Computer-Aided Design最新文献

A method of generating a continuous toolpath that can be biased in a user-specified direction of travel is proposed for the fabrication of density-based functionally graded parts through Additive Manufacturing (AM). The methodology utilizes Lin Kernighan's (LK) Travelling Salesman Problem (TSP) solver over a digitized grid within the contour domain to generate a toolpath with minimal lifts and a common start and end point. Three force-based methods of digitization, namely rectangular, circular, and contour adaptive, are proposed in this work. Each of these methods initialize from a structured or an unstructured grid, where the grid points are assumed to be connected with either linear (rectangular digitization) or a combination of linear and torsional springs (circular and contour adaptive digitization). Enforcing an equilibrium amongst the spring forces and appropriately selecting the ideal spring length, the necessary configuration of grid points can be generated for a desired toolpath.

The density of grid points (consequently, part density) can be varied through the user-defined input function or an image-based density map imposed on the ideal spring length over the contour domain. The proposed toolpath, as a case study, was implemented for printing a bone with density prescribed through a CT scan image stack. The CT scan of the printed part qualitatively establishes the conformity of the toolpath to the user-specified density gradient.

We introduce a progressive and iterative method for B-spline curve and surface approximation, incorporating parameter correction based on the Newton iterative method. While parameter corrections have been used in existing Geometric Approximation (GA) methods to enhance approximation quality, they suffer from low computational efficiency. Our approach unifies control point updates and parameter corrections in a progressive and iterative procedure, employing a one-step strategy for parameter correction. We provide a theoretical proof of convergence for the algorithm, demonstrating its superior computational efficiency compared to current GA methods. Furthermore, the provided convergence proof offers a methodology for proving the convergence of existing GA methods with location parameter correction.

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.

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.

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 $32^3$ to $128^3$. Our framework can be used as a starting point for generating novel near-optimal designs similar to topology-optimized designs.

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.

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.

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: https://github.com/Mauhing/hole-detection-on-triangle-mesh.

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.

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.