Abstract: In this work, we present a novel anisotropic lattice structure design and multi-scale optimization method that can generate conformal gradient lattice structures (CGLS). The goal of optimization is to achieve gradient density, adaptive orientation and variable scale (or periodic) lattice structures with the highest mechanical stiffness. The asymptotic homogenization method is employed for the calculation of the mechanical properties of various lattice structures. And an equation of elastic tensor and relative density of the unit cell is established. The established function above is then considered in the numerical optimization schemes. In the post-processing, we propose a numerical projecting method based on Fourier transform, which can synthesize conformal gradient lattice structure without changing the size and shape of the unit cells. Besides, the algorithm allows us to minimize distortion and prevent defects in the final lattice and keep the lattice structures smooth and continuous. Finally, in comparison with different parameters and methods are performed to demonstrate the superiority of our proposed method. The results show that the optimized anisotropic conformal gradient lattice structures are much stiffer and exhibit better structural robustness and buckling resistance than the uniform and the directly mapped designs.

Abstract: Computational analysis, modeling, and prediction of many phenomena in materials require a three-dimensional (3D) microstructure sample that embodies the salient features of the material system under study Since acquiring 3D microstructural images is expensive and time-consuming, an alternative approach is to extrapolate a 2D image (aka exemplar) into a virtual 3D sample and thereafter use the 3D image in the analyses and design In this paper, we introduce an efficient and novel approach based on transfer learning to accomplish this extrapolation-based reconstruction for a wide range of microstructures including alloys, porous media, and polycrystalline We cast the reconstruction task as an optimization problem where a random 3D image is iteratively refined to match its microstructural features to those of the exemplar VGG19, a pre-trained deep convolutional neural network, constitutes the backbone of this optimization where it is used to obtain the microstructural features and construct the objective function By augmenting the architecture of VGG19 with a permutation operator, we enable it to take 3D images as inputs and generate a collection of 2D features that approximate an underlying 3D feature map We demonstrate the applications of our approach with nine examples on various microstructure samples and image types (grayscale, binary, and RGB) As measured by independent statistical metrics, our approach ensures the statistical equivalency between the 3D reconstructed samples and the corresponding 2D exemplar quite well

Abstract: Point cloud filtering, the main bottleneck of which is removing noise (outliers) while preserving geometric features, is a fundamental problem in 3D field. The two-step schemes involving normal estimation and position update have been shown to produce promising results. Nevertheless, the current normal estimation methods including optimization ones and deep learning ones, often either have limited automation or cannot preserve sharp features. In this paper, we propose a novel feature-preserving normal estimation method for point cloud filtering with preserving geometric features. It is a learning method and thus achieves automatic prediction for normals. For training phase, we first generate patch based samples which are then fed to a classification network to classify feature and non-feature points. We finally train the samples of feature and non-feature points separately, to achieve decent results. Regarding testing, given a noisy point cloud, its normals can be automatically estimated. For further point cloud filtering, we iterate the above normal estimation and a current position update algorithm for a few times. Various experiments demonstrate that our method outperforms state-of-the-art normal estimation methods and point cloud filtering techniques, in terms of both quality and quantity.

Abstract: Four-dimensional (4D) printing, a new technology emerged from additive manufacturing (3D printing), is widely known for its capability of programming post-fabrication shape-changing into artifacts. Fused deposition modeling (FDM)-based 4D printing, in particular, uses thermoplastics to produce artifacts and requires computational analysis to assist the design processes of complex geometries. However, these artifacts are weak against structural loads, and the design quality can be limited by less accurate material models and numerical simulations. To address these issues, this paper propounds a composite structure design made of two materials – polylactic acid (PLA) and carbon fiber reinforced PLA (CFPLA) – to increase the structural strength of 4D printed artifacts and a workflow composed of several physical experiments and series of dynamic mechanical analysis (DMA) to characterize materials. We apply this workflow to 3D printed samples fabricated with different printed parameters to accurately characterize the materials and implement a sequential finite element analysis (FEA) to achieve accurate simulations. The accuracy of deformation induced by the triggering process is both computationally and experimentally verified with several creative design examples and is measured to be at least 95%, with a confidence interval of ( 0 . 972 , 0 . 985 ) . We believe the presented workflow is essential to the combination of geometry, material mechanism and design, and has various potential applications.

Abstract: Point cloud denoising has been an attractive problem in geometry processing. The main challenge is to eliminate noise while preserving different levels of features and preventing unnatural effects (such as over-sharpened artifacts on smoothly curved faces and cross artifacts on sharp edges). In this paper, we propose a novel feature-preserving framework to achieve these goals. Firstly, we newly define some discrete operators on point clouds, which can be used to construct a second order regularization for restoring a point normal field. Then, based on the filtered normals, we perform a feature detection step by a bi-tensor voting scheme. As will be seen, it is robust against noise and can locate underlying geometric features accurately. Finally, we reposition points with a multi-normal strategy by using a simple yet effective RANSAC-based algorithm. Intensive experimental results show that the proposed method performs favorably compared to other state-of-the-art approaches.

Abstract: In this paper, we propose a normal estimation method for unstructured 3D point clouds. In this method, a feature constraint mechanism called Local Plane Features Constraint (LPFC) is used and then a multi-scale selection strategy is introduced. The LPFC can be used in a single-scale point network architecture for a more stable normal estimation of the unstructured 3D point clouds. In particular, it can partly overcome the influence of noise on a large sampling scale compared to the other methods which only use regression loss for normal estimation. For more details, a subnetwork is built after point-wise features extracted layers of the network and it gives more constraints to each point of the local patch via a binary classifier in the end. Then we use multi-task optimization to train the normal estimation and local plane classification tasks simultaneously. Via LPFC, the normal estimation network could obtain more distinguish point-wise plane-aware features that can describe the differences of each point on the local patch. Finally, thanks to the distinguish features constraint, we can obtain a more robust and meaningful global feature that can be used to regress the normal of the local patch. Also, to integrate the advantages of multi-scale results, a scale selection strategy is adopted, which is a data-driven approach for selecting the optimal scale around each point and encourages subnetwork specialization. Specifically, we employed a subnetwork called Scale Estimation Network to extract scale weight information from multi-scale features. The multi-scale method can well reduce the cost time while persevere the estimation accuracy. More analysis is given about the relations between noise levels, local boundary, and scales in the experiment. These relationships can be a better guide to choosing particular scales for a particular model. Besides, the experimental result shows that our network can distinguish the points on the fitting plane accurately and this can be used to guide the normal estimation and our multi-scale method can improve the results well. Compared to some state-of-the-art surface normal estimators, our method is robust to noise and can achieve competitive results.

Abstract: The choice of knot vector has immense influence on the resulting accuracy of a B-spline approximation of a curve However, despite the significance of this problem and the various solutions that were proposed in the literature, optimizing the number and placement of knots remains a difficult task This paper presents a novel method for the approximation of a curve by a B-spline of arbitrary order, which automatically determines a knot vector that achieves high approximation quality At the core of our approach is a feature function that characterizes the amount and spatial distribution of geometric details in the input curve by estimating its derivatives Knots are then selected in such a way as to evenly distribute the feature contents across their intervals A comparison to the state of the art for a wide variety of curves shows that our method is faster and achieves more accurate reconstruction results, while typically reducing the number of necessary knots

Abstract: 3D printing techniques such as Fused Deposition Modeling (FDM) have enabled the fabrication of complex geometry quickly and cheaply Objects are produced by filling (a portion of) the 2D polygons of consecutive layers with contour-parallel extrusion toolpaths Uniform width toolpaths consisting of inward offsets from the outline polygons produce over- and underfill regions in the center of the shape, which are especially detrimental to the mechanical performance of thin parts In order to fill shapes with arbitrary diameter densely the toolpaths require adaptive width Existing approaches for generating toolpaths with adaptive width result in a large variation in widths, which for some hardware systems is difficult to realize accurately In this paper we present a framework which supports multiple schemes to generate toolpaths with adaptive width, by employing a function to decide the number of beads and their widths Furthermore, we propose a novel scheme which reduces extreme bead widths, while limiting the number of altered toolpaths We statistically validate the effectiveness of our framework and this novel scheme on a data set of representative 3D models, and physically validate it by developing a technique, called back pressure compensation, for off-the-shelf FDM systems to effectively realize adaptive width

Abstract: Designing the layouts and simulating the assembly of cables are based on flexible cable modeling technology. In this paper, we review the methods used to model deformable cable-like objects. At present, the physical models of one-dimensional cable-like flexible objects are mostly elastic. There are different types of models, which we can classify as mass–spring, multi-body, elastic rod, dynamic spline, finite element models, and so forth. There are a number of significant issues, such as how to couple these models in an appropriate way, take more physical behaviors into account, and develop a more sophisticated/comprehensive model. Some researchers have also studied how to model plastic cables, thin viscous threads, and branched cables; however, those issues are far from fully resolved and need to be studied further. Furthermore, we believe that in future research it will be important to model the cross-sections of cables with different or deformable shapes and complex internal structures, and consider the influence of temperature and alternating stress.

Abstract: Anisotropic mesh adaptation is important for accurately simulating physical phenomena at reasonable computational costs. Previous work in anisotropic mesh adaptation has been restricted to studies in two- or three-dimensional computational domains. However, in order to accurately simulate time-dependent physical phenomena in three dimensions, a four-dimensional mesh adaptation tool is needed. This work develops a four-dimensional anisotropic mesh adaptation tool to support time-dependent three-dimensional numerical simulations. Anisotropy is achieved through the use of a background metric field and the mesh is adapted using a dimension-independent cavity framework. Metric-conformity – in the sense of edge lengths, element quality and element counts – is effectively demonstrated on four-dimensional benchmark cases within a unit tesseract in which the background metric is prescribed analytically. Next, the metric field is optimized to minimize the approximation error of a scalar function with discontinuous Galerkin discretizations on four-dimensional domains. We demonstrate that this four-dimensional mesh adaptation algorithm achieves optimal element sizes and orientations. To our knowledge, this is the first presentation of anisotropic four-dimensional meshes.

Abstract: A new numerical method is presented for reconstructing three-dimensional (3D) microstructures from two-dimensional (2D) sections, imaged on orthogonal planes, by exploiting the complete red–green–blue (RGB) color space. The algorithm reconstructs 3D models through sampling voxel neighborhoods to representative 2D micrographs, based upon a Markovian assumption. The sampling is followed by an optimization procedure, ensuring smoothness across the orthogonal sections of the synthesized voxels. Previous 3D Markov random field (MRF) microstructure reconstruction techniques were restricted to traditional grayscale images only. This method now enables the use of the entire RGB spectrum, employing a histogram matching step. This paper examines the algorithm’s accurate representation of orientations and morphologies, encompassing a variety of micrographs from electron backscatter diffraction (EBSD) and polarized light microscopy.

Abstract: The newly emerged hybrid manufacturing platform that incorporates both additive manufacturing (AM) and five-axis machining modules makes it possible to manufacture parts of complex shapes with high finish-surface quality that are impossible to be produced solely by either machining or additive manufacturing. In general, a hybrid manufacturing process is signified by an alternating sequence of AM operations and machining operations that alternatingly build and machine an in-process workpiece into the final design shape. Aside from other considerations, collision avoidance between the in-process workpiece and both the cutting tool and the material-dispensing nozzle is one of the most critical constraints that affect the determination of the alternating sequence. Due to the newness of hybrid manufacturing technology, currently there has been few systematic studies of this collision avoidance problem in which the obstacles are in a constant state of growing, especially on nozzle collision avoidance which – though never an issue in the traditional 2.5-axis AM because the in-process workpiece is always below the printing nozzle – now becomes a real concern in hybrid manufacturing as the in-process workpiece now dynamically grows and is not constrained by the current build layer. The nozzle collision problem is particularly pronounced in metallic hybrid manufacturing where the nozzle compartment typically is large and has a complex shape. In this paper, we conduct a thorough study of this collision avoidance problem in hybrid manufacturing and present a deterministic algorithm for automatically generating a collision-free sequence of hybrid manufacturing with the least alternations for a solid part. Specifically, as long as the part can be represented in the so-called columnar form, and the build layers are either planar or on concentric conic surfaces, for any given tool and nozzle, our algorithm will automatically generate an alternating sequence of minimum length whose corresponding hybrid manufacturing process is guaranteed to be free of collision with either the tool or nozzle The columnar representation actually embodies a large class of industrial parts such as aero-engine blisks and gears while concentric conic build layers are the most common type of slicing strategy adopted in multi-axis 3D printing. Ample computer simulation tests of the proposed algorithm are performed and the results confirm the correctness and effectiveness of the proposed algorithm.

Abstract: Rivet detection is usually the first step for almost all surface and rivet inspection methods in aircraft skins. With 3D laser scanners, one can rapidly obtain the precise 3D information, i.e. point cloud, of the surface and rivets. Subsequently, rivet detection can be converted to a multiple-structure fitting problem from 3D point clouds. However, robust structure fitting from scanned 3D point cloud remains an open problem due to its challenging nature, such as noise and outliers, irregular sampling density and missing scanning. To reduce the fitting variability, this paper presents an automated density-aware multiple-structure fitting algorithm to perform rivet detection based on a 3D point cloud. The key observation is that the local density of points belonging to the rivet contour is relatively higher. We hereby formulate rivet detection as a multiple structure fitting problem with a density-based significance measure. By considering the local distribution characteristics, we first perform adaptive density enhancement on the basic local density. Subsequently, we detect the potential circle hypotheses and thereby extract rivet contours. By performing the mode-seeking algorithm on hypergraphs, all the circle structures can be obtained simultaneously. Overall, the proposed extraction algorithm is able to efficiently and effectively detect rivets from the raw scanned point clouds. We also demonstrate that the proposed algorithm achieves significant superiority over several state-of-the-art model fitting methods on the real scanned point cloud via experimental results. Moreover, we give the application of our algorithm on rivet flush inspection, showing that our method can assist in the rapid measurement of riveting quality.

Abstract: Normal filtering is a fundamental step of feature-preserving mesh denoising. Methods based on convolutional neural networks (CNNs) have recently made their debut for normal filtering. However, they require complicated voxelization and/or projection operations for regularization, and afford an overall denoising accuracy with few powers of preserving surface features. We devise a novel normal filtering neural network algorithm, which we call as NormalF-Net. NormalF-Net consists of two cascaded subnetworks with a comprehensive loss function. The first subnetwork learns mapping from non-local patch-group normal matrices (NPNMs) to their ground-truth low-rank counterparts for denoising, and the second subnetwork learns mapping from the recovered NPNMs to the ground-truth normals for normal refinement. Different from existing learning-based methods, NormalF-Net, which bridges the connection between CNNs and geometry domain knowledge of non-local similarity, can not only preserve surface features when removing different levels and types of noise, but be free of voxelization/projection. NormalF-Net has been validated on different datasets of meshes with multi-scale features yet corrupted by noise of different distributions. Experimental results consistently demonstrate clear improvements of our method over the state-of-the-arts in both noise-robustness and feature awareness.

Abstract: The present research develops a direct multiscale topology optimization method for additive manufacturing (AM) of coated structures with nonperiodic infill by employing an adaptive mapping technique of adaptive geometric components (AGCs). The AGCs consist of a framework of macro-sandwich bars that represent the macrostructure with the solid coating and a network of micro-solid bars that represent the nonperiodic infill at the microstructural scale. The macrostructure including the coating skin and the internal architecture of the microstructures of cellular structures is simultaneously optimized by straightforwardly searching optimal geometries of the AGCs. Compared with most existing methods, the proposed method does not require material homogenization technique at the microscale; the continuity of microstructures and structural porosities are ensured without additional constraints; Finite element analysis (FEA) and geometric parameter updates are required only once for each optimization iteration. AGCs allow us to model coated structures with porosity infill on a coarse finite element mesh. The adaptive mapping technique may reduce mapping time by up to 50%. Besides, it is easy to control the length scales of the coating and infill as desired to make it possible with AM. This investigation also explores the ability to realize concurrent designs of coated structures with nonperiodic infill patterns using 3D printing techniques.

Abstract: We develop a framework that creates a new polygonal mesh representation of the sparse infill domain of a layer-by-layer 3D printing job. We guarantee the existence of a single, continuous tool path covering each connected piece of the domain in every layer in this graphical model. We also present a tool path algorithm that traverses each such continuous tool path with no crossovers. The key construction at the heart of our framework is a novel Euler transformation which converts a 2-dimensional cell complex K into a new 2-complex K ˆ such that every vertex in the 1-skeleton G ˆ of K ˆ has even degree. Hence G ˆ is Eulerian, and an Eulerian tour can be followed to print all edges in a continuous fashion without stops. We start with a mesh K of the union of polygons obtained by projecting all layers to the plane. First we compute its Euler transformation K ˆ . In the slicing step, we clip K ˆ at each layer using its polygon to obtain a complex that may not necessarily be Euler. We then patch this complex by adding edges such that any odd-degree nodes created by slicing are transformed to have even degrees again. We print extra support edges in place of any segments left out to ensure there are no edges without support in the next layer above. These support edges maintain the Euler nature of the complex. Finally, we describe a tree-based search algorithm that builds the continuous tool path by traversing “concentric” cycles in the Euler complex. Our algorithm produces a tool path that avoids material collisions and crossovers, and can be printed in a continuous fashion irrespective of complex geometry or topology of the domain (e.g., holes). We implement our test our framework on several 3D objects. Apart from standard geometric shapes including a nonconvex star, we demonstrate the framework on the Stanford bunny. Several intermediate layers in the bunny have multiple components as well as complicated geometries.

Abstract: Geometric predicates are a basic ingredient to implement a vast range of algorithms in computational geometry. Modern implementations employ floating point filtering techniques to combine efficiency and robustness, and state-of-the-art predicates are guaranteed to be always exact while being only slightly slower than corresponding (inexact) floating point implementations. Unfortunately, if the input to these predicates is an intermediate construction of an algorithm, its floating point representation may be affected by an approximation error, and correctness is no longer guaranteed. This paper introduces the concept of indirect geometric predicate: instead of taking the intermediate construction as an explicit input, an indirect predicate considers the primitive geometric elements which are combined to produce such a construction. This makes it possible to keep track of the floating point approximation, and thus to exploit efficient filters and expansion arithmetic to exactly resolve the predicate with minimal overhead with respect to a naive floating point implementation. As a representative example, we show how to extend standard predicates to the case of points of intersection of linear elements (i.e. lines and planes) and show that, on classical problems, this approach outperforms state-of-the-art solutions based on lazy exact intermediate representations.

Abstract: Trochoidal milling is widely used in slotting and pocketing operation owing to its unique cyclic pattern that restricts the tool-workpiece engagement and hence reduces the cutting force load and helps heat dissipation. Especially when cutting extremely hard materials such as super titanium alloy, trochoidal tool path has been a good milling strategy for reducing tool wear and restraining heat generation. However, the conventional trochoidal milling is two-dimensional in nature and thus can only apply to 2.5D machining. Aiming at further extending the application of trochoidal milling, in this paper we propose a novel five-axis trochoidal flank milling strategy applicable to machining more complex 3D shaped cavities. Rather than the traditional circular trochoidal pattern, our proposed method can adaptively generate a spatial cubic curve-based cyclic five-axis tool path according to the given complex 3D cavity, and, subject to the given tool-workpiece engagement threshold, the material removal rate is maximized in the process of tool path generation. In addition, we also present a scheme of adjusting the tool orientation at the boundary surfaces of the cavity to mitigate the overcut in case they are non-developable. Both computer simulation and physical cutting experiments are conducted and the preliminary results have given a definitive confirmation on the correctness and effectiveness of the proposed method.

Abstract: Functionally graded conformal lattice structures (FGCLSs) are a particular type of lattice structure in which lattice unit cells are populated following structural boundaries and the density of the lattice unit cells is optimally distributed. Additionally, additively manufactured parts are reported to have anisotropic mechanical properties that highly depend on the part build orientations. This is extremely important in designing FGCLS parts where orientations of lattice unit cells are not uniform, making the build orientation selection more challenging. In this study, a concurrent density distribution and build orientation optimization framework of additively manufactured FGCLSs for structure-performance maximization was developed. The proposed approach was validated via case studies on lightweight part design for compliance minimization, with three design examples having geometric complexity levels varying from low to high. The results showed that the proposed concurrent optimization method was more effective at enhancing structural performance than optimizing only the density distribution of the structure. In addition, the build orientation configurations determined by the proposed method provided better structural performance compared to those determined using other slicing software. Moreover, compared to the pseudo-worst build orientation configuration, the configuration obtained from the proposed approach could enhance structural performance by up to 47.56%.

Abstract: Process planning for additive manufacturing (AM) today relies heavily on multi-physics, multi-scale simulation. The focus of this paper is on one aspect of AM simulation, namely, part-level elasto-plastic simulation for residual stress and distortion predictions. This is one of the crucial steps in AM process optimization, but is computationally expensive, often requiring the use of large computer clusters. The primary bottleneck in elasto-plastic simulation is the repeated solution of large linear systems of equations. While there is a wide range of linear solvers, most cannot exploit the unique structured nature of the mesh underlying AM simulation. Here, we revisit a specific matrix-free solver, namely rigid-body deflated solver that has been successfully deployed for solving large linear elastic problems in such scenarios. The salient feature of this solver is that the stiffness matrix is never assembled, thereby reducing the memory requirements significantly, leading to large computational gains. The objective of this paper is to extend the above solver to elasto-plasticity by efficiently updating the element tangent stiffness matrices, and the corresponding deflation matrix. The performance of the proposed method is evaluated on a benchmark problem using multi-core CPU and GPU architectures, and compared against ANSYS. Then, part-level residual stresses and distortion are predicted using the proposed solver. The present work is restricted to associative plasticity with von-Mises yield criteria, but can be extended to other plasticity models.

Abstract: A framework is proposed for facilitating the exploration process during the early design phase through computational sketch synthesis and interactive 3D reconstruction. In that phase, designers concentrate on developing concepts through numerous alternatives. Therefore, they constantly sketch so that they can rapidly visualize their ideas. Recently, the design industry has attempted to streamline the design process by implementing 3D model generation in the early design phase so that ideas may be more thoroughly explored, thus improving concept and final design conformance; however, efficiency issues have arisen. In this study, a 3D computational sketch synthesis framework was developed comprising two major components. First, a robust method was proposed to synthesize design alternatives by interpolating an input sketch with sketches in a database so that unvisited combinations may be explored. Secondly, a novel interactive 3D model reconstruction method was developed to facilitate the shape transition of design elements so that designers can quickly evaluate the potential of a large number of design variations. Finally, an interface for design refinement was developed so that designs may be embodied by sketching over the 3D model. To test the proposed methodology, expert designers were recruited for a validation experiment with two conditions followed up by in-depth interviews. In the first condition, the participants were asked to sketch based on a design brief in their current working manner. In the second condition, they were asked to create designs using the proposed framework. It was tested whether there was a difference in the design outcomes. It was demonstrated that the proposed framework resulted in more satisfactory and higher-quality designs and generated design alternatives faster and in greater quantities. All participants agreed that the framework could be useful in the early design phase and responded that the proposed system provides more design inspiration than traditional design methods. Most importantly, it was demonstrated that the proposed framework could enhance the reevaluation potential of design concepts and assist in making better-informed design decisions.

Abstract: This paper presents a novel jerk minimization algorithm in the context of multi-axis flank CNC machining. The toolpath of the milling axis in a flank milling process, a ruled surface, is reparameterized by a B-spline function, whose control points and knot vector are unknowns in an optimization-based framework. The total jerk of the tool’s motion is minimized, implying the tool is moving as smooth as possible, without changing the geometry of the given toolpath. Our initialization stage stems from measuring the ruling distance metric (RDM) of the ruled surface. We show on several examples that this initialization reliably finds close initial guesses of jerk-minimizers and is also computationally efficient. The applicability of the presented approach is illustrated by some practical case studies.

Abstract: This paper presents a simple yet effective and efficient method for feature-preserving surface smoothing. Through analyzing the differential property of surfaces, we show that the conventional discrete Laplacian operator with uniform weights is not applicable to feature points at which the surface is non-differentiable and the second order derivatives do not exist. To overcome this difficulty, we propose a Half-kernel Laplacian Operator (HLO) as an alternative to the conventional Laplacian. Given a vertex v , HLO first finds all pairs of its neighboring vertices and divides each pair into two subsets (called half windows); then computes the uniform Laplacians of all such subsets and subsequently projects the computed Laplacians to the full-window uniform Laplacian to alleviate flipping and degeneration. The half window with least regularization energy is then chosen for v . We develop an iterative approach to apply HLO for surface denoising. Our method is conceptually simple and easy to use because it has a single parameter, i.e., the number of iterations for updating vertices. We show that our method can preserve features better than the popular uniform Laplacian-based denoising and it significantly alleviates the shrinkage artifact. Extensive experimental results demonstrate that HLO is better than or comparable to state-of-the-art techniques both qualitatively and quantitatively and that it is particularly good at handling meshes with high noise. Also, it outperforms all other compared methods in terms of computational time. We make our executable program publicly available.

Abstract: We present an approach to map Additive Manufacturing (AM) process parameters and a given tool path to a representation of the as-manufactured shape that captures machine-specific manufacturing uncertainty. Multi-physics models that capture the deposition process at the smallest manufacturing scale are solved to accurately simulate local material accumulation. A surrogate model for the multiphysics simulation is used to practically simulate the material accumulation by locally varying the spatial distribution of material along the tool path. This generates a training set representing a variational class of as-manufactured shapes. Machine specific manufacturing uncertainty is then represented as a 3D kernel obtained by deconvolving the simulated as-printed shape with the tool path. This kernel provides a good estimate of the probability of local material accumulation independent of the chosen part and tool-path. Convolution of the kernel with a tool-path combined with an appropriate super-level-set of the resulting field provides a computationally efficient way to estimate the as-manufactured shape of AM parts. The efficiency results from the highly parallelized implementation of convolution on the GPU. We demonstrate high-resolution shape estimation and visualization of as-printed parts constructed using this approach. We validate the method using data generated by simulating a build process for droplet-based AM, by performing model order reduction of a system of partial differential equations for the 3D Navier–Stokes multiphase flows coupled with heat-transfer and phase change.

Abstract: This paper presents a fast and accurate method using the Allen–Cahn (AC) equation with a fidelity term for curves smoothing of 2 D shapes and volume smoothing of 3 D shapes. The modified AC equation has a good smoothing dynamics and it is coupled with a fidelity term. The fidelity term forces the solution of the equation to be a close approximation to the original data. We use a hybrid explicit finite difference method to solve the equation. Therefore, we do not have any restriction on the shape of the computational domains. Several numerical tests for both the curve and surface smoothing problems are performed to demonstrate the robustness and efficiency of the proposed method. In particular, the proposed algorithm is useful for the 3D printing applications.

Abstract: The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This work is supported by National Natural Science Foundation of China (61772016, 61772312), the NSFC-Zhejiang Joint Fund for the Integration of Industrialization and Informatization (U1909210), the Dalian University of Technology 2019 Discipline Platform Fund (1000-82212201), the National Young Talents Program of China, and the Strategic Priority Research Program of Chinese Academy of Science (XDA21010205).

Abstract: Functionally (implicitly) defined 3D objects allow us to quite easily model parts with complex topology such as lattices and organic-like structures with a high level of flexibility. Previous works in this area are based on the direct generation of CNC programs for the 3D printing of these objects and are backed by the growing support for this input format from hardware manufacturers. Efficient contouring of functionally defined models, however, is not an easy task. In this paper, we develop an algorithm for contour extraction of implicitly defined objects for direct additive manufacturing (AM). By comparing various adaptive and exhaustive (non-adaptive) methods of the function representation contouring for AM (FRepCAM), we make a set of recommendations for its usage depending on the specific resolution of the printer. In particular, we use a novel criterion based on affine arithmetic to maintain efficiency while preserving the robustness of the contouring process. The techniques mentioned were evaluated for algebraic and non-algebraic solids and heterogeneous models under a resolution that is comparable with that of current AM technology. The results show that the chosen adaptation criteria allow us to efficiently obtain a contour for complex models and generally outperform those of traditional algorithms based on exhaustive enumeration, especially for high-resolution contouring. In addition, the results present proof of the printability of implicitly defined objects with different 3D printing techniques.