Computer-Aided Design最新文献

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 : 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。

{"title":"RLCAD: Reinforcement learning training gym for revolution involved CAD command sequence generation","authors":"Xiaolong Yin , Xingyu Lu , Jiahang Shen , Jingzhe Ni , Hailong Li , Ruofeng Tong , Min Tang , Peng Du","doi":"10.1016/j.cad.2025.104027","DOIUrl":"10.1016/j.cad.2025.104027","url":null,"abstract":"<div><div>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.</div><div>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.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"192 ","pages":"Article 104027"},"PeriodicalIF":3.1,"publicationDate":"2025-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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 : 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

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 : 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。

{"title":"Multi-axis rough milling tool path generation based on 3D Hodge decomposition of vector fields","authors":"XuLin Cai, Wen-An Yang, XueFeng Yang, YouPeng You","doi":"10.1016/j.cad.2025.104028","DOIUrl":"10.1016/j.cad.2025.104028","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"192 ","pages":"Article 104028"},"PeriodicalIF":3.1,"publicationDate":"2025-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790738","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Self-intersection detection algorithm of sweep surfaces based on geometric features of spine curves 基于脊柱曲线几何特征的扫描曲面自交检测算法

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

Computer-Aided Design

Pub Date : 2025-12-09 DOI: 10.1016/j.cad.2025.104024

Chuan He , Aizeng Wang , Gang Zhao

In modern CAD/CAM workflows, sweep surfaces play a pivotal role in aerospace and automotive design, yet robust self‐intersection analysis remains an open challenge. This paper presents an approach for detecting self‐intersections in parametric sweep surfaces generated by a planar profile along a planar spine. We first classify self‐intersections into local and global categories and further distinguish those arising from individual offset‐curve interactions versus offset‐strip interactions. For local self‐intersections, we develop an efficient algorithm based on curvature extrema and offset‐distance extrema. For global self‐intersections caused by single offset curve, we address spine‐curve minimal‐distance pairs by decomposing the NURBS spine into curvature‐monotonic and globally convex Bézier segments; and introduce a critical offset distance concept for detecting endpoint‐induced self-intersections. For global self‐intersections caused by offset‐strip self‐intersections, we reduce detection to curve–curve intersection and curve–surface intersection subproblems. Numerical experiments demonstrate the proposed methods’ completeness, numerical stability, and applicability to high‐precision sweep surface modeling and downstream process verification.

在现代CAD/CAM工作流程中，扫描曲面在航空航天和汽车设计中发挥着关键作用，但强大的自交分析仍然是一个开放的挑战。本文提出了一种检测由平面轮廓沿平面脊线生成的参数化扫描曲面的自交的方法。我们首先将自交分为局部和全局两类，并进一步区分由个别偏移曲线相互作用和偏移带相互作用产生的自交。对于局部自交，我们提出了一种基于曲率极值和偏移距离极值的有效算法。对于由单偏移曲线引起的全局自交，我们通过将NURBS脊柱分解为曲率单调段和全局凸段来解决脊柱-曲线最小距离对；并引入了检测端点诱导自交的临界偏移距离概念。对于偏置条自交引起的全局自交，我们将检测简化为曲线-曲线交和曲线-曲面交子问题。数值实验证明了该方法的完备性、数值稳定性以及对高精度扫描曲面建模和下游工艺验证的适用性。

{"title":"Self-intersection detection algorithm of sweep surfaces based on geometric features of spine curves","authors":"Chuan He , Aizeng Wang , Gang Zhao","doi":"10.1016/j.cad.2025.104024","DOIUrl":"10.1016/j.cad.2025.104024","url":null,"abstract":"<div><div>In modern CAD/CAM workflows, sweep surfaces play a pivotal role in aerospace and automotive design, yet robust self‐intersection analysis remains an open challenge. This paper presents an approach for detecting self‐intersections in parametric sweep surfaces generated by a planar profile along a planar spine. We first classify self‐intersections into local and global categories and further distinguish those arising from individual offset‐curve interactions versus offset‐strip interactions. For local self‐intersections, we develop an efficient algorithm based on curvature extrema and offset‐distance extrema. For global self‐intersections caused by single offset curve, we address spine‐curve minimal‐distance pairs by decomposing the NURBS spine into curvature‐monotonic and globally convex Bézier segments; and introduce a critical offset distance concept for detecting endpoint‐induced self-intersections. For global self‐intersections caused by offset‐strip self‐intersections, we reduce detection to curve–curve intersection and curve–surface intersection subproblems. Numerical experiments demonstrate the proposed methods’ completeness, numerical stability, and applicability to high‐precision sweep surface modeling and downstream process verification.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"192 ","pages":"Article 104024"},"PeriodicalIF":3.1,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145790214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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 : 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

Gen-Porous: An INR-based generative framework for multiscale TPMS-like porous structure design and optimization Gen-Porous：一个基于inr的多尺度tpms类多孔结构设计和优化生成框架

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

Computer-Aided Design

Pub Date : 2025-12-02 DOI: 10.1016/j.cad.2025.104020

Shengfa Wang , Hao Zheng , Jiangbei Hu , Yu Jiang , Liang Du , Hao Du , Na Lei , Zhongxuan Luo

Porous structures originating from triply periodic minimal surfaces (TPMSs), referred to as TPMS-like porous structures, have been widely applied across various domains due to their advantageous structural properties. However, the limited morphological diversity and the simulation challenges posed by the complex features have impeded the further development and practical utilization of TPMS-like porous structures. Recent breakthroughs in artificial intelligence have demonstrated remarkable potential for creativity in industrial design. Capitalizing on these developments, we propose Gen-Porous - a novel framework employing implicit neural representations (INR) to design and optimize TPMS-like porous structures. The proposed methodology delineates a comprehensive paradigm for the acquisition and synthesis of various TPMS-like porous structures through Implicit Neural Representation (INR), facilitating simulation-driven optimization in a meshfree manner directly within the acquired latent space. Initially, we collect a dataset comprising multiscale TPMS-like porous structures, employing implicit functions to achieve this. Subsequently, we utilize an Auto-Decoder network architecture to encode these structures into a compact latent space via implicit neural representation learning, thereby permitting the generation of novel configurations with augmented morphological diversity. Moreover, we develop a differentiable computational framework using neural meshfree simulations. This integration not only makes optimization more efficient, but also simplifies sensitivity analysis through automatic differentiation, enabling diverse constraints and objectives to be more easily incorporated. We demonstrate the efficacy of the framework through a lightweight design case study, where optimized solutions are identified through latent space exploration. The core innovation lies in the neural unification of representation and simulation, achieving significant improvements in computational efficiency by circumventing traditional meshing bottlenecks and enabling full differentiability.

源自三周期极小表面（tpms）的多孔结构被称为类tpms多孔结构，由于其优越的结构特性而被广泛应用于各个领域。然而，有限的形态多样性和复杂特征带来的模拟挑战阻碍了tpms类多孔结构的进一步发展和实际应用。最近人工智能的突破显示了工业设计创造力的巨大潜力。利用这些发展，我们提出了Gen-Porous -一个采用隐式神经表征（INR）来设计和优化类似tpms的多孔结构的新框架。所提出的方法描述了通过隐式神经表征（INR）获取和合成各种类似tpms的多孔结构的综合范例，促进了在获取的潜在空间内直接以无网格方式进行模拟驱动的优化。首先，我们收集了一个包含多尺度tpms类多孔结构的数据集，采用隐式函数来实现这一目标。随后，我们利用Auto-Decoder网络架构通过隐式神经表征学习将这些结构编码到紧凑的潜在空间中，从而允许生成具有增强形态多样性的新配置。此外，我们开发了一个可微计算框架使用神经网格模拟。这种集成不仅提高了优化效率，而且通过自动区分简化了敏感性分析，使不同的约束和目标更容易合并。我们通过轻量级设计案例研究证明了该框架的有效性，其中通过潜在的空间探索确定了优化的解决方案。核心创新在于表征和模拟的神经统一，通过绕过传统网格瓶颈和实现完全可微性，显著提高了计算效率。

{"title":"Gen-Porous: An INR-based generative framework for multiscale TPMS-like porous structure design and optimization","authors":"Shengfa Wang , Hao Zheng , Jiangbei Hu , Yu Jiang , Liang Du , Hao Du , Na Lei , Zhongxuan Luo","doi":"10.1016/j.cad.2025.104020","DOIUrl":"10.1016/j.cad.2025.104020","url":null,"abstract":"<div><div>Porous structures originating from triply periodic minimal surfaces (TPMSs), referred to as TPMS-like porous structures, have been widely applied across various domains due to their advantageous structural properties. However, the limited morphological diversity and the simulation challenges posed by the complex features have impeded the further development and practical utilization of TPMS-like porous structures. Recent breakthroughs in artificial intelligence have demonstrated remarkable potential for creativity in industrial design. Capitalizing on these developments, we propose <em>Gen-Porous</em> - a novel framework employing implicit neural representations (INR) to design and optimize TPMS-like porous structures. The proposed methodology delineates a comprehensive paradigm for the acquisition and synthesis of various TPMS-like porous structures through Implicit Neural Representation (INR), facilitating simulation-driven optimization in a meshfree manner directly within the acquired latent space. Initially, we collect a dataset comprising multiscale TPMS-like porous structures, employing implicit functions to achieve this. Subsequently, we utilize an Auto-Decoder network architecture to encode these structures into a compact latent space via implicit neural representation learning, thereby permitting the generation of novel configurations with augmented morphological diversity. Moreover, we develop a differentiable computational framework using neural meshfree simulations. This integration not only makes optimization more efficient, but also simplifies sensitivity analysis through automatic differentiation, enabling diverse constraints and objectives to be more easily incorporated. We demonstrate the efficacy of the framework through a lightweight design case study, where optimized solutions are identified through latent space exploration. The core innovation lies in the neural unification of representation and simulation, achieving significant improvements in computational efficiency by circumventing traditional meshing bottlenecks and enabling full differentiability.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"192 ","pages":"Article 104020"},"PeriodicalIF":3.1,"publicationDate":"2025-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145737144","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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 : 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。

{"title":"An efficient multi-threaded partitioning parallel strategy for tetrahedral mesh improvement","authors":"Yunyun Du , Yingjian Fu , Junhe Xie , Guozhong Zhao , S.H. Lo , Leiping Xu , Zhenqun Guan","doi":"10.1016/j.cad.2025.104021","DOIUrl":"10.1016/j.cad.2025.104021","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"192 ","pages":"Article 104021"},"PeriodicalIF":3.1,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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 : 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

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 : 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。

{"title":"An STL-free method for concurrent optimization and fabrication of morphing strut-based lattice structures","authors":"Chao Feng, Liang Gao, Hao Li","doi":"10.1016/j.cad.2025.104012","DOIUrl":"10.1016/j.cad.2025.104012","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"192 ","pages":"Article 104012"},"PeriodicalIF":3.1,"publicationDate":"2025-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145685268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

Computer-Aided Design

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。

{"title":"Novel Kresling variant patterns for inverse origami design","authors":"Yan Zhao , Qingyue Liu , Yinglei Wei","doi":"10.1016/j.cad.2025.104008","DOIUrl":"10.1016/j.cad.2025.104008","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":"191 ","pages":"Article 104008"},"PeriodicalIF":3.1,"publicationDate":"2025-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145579685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0