methods in accuracy. In reactor pressure vessel simulations, it achieves a pressure distribution error of 0.586% and a maximum flow distribution error of 1.645% compared to continuous mesh solutions. These results validate the method’s high accuracy and reliability in simulating diverse flow regimes, thus facilitating precise analyses for complex engineering problems.
本文介绍了一种物理驱动的方法来改进具有非匹配界面的多体几何的流体动力学模拟。由于缺乏健壮的物理模型,传统的方法往往存在不准确性。该解决方案集成了计算流体动力学(CFD)技术,提出了一种不需要修改网格即可解决界面不匹配的保守插值算法。该算法采用基于重叠人脸区域的双重加权方案,在保证高计算效率的同时保证了子域间通量的一致性。该方法既适用于结构化网格,也适用于非结构化网格,并已在通用CFD软件中实现,并通过复杂案例进行了验证。具体而言,在同心圆柱体之间的Couette流中,相对于解析解的速度分布,其相对误差最大为1.556%,在精度上优于连续网格方法。在反应器压力容器模拟中,与连续网格方案相比,其压力分布误差为0.586%,最大流量分布误差为1.645%。这些结果验证了该方法在模拟不同流型时的高精度和可靠性,从而为复杂工程问题的精确分析提供了便利。
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引用次数: 0
Linking Model-Based Definition and Non-Intrusive Finite Element Analysis for Automated Variation Simulation 链接基于模型的定义和非侵入式有限元分析的自动化变分仿真
IF 3.1 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2025-10-30 DOI: 10.1016/j.cad.2025.104003
Martin Roth , Jan Kopatsch , Kristina Wärmefjord , Rikard Söderberg , Stefan Goetz
Computer-Aided Tolerancing (CAT) software has become the standard for statistically analyzing the effects of geometrical part variations on product quality. Irrespective of CAT’s scope and technical depth, Finite Element Analysis (FEA) software, used to simulate the physical product behavior for ideal part geometry in the first place, is also often used for studies with geometrical shapes deviating from their nominal. However, this requires a manual translation of the tolerances specified in the design phase into geometrical variations represented by Finite Element (FE) meshes and their transfer to the FEA software. The method presented in this article exploits the potential of Model-Based Definition by establishing a link between Computer-Aided Design and FEA software to empower the latter for variation simulation based on semantic Geometric Dimensioning and Tolerancing (GD&T) information. To transfer this information exchanged via the Quality Information Framework (QIF) standard, a new mapping algorithm is presented that automatically decomposes FE meshes into geometrical face elements and creates a semantic link with the GD&T information carried in QIF. As a result, geometrical features are simultaneously described through meshes with nodes in the 3D Euclidean space and mathematical geometrical faces in the 2D parameter space. Exploiting this duality, mesh deviations are modeled indirectly by adjusting the mapped feature descriptions. An exemplary implementation in ANSYS® and its usage for non-intrusive structural simulations illustrates that sharing tolerancing information via QIF enables an automated, GD&T standards-compliant variation simulation within FEA software environments and is one step closer to a seamless digital thread for geometry assurance.
计算机辅助公差(CAT)软件已成为统计分析零件几何变化对产品质量影响的标准。无论CAT的范围和技术深度如何,首先用于模拟理想零件几何形状的物理产品行为的有限元分析(FEA)软件也经常用于偏离其标称几何形状的研究。然而,这需要人工将设计阶段指定的公差转换为由有限元(FE)网格表示的几何变化,并将其转移到有限元分析软件中。本文提出的方法通过建立计算机辅助设计和有限元分析软件之间的联系,利用基于模型的定义的潜力,使后者能够基于语义几何尺寸和公差(GD&;T)信息进行变化仿真。为了传递通过质量信息框架(QIF)标准交换的信息,提出了一种新的映射算法,该算法自动将有限元网格分解为几何面元,并与QIF中携带的GD&;T信息建立语义链接。通过三维欧几里德空间中的节点网格和二维参数空间中的数学几何面网格同时描述几何特征。利用这种二元性,通过调整映射的特征描述来间接建模网格偏差。ANSYS®中的一个示例实施及其在非侵入式结构模拟中的使用表明,通过QIF共享公差信息可以在FEA软件环境中实现自动化的、符合GD&;T标准的变化模拟,并且更接近于实现几何保证的无缝数字线程。
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引用次数: 0
CADialogue: A multimodal LLM-powered conversational assistant for intuitive parametric CAD modeling 一个多模态llm驱动的对话助手,用于直观的参数化CAD建模
IF 3.1 3区 计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING Pub Date : 2025-10-28 DOI: 10.1016/j.cad.2025.104006
Jiwei Zhou , Jorge D. Camba , Pedro Company
Recent advances in generative Artificial Intelligence (AI)—particularly Large Language Models (LLMs)—offer a new paradigm for CAD interaction by enabling natural and intuitive input through texts, images, and context-aware selections. In this study, we present CADialogue, a multimodal LLM-powered conversational assistant to enable intuitive parametric CAD modeling through natural language, speech, image, and selection-based geometry interactions. Built on a general-purpose large language model, CADialogue translates user prompts into executable code to support geometry creation and context-aware editing. The system features a modular architecture that decouples prompt handling, refinement logic, and execution—allowing seamless model replacement as LLMs develop—and includes caching for rapid reuse of validated designs. We evaluate the system on 70 modeling and 10 editing tasks across varying difficulty levels, assessing performance in terms of accuracy, refinement behavior, and execution time. Results show an overall success rate of 95.71%, combining a 91.43% baseline under Text-Only input with additional recoveries enabled by Text + Image input, with robust recovery from failure via self-correction and human-in-the-loop refinement. Comparative analysis reveals that image input improves success in semantically complex prompts but introduces additional processing time. Furthermore, caching confirmed macros yields over 85.71% speedup in repeated executions. These findings highlight the potential of general-purpose LLMs for enabling accessible, iterative, and accurate CAD modeling workflows without domain-specific fine-tuning. The source code and dataset for CADialogue are available at https://github.com/Hiram31/CADialogue.
生成式人工智能(AI)的最新进展-特别是大型语言模型(llm) -通过文本,图像和上下文感知选择实现自然和直观的输入,为CAD交互提供了新的范例。在这项研究中,我们提出了cadialog,一个多模态llm驱动的会话助手,通过自然语言,语音,图像和基于选择的几何交互实现直观的参数化CAD建模。建立在通用的大型语言模型之上,cadialog将用户提示转换为可执行代码,以支持几何图形创建和上下文感知编辑。该系统采用模块化架构,将快速处理、优化逻辑和执行分离开来,允许在llm开发过程中无缝替换模型,并包括缓存,以便快速重用经过验证的设计。我们在不同难度的70个建模和10个编辑任务上对系统进行了评估,评估了准确性、改进行为和执行时间方面的性能。结果显示,总体成功率为95.71%,将纯文本输入下的91.43%基线与文本+图像输入支持的额外恢复相结合,并通过自我校正和人在循环中改进从失败中健壮地恢复。对比分析表明,图像输入提高了语义复杂提示的成功率,但引入了额外的处理时间。此外,缓存确认的宏在重复执行中产生超过85.71%的加速。这些发现突出了通用llm在实现可访问的、迭代的和精确的CAD建模工作流方面的潜力,而无需特定领域的微调。cadialog的源代码和数据集可从https://github.com/Hiram31/CADialogue获得。
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引用次数: 0
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Computer-Aided Design
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