{"title":"Neural PDE Solvers for Irregular Domains","authors":"Biswajit Khara , Ethan Herron , Aditya Balu , Dhruv Gamdha , Chih-Hsuan Yang , Kumar Saurabh , Anushrut Jignasu , Zhanhong Jiang , Soumik Sarkar , Chinmay Hegde , Baskar Ganapathysubramanian , Adarsh Krishnamurthy","doi":"10.1016/j.cad.2024.103709","DOIUrl":"https://doi.org/10.1016/j.cad.2024.103709","url":null,"abstract":"<div><p>Neural network-based approaches for solving partial differential equations (PDEs) have recently received special attention. However, most neural PDE solvers only apply to rectilinear domains and do not systematically address the imposition of boundary conditions over irregular domain boundaries. In this paper, we present a neural framework to solve partial differential equations over domains with irregularly shaped (non-rectilinear) geometric boundaries. Given the shape of the domain as an input (represented as a binary mask), our network is able to predict the solution field, and can generalize to novel (unseen) irregular domains; the key technical ingredient to realizing this model is a physics-informed loss function that directly incorporates the interior-exterior information of the geometry. We also perform a careful error analysis which reveals theoretical insights into several sources of error incurred in the model-building process. Finally, we showcase various applications in 2D and 3D, along with favorable comparisons with ground truth solutions.</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140633402","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}
{"title":"Denoising point clouds with fewer learnable parameters","authors":"Huankun Sheng , Ying Li","doi":"10.1016/j.cad.2024.103708","DOIUrl":"10.1016/j.cad.2024.103708","url":null,"abstract":"<div><p>Point cloud denoising is a crucial task in the field of geometric processing. Recent years have witnessed significant advancements in deep learning-based point cloud denoising algorithms. These methods, compared to traditional techniques, demonstrate enhanced robustness against noise and produce point cloud data of higher fidelity. Despite their impressive performance, achieving a balance between denoising efficacy and computational efficiency remains a formidable challenge in learning-based methods. To solve this problem, we introduce LPCDNet, a novel lightweight point cloud denoising network. LPCDNet consists of three main components: a lightweight feature extraction module utilizing trigonometric functions for relative position encoding; a non-parametric feature aggregation module to leverage semantic similarities for global context comprehension; and a decoder module designed to realign noise points with the underlying surface. The network is designed to capture both local details and non-local structures, thereby ensuring high-quality denoising outcomes with a minimal parameter count. Extensive experimental evaluations demonstrate that LPCDNet achieves comparable or superior performance to state-of-the-art methods, while significantly reducing the number of learnable parameters and the necessary running time.</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140401215","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}
{"title":"Latent Diffusion Models for Structural Component Design","authors":"Ethan Herron, Jaydeep Rade, Anushrut Jignasu, Baskar Ganapathysubramanian, Aditya Balu, Soumik Sarkar, Adarsh Krishnamurthy","doi":"10.1016/j.cad.2024.103707","DOIUrl":"https://doi.org/10.1016/j.cad.2024.103707","url":null,"abstract":"<div><p>Recent advances in generative modeling, namely Diffusion models, have revolutionized generative modeling, enabling high-quality image generation tailored to user needs. This paper proposes a framework for the generative design of structural components. Specifically, we employ a Latent Diffusion model to generate potential designs of a component that can satisfy a set of problem-specific loading conditions. One of the distinct advantages our approach offers over other generative approaches is the editing of existing designs. We train our model using a dataset of geometries obtained from structural topology optimization utilizing the SIMP algorithm. Consequently, our framework generates inherently near-optimal designs. Our work presents quantitative results that support the structural performance of the generated designs and the variability in potential candidate designs. Furthermore, we provide evidence of the scalability of our framework by operating over voxel domains with resolutions varying from <span><math><mrow><mn>3</mn><msup><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span> to <span><math><mrow><mn>12</mn><msup><mrow><mn>8</mn></mrow><mrow><mn>3</mn></mrow></msup></mrow></math></span>. Our framework can be used as a starting point for generating novel near-optimal designs similar to topology-optimized designs.</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140330715","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}
{"title":"A study on the design method of multivariable control chalice-shaped columns considering horizontal forces based on multi-objective optimization","authors":"Han Zhang , Hang Dai , Wenjing Ren","doi":"10.1016/j.cad.2024.103706","DOIUrl":"10.1016/j.cad.2024.103706","url":null,"abstract":"<div><p>This study proposes a design method to generate multivariable control chalice-shaped columns based on multi-objective optimization leveraging SubD modelling technology to smooth the geometric transition between slab and column. Taking horizontal force into consideration, the paper introduces total material usage as both an optimization objective and an important basis for final solution selection to gain a more elegant and dynamic form needed in architectural design. The paper applies the method to examples of both single-column and multi-column structures. The outcome is chalice-shaped columns balancing structural efficiency and aesthetic requirements.</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198554","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}
{"title":"Periodic implicit representation, design and optimization of porous structures using periodic B-splines","authors":"Depeng Gao, Yang Gao, Hongwei Lin","doi":"10.1016/j.cad.2024.103703","DOIUrl":"https://doi.org/10.1016/j.cad.2024.103703","url":null,"abstract":"<div><p>Porous structures are intricate solid materials with numerous small pores, extensively used in fields like medicine, chemical engineering, and aerospace. However, the design of such structures using computer-aided tools is a time-consuming and tedious process. In this study, we propose a novel representation method and design approach for porous units that can be infinitely spliced to form a porous structure. We use periodic B-spline functions to represent periodic or symmetric porous units. Starting from a voxel representation of a porous sample, the discrete distance field is computed. To fit the discrete distance field with a periodic B-spline, we introduce the constrained least squares progressive-iterative approximation algorithm, which results in an implicit porous unit. This unit can be subject to optimization to enhance connectivity and utilized for topology optimization, thereby improving the model’s stiffness while maintaining periodicity or symmetry. The experimental results demonstrate the potential of the designed complex porous units in enhancing the mechanical performance of the model. Consequently, this study has the potential to incorporate remarkable structures derived from artificial design or nature into the design of high-performing models, showing the promise for biomimetic applications.</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140121990","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}
Mauhing Yip , Annette Stahl , Christian Schellewald
{"title":"Robust Hole-Detection in Triangular Meshes Irrespective of the Presence of Singular Vertices","authors":"Mauhing Yip , Annette Stahl , Christian Schellewald","doi":"10.1016/j.cad.2024.103696","DOIUrl":"https://doi.org/10.1016/j.cad.2024.103696","url":null,"abstract":"<div><p>In this work, we present a boundary and hole detection approach that traverses all the boundaries of an edge-manifold triangular mesh, irrespectively of the presence of singular vertices, and subsequently determines and labels all holes of the mesh. The proposed automated hole-detection method is valuable to the computer-aided design (CAD) community as all boundary-edges within the mesh are utilized and for each boundary-edge the algorithm guarantees both the existence and the uniqueness of the boundary associated to it. As existing hole-detection approaches assume that singular vertices are absent or may require mesh modification, these methods are ill-equipped to detect boundaries/holes in real-world meshes that contain singular vertices. We demonstrate the method in an underwater autonomous robotic application, exploiting surface reconstruction methods based on point cloud data. In such a scenario the determined holes can be interpreted as information gaps, enabling timely corrective action during the data acquisition. However, the scope of our method is not confined to these two sectors alone; it is versatile enough to be applied on any edge-manifold triangle mesh. An evaluation of the method is performed on both synthetic and real-world data (including a triangle mesh from a point cloud obtained by a multibeam sonar). The source code of our reference implementation is available: <span>https://github.com/Mauhing/hole-detection-on-triangle-mesh</span><svg><path></path></svg>.</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S001044852400023X/pdfft?md5=15189e6bb47b6319e85b8bbbfd406777&pid=1-s2.0-S001044852400023X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140024119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jean-Philippe Jasienski , Yuchi Shen , Patrick Ole Ohlbrock , Denis Zastavni , Pierluigi D'Acunto
{"title":"A computational implementation of Vector-based 3D Graphic Statics (VGS) for interactive and real-time structural design","authors":"Jean-Philippe Jasienski , Yuchi Shen , Patrick Ole Ohlbrock , Denis Zastavni , Pierluigi D'Acunto","doi":"10.1016/j.cad.2024.103695","DOIUrl":"10.1016/j.cad.2024.103695","url":null,"abstract":"<div><p>This article presents a computational implementation for the Vector-based Graphic Statics (VGS) framework making it an effective CAD tool for the design of spatial structures in static equilibrium (VGS-tool). The paper introduces several key features that convert a purely theoretical graph and geometry based framework into a fully automated computational procedure, including the following new contributions: a general algorithm for constructing 3-dimensional interdependent force and force diagrams; the implementation of a procedure that allows the interdependent transformation of both diagrams; an approach to apply specific constraints to the computationally generated diagrams; the integration of the algorithms as a plug-in for a CAD environment (Grasshopper3D of Rhino3D). The main features of the proposed framework are highlighted with a design case study developed using the newly introduced CAD plug-in (namely the VGS-tool). This plugin uses synthetic-oriented and intuitive graphical representation to allow the user to design spatial structures in equilibrium as three-dimensional trusses. The goal is to facilitate collaboration between structural engineers and architects during the conceptual phase of the design process.</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139956210","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}
Marián Fabian, Pavel Chalmovianský, Martina Bátorová
{"title":"Homotopy Based Skinning of Spheres","authors":"Marián Fabian, Pavel Chalmovianský, Martina Bátorová","doi":"10.1016/j.cad.2024.103686","DOIUrl":"https://doi.org/10.1016/j.cad.2024.103686","url":null,"abstract":"<div><p>This paper deals with surfaces covering a set of spheres, whose centers form polyhedra. We propose novel methods of skinning based on homotopic deformation for the considered case. A method starts with a regular surface with a simple construction which can be deformed in a many ways. We demonstrate some of them in a few examples. The method is compared to the existing solutions by the new approach implementation and the visualization of the obtained results.</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0010448524000137/pdfft?md5=8a10d41ad4d81b9aa8d4f06921111f99&pid=1-s2.0-S0010448524000137-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139907355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Novel Topological Method for Automated and Exhaustive Wire Harness Design","authors":"Arun Rehal , Dibakar Sen","doi":"10.1016/j.cad.2024.103694","DOIUrl":"https://doi.org/10.1016/j.cad.2024.103694","url":null,"abstract":"<div><p>The current practice of manual wire harness design is labor-intensive, time-consuming, costly, and error-prone. In this paper, we present a methodology for completely automated wire harness design. We propose a topological approach that yields all the possible electrically admissible but topologically distinct harness system layouts that can be used to connect the specified terminals. Each generated layout represents a possible harness design. For layout generation, the proposed method utilizes the so-called routing graphs associated with the closed surfaces bounding the product. The developed methods are able to handle both — (1) On-Surface routing, when the wires are required to be constrained to the surface of the product, and (2) In-Air routing, when in addition to the surface the wires are also allowed to be embedded in product’s ambiance. For the final geometric embedding of the generated harnesses, we present an optimization-based methodology that determines the optimum lengths of the segments over which the wires should be bundled together. The results presented demonstrate the efficacy of the proposed approach through multiple realistic examples.</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139738051","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}
Pedro López-Adeva Fernández-Layos, Luis F.S. Merchante
{"title":"Convex Body Collision Detection Using the Signed Distance Function","authors":"Pedro López-Adeva Fernández-Layos, Luis F.S. Merchante","doi":"10.1016/j.cad.2024.103685","DOIUrl":"10.1016/j.cad.2024.103685","url":null,"abstract":"<div><p>We present a new algorithm to compute the minimum distance and penetration depth between two convex bodies represented by their Signed Distance Function (SDF). First, we formulate the problem as an optimization problem suitable for arbitrary non-convex bodies, and then we propose the ellipsoid algorithm to solve the problem when the two bodies are convex. Finally, we benchmark the algorithm and compare the results in collision detection against the popular Gilbert–Johnson–Keerthi (GJK) and Minkowski Portal Refinement (MPR) algorithms, which represent bodies using the support function. Results show that our algorithm has similar performance to both, providing penetration depth like MPR and, with better robustness, minimum distance like GJK. Our algorithm provides accurate and fast collision detection between implicitly modeled convex rigid bodies and is able to substitute existing algorithms in previous applications whenever the support function is replaced with the SDF.</p></div>","PeriodicalId":50632,"journal":{"name":"Computer-Aided Design","volume":null,"pages":null},"PeriodicalIF":4.3,"publicationDate":"2024-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0010448524000125/pdfft?md5=8461bf077f6c01f40cc9b071ee24014f&pid=1-s2.0-S0010448524000125-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139667516","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}