Computer-Aided Design最新文献

英文中文

Multi-axis rough milling tool path generation based on 3D Hodge decomposition of vector fields 基于矢量场三维Hodge分解的多轴粗铣刀轨迹生成

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2026-03-01 Epub Date: 2025-12-14 DOI: 10.1016/j.cad.2025.104028

XuLin Cai, Wen-An Yang, XueFeng Yang, YouPeng You

This study develops a novel framework for generating multi-axis rough milling tool path by leveraging a full 3D Hodge decomposition of the volume-vector field (VFD). First, the stock material is tetrahedralized to form a computational mesh, on which a discrete five-term Hodge decomposition is performed. This process yields two orthogonal harmonic fields: a normal field that delineates the “near-net” rough-machining layers conforming precisely to the target geometry, and a tangential field that generates smooth, raster cutter-contact (CC) curves on each layer. Moreover, by taking the cross-product of these two fields, one can derive continuous, smooth circumferential CC curves. By enforcing mixed boundary conditions and incorporating a scallop-height-constrained scalar field, the method achieves graded layer thickness for material removal while precisely controlling residual heights. A tool-orientation planning module assigns collision-free, smoothly varying orientations along each CC curve, and CC-curve sequencing is optimized to minimize tool repositioning and idle motion. Comparative experiments on complex parts demonstrate that the VFD-based method not only guarantees complete, collision-free rough machining but also reduces total toolpath length and machining time while achieving effective residual-height control—outperforming both 3D area-clearance and blisk area-clearance strategies. Relative to an advanced geodesic-distance–based method, the VFD-based method shows markedly lower sensitivity to mesh resolution and therefore greater robustness. This work constitutes the first rigorous application of 3D Hodge theory to CNC rough machining and provides a flexible, efficient solution for five-axis volumetric machining.

本研究通过利用体积矢量场（VFD）的完整3D Hodge分解，开发了一种新的框架，用于生成多轴粗铣刀轨迹。首先，将原始材料四面体化，形成计算网格，在计算网格上进行离散五项霍奇分解。这一过程产生了两个正交谐波场：一个法向场描绘了精确符合目标几何形状的“近净”粗加工层，一个切向场在每一层上产生光滑的栅格刀具接触（CC）曲线。此外，通过取这两个场的外积，可以得到连续的、光滑的周向CC曲线。通过执行混合边界条件并结合扇贝高度约束标量场，该方法在精确控制残余高度的同时实现了材料去除的渐变层厚度。刀具方向规划模块沿着每条CC曲线分配无碰撞、平滑变化的方向，并优化CC曲线排序，以最大限度地减少刀具重新定位和空闲运动。在复杂零件上的对比实验表明，基于vfd的方法不仅保证了完整的、无碰撞的粗加工，而且减少了总刀路长度和加工时间，实现了有效的剩余高度控制，优于三维面积间隙和叶片面积间隙策略。相对于先进的基于测地线距离的方法，基于vfd的方法对网格分辨率的灵敏度明显较低，因此具有更强的鲁棒性。这项工作构成了3D Hodge理论在CNC粗加工中的首次严格应用，并为五轴体积加工提供了灵活，高效的解决方案。

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引用次数: 0

An efficient multi-threaded partitioning parallel strategy for tetrahedral mesh improvement 面向四面体网格改进的高效多线程分区并行策略

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2026-03-01 Epub Date: 2025-11-28 DOI: 10.1016/j.cad.2025.104021

Yunyun Du , Yingjian Fu , Junhe Xie , Guozhong Zhao , S.H. Lo , Leiping Xu , Zhenqun Guan

The improvement of large-scale meshes is a time-consuming process. In this study, a new coarse-grained multi-threaded parallel strategy is proposed to accelerate the improvement process. This strategy is characterized by the following features: (i) The improvement process is divided into two stages, which are parallelized independently. The first stage aims to improve the entire mesh, whereas the second stage targets low-quality elements; (ii) The background grid is utilized for partitioning. For the first stage, an adjacent-first search algorithm based on the uniform grid is proposed. This algorithm effectively addresses the demands of load balancing for task decomposition and demonstrates high efficiency on large meshes. For the second stage, the octree is employed given its enhanced adaptability to irregularly distributed low-quality elements; (iii) To ensure effective improvement, during parallel improvement, elements located near inter-partition boundaries that lack sufficient improvement space are collected and processed iteratively. A parallel partition expansion algorithm is proposed that predicts and occupies the space required for improving partitions, and employs atomic operations to avoid data races. This algorithm strives to maximize the available space for the partitions and accelerate the iterative process. Experimental results indicate that, without compromising improvement effectiveness, the parallel efficiency of the first stage can reach 73 % at 48 threads, whereas the second stage can achieve 77 % at 24 threads. The time required to improve one billion tetrahedra can be reduced from over 2.5 h to approximately 10 min.

大规模网格的改进是一个耗时的过程。在本研究中，提出了一种新的粗粒度多线程并行策略来加速改进过程。该策略具有以下特点：(i)改进过程分为两个阶段，每个阶段独立并行。第一阶段的目标是改善整个网格，第二阶段的目标是低质量的元素；利用背景网格进行分区。第一阶段，提出一种基于均匀网格的邻接优先搜索算法。该算法有效地解决了任务分解的负载均衡问题，在大网格下具有较高的效率。在第二阶段，由于八叉树对不规则分布的低质量元素具有较强的适应性，因此采用八叉树；（iii）为了确保有效改进，在并行改进时，收集位于分区间边界附近缺乏足够改进空间的元素，并对其进行迭代处理。提出了一种并行分区扩展算法，该算法预测和占用分区改进所需的空间，并采用原子操作避免数据竞争。该算法力求最大限度地利用分区的可用空间，加快迭代过程。实验结果表明，在不影响改进效果的前提下，第一级并行效率在48线程时可达73%，第二级并行效率在24线程时可达77%。改善10亿个四面体所需的时间可以从超过2.5小时减少到大约10分钟。

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引用次数: 0

RLCAD: Reinforcement learning training gym for revolution involved CAD command sequence generation RLCAD：革命强化学习训练馆，涉及CAD命令序列生成

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2026-03-01 Epub Date: 2025-12-17 DOI: 10.1016/j.cad.2025.104027

Xiaolong Yin , Xingyu Lu , Jiahang Shen , Jingzhe Ni , Hailong Li , Ruofeng Tong , Min Tang , Peng Du

A CAD command sequence is a typical parametric design paradigm in 3D CAD systems where a model is constructed by overlaying 2D sketches with operations such as extrusion, revolution, and Boolean operations. Although there is growing academic interest in the automatic generation of command sequences, existing methods and datasets only support operations such as 2D sketching, extrusion, and Boolean operations. This limitation makes it challenging to represent more complex geometries.

In this paper, we present a reinforcement learning (RL) training gym specifically designed for CAD model generation, along with an RL-based algorithm that generates command sequences from boundary representation (B-Rep) geometry within this training gym. Given an input B-Rep, the policy network of the RL algorithm first outputs an action. This action, together with previously generated actions, is processed within the gym to produce the corresponding CAD geometry, which is then fed back into the policy network. Rewards, computed by the difference between the generated and target geometries within the gym, are used to update the RL network. Our method supports operations beyond sketches, Boolean, and extrusion, including revolution operations. With this training gym, we achieve state-of-the-art (SOTA) quality in generating command sequences from B-Rep geometries.

CAD命令序列是3D CAD系统中典型的参数化设计范例，其中通过将2D草图与挤压、旋转和布尔运算等操作叠加来构建模型。尽管学术界对命令序列的自动生成越来越感兴趣，但现有的方法和数据集只支持2D草图绘制、挤压和布尔运算等操作。这一限制使得表示更复杂的几何形状具有挑战性。在本文中，我们提出了一个专门为CAD模型生成设计的强化学习（RL）训练馆，以及一个基于RL的算法，该算法从该训练馆内的边界表示（B-Rep）几何生成命令序列。给定输入B-Rep， RL算法的策略网络首先输出一个动作。此动作与先前生成的动作一起在体育馆内进行处理，生成相应的CAD几何图形，然后将其反馈到策略网络中。根据生成的几何形状和目标几何形状之间的差异计算奖励，用于更新RL网络。我们的方法支持绘图、布尔和挤压以外的操作，包括旋转操作。有了这个训练健身房，我们在生成B-Rep几何图形的命令序列方面达到了最先进的（SOTA）质量。

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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

Computer-Aided Design

Pub Date : 2026-03-01 Epub 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

An efficient layer-based rough machining framework for subtractive manufacturing 一种高效的分层粗加工框架

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2026-03-01 Epub Date: 2025-12-06 DOI: 10.1016/j.cad.2025.104025

Li-Yong Shen , Chang Liu , Hong-Yu Ma , Chun-Ming Yuan , Shuo-Peng Chen , Shi-Chu Li , Bo-Wen Zhang

Rough machining, which directly determines overall subtractive machining efficiency, aims to efficiently remove 70%–90% of the stock material to approximate the final workpiece geometry. Prior mainstream tool path generation algorithms for roughing primarily adopt the Contour Parallel method, which can ensure quality but generate curved paths with frequent acceleration/deceleration, limiting efficiency. To address this challenge, this paper presents a comprehensive high-efficiency rough machining framework that optimizes tool retraction count (idle paths) and path smoothness (encouraging linear trajectories in material-removal zones to enhance feedrates), is compatible with multiple tools and generates single start-end tool paths for simply connected regions. Experiments show an efficiency gain of

>

14% over the Contour Parallel method, effectively resolving the core trade-off of balancing quality and efficiency in the rough machining phase.

粗加工的目的是有效地去除70%-90%的库存材料，以接近最终工件的几何形状，直接决定整体减法加工效率。目前主流的粗加工刀具轨迹生成算法主要采用轮廓平行法，该方法能保证加工质量，但产生的曲线轨迹加减速频繁，限制了加工效率。为了解决这一挑战，本文提出了一个全面的高效粗加工框架，该框架优化了刀具回撤次数（空闲路径）和路径平滑度（鼓励材料去除区域的线性轨迹以提高进给速度），与多个刀具兼容，并为单连通区域生成单一的起止刀具路径。实验结果表明，该方法的效率提高了14%，有效地解决了粗加工阶段质量与效率之间的平衡问题。

引用次数: 0

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

Computer-Aided Design

Pub Date : 2026-03-01 Epub 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。

引用次数: 0

CAD model reconstruction of spherical-jointed lattice structures from point clouds with discrete planar convex hulls 基于离散平面凸壳点云的球节点阵结构CAD模型重建

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2026-03-01 Epub Date: 2025-12-22 DOI: 10.1016/j.cad.2025.104030

Bohan Zhang , Xiao Xiao , Mulin Yu , Chunjiang Wang , Zhiyuan Tang , Xiangdong Sun

Lattice structures consist of spatially discrete bars interconnected by joints. The complex geometric configurations of these lightweight structures present a challenge for point cloud segmentation, which is essential for CAD model reconstruction. We propose an efficient and robust pipeline to reconstruct CAD models of lattice structures from point clouds. The point cloud is first fitted by a set of planar convex hulls, which are optimized by local geometric operators guided by an energy function. The edges of discrete convex hulls are stored in an AABB tree for efficient hull adjacency queries. The convex hulls are then segmented based on their consistently oriented normals. Structural primitives are classified using principal component analysis of these oriented normals, and their dimensions are determined with least squares fitting of the associated points. The final CAD model is assembled from the detected primitives. The method has been validated using point clouds of various scales and complexities including real-scanned data. It shows robustness in the presence of uniform noise, outliers and data loss. Furthermore, its advantages in terms of reconstruction accuracy and efficiency are further highlighted in comparison to conventional and deep learning approaches.

点阵结构由空间上离散的由节点连接的杆组成。这些轻量化结构的复杂几何构型给点云分割带来了挑战，而点云分割是CAD模型重建的关键。我们提出了一种有效的、鲁棒的管道来从点云重建点阵结构的CAD模型。首先用一组平面凸包对点云进行拟合，然后用能量函数指导下的局部几何算子对凸包进行优化。为了实现高效的凸壳邻接查询，离散凸壳的边缘存储在AABB树中。然后根据它们一致的定向法线对凸包进行分割。结构基元的分类使用这些定向法线的主成分分析，并确定其尺寸与最小二乘拟合的相关点。最终的CAD模型由检测到的原语组装而成。该方法已在不同尺度和复杂程度的点云（包括实际扫描数据）上进行了验证。该方法在均匀噪声、异常值和数据丢失的情况下均表现出鲁棒性。此外，与传统和深度学习方法相比，该方法在重建精度和效率方面的优势进一步突出。

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引用次数: 0

Collocation and mass matrix in least-squares isogeometric analysis 最小二乘等几何分析中的配置与质量矩阵

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2026-03-01 Epub Date: 2025-12-16 DOI: 10.1016/j.cad.2025.104026

Gengchen Li, Hongwei Lin

In this paper, we conduct a systematic numerical analysis of the spectral properties of the collocation and mass matrices in the isogeometric least-squares collocation method (IGA-L), for the approximation of the Poisson problem with homogeneous Dirichlet boundary conditions. This study primarily focuses on the spectral properties of the IGA-L collocation and mass matrices in relation to the isogeometric discretization parameters, such as the mesh size, degree, regularity, spatial dimension, and the number and distribution of the collocation points. Through a comprehensive numerical investigation, we provide estimations for the condition number, as well as the maximum and minimum singular values, in relation to the mesh size, degree and regularity. Moreover, in this paper we also study the effects of the number and distribution of the collocation points on the spectral properties of the collocation matrix, providing insights into the optimization of the collocation points for achieving better-conditioned linear systems.

本文针对齐次Dirichlet边界条件下泊松问题的近似问题，对等几何最小二乘配点法（IGA-L）中配点法和质量矩阵的谱性质进行了系统的数值分析。本研究主要关注IGA-L配置矩阵和质量矩阵的光谱特性与等几何离散化参数的关系，如网格大小、度、规则性、空间维度以及配置点的数量和分布。通过全面的数值研究，我们提供了条件数的估计，以及最大和最小的奇异值，与网格尺寸，程度和规则有关。此外，本文还研究了搭配点的数量和分布对搭配矩阵谱性质的影响，为实现更好条件线性系统的搭配点优化提供了见解。

引用次数: 0

DFS-PINN: A Dynamic Feature Separation Physics-Informed Neural Network 动态特征分离物理信息神经网络

IF 3.1 3区计算机科学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Computer-Aided Design

Pub Date : 2026-02-01 Epub Date: 2025-10-14 DOI: 10.1016/j.cad.2025.103992

Zhuo Zhang , Sen Zhang , Yuan Zhao , Wei Wang , Hongzhou Wu , Xi Yang , Canqun Yang

Physics-Informed Neural Networks (PINNs) have shown great promise for solving partial differential equations (PDEs), but their application to multi-dimensional problems often suffers from the curse of dimensionality, leading to exponential growth in computational and memory requirements. Moreover, accurately capturing complex local features, such as those found in fluid flows, remains a significant challenge for existing approaches. To address these challenges, we propose the Dynamic Feature Separation Physics-Informed Neural Network (DFS-PINN), which introduces an innovative input-decoupling and dynamic interaction mechanism. This approach reduces computational complexity from

O (N^{d})

O (N \times d)

, enabling efficient training and improved accuracy for multi-dimensional problems, especially in real-time rendering and fluid simulations. When applied to the lid-driven cavity flow problem, DFS-PINN achieves a 6

\times

reduction in runtime and a 62

\times

reduction in memory usage with

2^{15}

collocation points, compared to standard PINNs. For large-scale datasets with over

2^{20}

points, DFS-PINN attains a mean squared error (MSE) of 0.000122, showcasing its superior computational efficiency and predictive accuracy. These results position DFS-PINN as a scalable and robust framework for solving multi-dimensional PDEs, demonstrating substantial improvements in both computational efficiency and modeling accuracy.

物理信息神经网络（pinn）在解决偏微分方程（PDEs）方面显示出了巨大的希望，但它们在多维问题上的应用经常受到维度的诅咒，导致计算和内存需求呈指数级增长。此外，准确捕捉复杂的局部特征，例如在流体流动中发现的特征，仍然是现有方法面临的重大挑战。为了解决这些挑战，我们提出了动态特征分离物理信息神经网络（DFS-PINN），它引入了一种创新的输入解耦和动态交互机制。这种方法将计算复杂度从0 （Nd）降低到0 (N×d)，实现了多维问题的高效训练并提高了精度，特别是在实时渲染和流体模拟中。当应用于盖子驱动的腔流问题时，与标准pinn相比，DFS-PINN在215个并置点上实现了6倍的运行时间减少和62倍的内存使用减少。对于超过220个点的大规模数据集，DFS-PINN的均方误差（MSE）为0.000122，显示出优越的计算效率和预测精度。这些结果将DFS-PINN定位为解决多维偏微分方程的可扩展和健壮的框架，在计算效率和建模精度方面都有实质性的改进。

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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

Computer-Aided Design

Pub Date : 2026-02-01 Epub 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。

引用次数: 0

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