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TPMS is consistently described in the functional representation (F-rep) format, while modern CAD/CAM/CAE tools are built upon the boundary representation (B-rep) format. To solve this issue, translating TPMS to STEP is needed, called TPMS2STEP. This paper provides constraint matrices and convergence proof of TPMS2STEP so that $C^2$ continuity and an error bound of $2\epsilon$ on the deviation can be ensured during the translation., Comment: arXiv admin note: text overlap with arXiv:2405.07946

This paper presents a learning-based method to solve the traditional parameterization and knot placement problems in B-spline approximation. Different from conventional heuristic methods or recent AI-based methods, the proposed method does not assume ordered or fixed-size data points as input. There is also no need for manually setting the number of knots. It casts the parameterization and knot placement problems as a sequence-to-sequence translation problem, a generative process automatically determining the number of knots, their placement, parameter values, and their ordering. Once trained, SplineGen demonstrates a notable improvement over existing methods, with a one to two orders of magnitude increase in approximation accuracy on test data.

Lattice structures have been widely used in applications due to their superior mechanical properties. To fabricate such structures, a geometric processing step called triangulation is often employed to transform them into the STL format before sending them to 3D printers. Because lattice structures tend to have high geometric complexity, this step usually generates a large amount of triangles, a memory and compute-intensive task. This problem manifests itself clearly through large-scale lattice structures that have millions or billions of struts. To address this problem, this paper proposes to transform a lattice structure into an intermediate model called meta-mesh before undergoing real triangulation. Compared to triangular meshes, meta-meshes are very lightweight and much less compute-demanding. The meta-mesh can also work as a base mesh reusable for conveniently and efficiently triangulating lattice structures with arbitrary resolutions. A CPU+GPU asynchronous meta-meshing pipeline has been developed to efficiently generate meta-meshes from lattice structures. It shifts from the thread-centric GPU algorithm design paradigm commonly used in CAD to the recent warp-centric design paradigm to achieve high performance. This is achieved by a new data compression method, a GPU cache-aware data structure, and a workload-balanced scheduling method that can significantly reduce memory divergence and branch divergence. Experimenting with various billion-scale lattice structures, the proposed method is seen to be two orders of magnitude faster than previously achievable.

Triply periodic minimal surface (TPMS) is emerging as an important way of designing microstructures. However, there has been limited use of commercial CAD/CAM/CAE software packages for TPMS design and manufacturing. This is mainly because TPMS is consistently described in the functional representation (F-rep) format, while modern CAD/CAM/CAE tools are built upon the boundary representation (B-rep) format. One possible solution to this gap is translating TPMS to STEP, which is the standard data exchange format of CAD/CAM/CAE. Following this direction, this paper proposes a new translation method with error-controlling and $C^2$ continuity-preserving features. It is based on an approximation error-driven TPMS sampling algorithm and a constrained-PIA algorithm. The sampling algorithm controls the deviation between the original and translated models. With it, an error bound of $2\epsilon$ on the deviation can be ensured if two conditions called $\epsilon$-density and $\epsilon$-approximation are satisfied. The constrained-PIA algorithm enforces $C^2$ continuity constraints during TPMS approximation, and meanwhile attaining high efficiency. A theoretical convergence proof of this algorithm is also given. The effectiveness of the translation method has been demonstrated by a series of examples and comparisons.

Recent advancements in implicit 3D representations and generative models have markedly propelled the field of 3D object generation forward. However, it remains a significant challenge to accurately model geometries with defined sharp features under parametric controls, which is crucial in fields like industrial design and manufacturing. To bridge this gap, we introduce a framework that employs Large Language Models (LLMs) to generate text-driven 3D shapes, manipulating 3D software via program synthesis. We present 3D-PreMise, a dataset specifically tailored for 3D parametric modeling of industrial shapes, designed to explore state-of-the-art LLMs within our proposed pipeline. Our work reveals effective generation strategies and delves into the self-correction capabilities of LLMs using a visual interface. Our work highlights both the potential and limitations of LLMs in 3D parametric modeling for industrial applications., Comment: 10 pages, 6 figures

Kagome lattice hosts a plethora of quantum states arising from the interplay of topology, spin-orbit coupling, and electron correlations. Here, we report symmetry-breaking electronic orders tunable by an applied magnetic field in a model Kagome magnet FeSn consisting of alternating stacks of two-dimensional Fe3Sn Kagome and Sn2 honeycomb layers. On the Fe3Sn layer terminated FeSn thin films epitaxially grown on SrTiO3(111) substrates, we observe trimerization of the Kagome lattice using scanning tunneling microscopy/spectroscopy, breaking its six-fold rotational symmetry while preserving the transitional symmetry. Such a trimerized Kagome lattice shows an energy-dependent contrast reversal in dI/dV maps, which is significantly enhanced by bound states induced by Sn vacancy defects. This trimerized Kagome lattice also exhibits stripe modulations that are energy-dependent and tunable by an applied in-plane magnetic field, indicating symmetry-breaking nematicity from the entangled magnetic and charge degrees of freedom in antiferromagnet FeSn.

Parametric optimization is an important product design technique, especially in the context of the modern parametric feature-based CAD paradigm. Realizing its full potential, however, requires a closed loop between CAD and CAE (i.e., CAD/CAE integration) with automatic design modifications and simulation updates. Conventionally the approach of model conversion is often employed to form the loop, but this way of working is hard to automate and requires manual inputs. As a result, the overall optimization process is too laborious to be acceptable. To address this issue, a new method for parametric optimization is introduced in this paper, based on a unified model representation scheme called eXtended Voxels (XVoxels). This scheme hybridizes feature models and voxel models into a new concept of semantic voxels, where the voxel part is responsible for FEM solving, and the semantic part is responsible for high-level information to capture both design and simulation intents. As such, it can establish a direct mapping between design models and analysis models, which in turn enables automatic updates on simulation results for design modifications, and vice versa -- effectively a closed loop between CAD and CAE. In addition, robust and efficient geometric algorithms for manipulating XVoxel models and efficient numerical methods (based on the recent finite cell method) for simulating XVoxel models are provided. The presented method has been validated by a series of case studies of increasing complexity to demonstrate its effectiveness. In particular, a computational efficiency improvement of up to 55.8 times the existing FCM method has been seen., Comment: 22 pages

A two dimensional topological insulator exhibits helical edge states topologically protected against single particle backscattering. Such protection breaks down, however, when electron electron interactions are significant or when edge reconstruction occurs, leading to suppressed density of states (DOS) at Fermi level that follows universal scaling with temperature and energy, characteristic of Tomonaga Luttinger liquid (TLL). Here, we grow multilayer FeSe on SrTiO3 by molecular beam epitaxy, and observe robust edge states at both {100}Se and {110}Se steps using scanning tunneling microscopy/spectroscopy. We determine the DOS follows a power law, resulting in Luttinger parameter K of 0.26 +/- 0.02 and 0.43 +/- 0.07 for {100}Se and {110}Se edges, respectively. The smaller K for the {100}Se edge also indicates strong correlations, attributed to ferromagnetic ordering likely present due to checkerboard antiferromagnetic fluctuations in FeSe. These results demonstrate TLL in FeSe helical edge channels, providing an exciting model system for novel topological excitations arising from superconductivity and interacting helical edge states., Comment: 28 pages

Solid modeling is a technique underlying CAD software as we see it today, and its theories and algorithms are among the most fundamental milestones in the historical development of CAD. Basically, it has answered the question of what geometric information a computer should store and how to store/manipulate them in order for the computer to aid the processes of design and manufacturing. This paper provides a brief review (in Chinese) on the historical development of solid modeling, its fundamental research problems, as well as their challenges and state of the art. It then concludes with three prospective trends of solid modeling, especially the promising paradigm shift from "Computer-Aided Design" to "Computer-Automated Design"., Comment: in Chinese language, a prevision of the published paper: Journal of Graphics, 2022, 43(6): 987-1001

This paper presents a brief survey (in Chinese) on path planning and feedrate interpolation. Numerical control technology is widely employed in the modern manufacturing industry, and related research has been emphasized by academia and industry. The traditional process of numerical control technology is mainly composed of tool path planning and feedrate interpolation. To attain the machining of high speed and precision, several problems in tool path planning and feedrate interpolation are usually transformed into mathematical optimization models. To better undertake the research on the integrated design and optimization idea of tool path planning and feedrate interpolation, it is necessary to systematically review and drawn on the existing representative works. We will introduce the relevant methods and technical progress of tool path planning and feedrate interpolation in CNC machining successively, including tool path planning based on end milling, tool orientation optimization, G-code processing and corner transition, feedrate planning of parameter curves, and some new machining optimization methods proposed recently., Comment: in Chinese language, a prevision of the published paper: Journal of Graphics, 2022, 43(6): 967-986

Electronic states within superconducting vortices hold crucial information about paring mechanisms and topology. While scanning tunneling microscopy/spectroscopy(STM/S) can image the vortices, it is difficult to isolate the intrinsic electronic states from extrinsic effects like subsurface defects and disorders. We combine STM/S with unsupervised machine learning to develop a method for screening out the vortices pinned by embedded disorder in Fe-based superconductors. The approach provides an unbiased way to reveal intrinsic vortex-core states and may address puzzles on Majorana zero modes.

Scanning tunneling microscopy (STM) is a powerful technique for imaging atomic structure and inferring information on local elemental composition, chemical bonding, and electronic excitations. However, traditional methods of visual inspection can be challenging for such determination in multi-component alloys, particularly beyond the dilute limit due to chemical disorder and electronic inhomogeneity. One viable solution is to use machine learning to analyze STM data and identify patterns and correlations that may not be immediately apparent through visual inspection alone. Here, we apply this approach to determine the Se/S concentration in superconducting single-layer FeSe1-xSx alloy epitaxially grown on SrTiO3(100) substrate by molecular beam epitaxy. First, defect-related dI/dV tunneling spectra are identified by the K-means clustering method, followed by singular value decomposition to distinguish between those from S and Se. Such analysis provides an efficient and reliable determination of local elemental composition, and further reveals correlations of nanoscale chemical inhomogeneity to superconductivity in single-layer iron chalcogenide films.

Abstract: Layered transition-metal dichalcogenides (TMDCs) down to the monolayer (ML) limit provide a fertile platform for exploring charge-density waves (CDWs). Though bulk NbTe2 is known to harbor a single axis 3*1 CDW coexisting with non-trivial quantum properties, the scenario in the ML limit is still experimentally unknown. In this study, we unveil the richness of the CDW phases in ML NbTe2, where not only the theoretically predicted 4*4 and 4*1 phases, but also two unexpected sqrt(28)*sqrt(28) and sqrt(19)*sqrt(19) phases, can be realized. For such a complex CDW system, we establish an exhaustive growth phase diagram via systematic efforts in the material synthesis and scanning tunneling microscope characterization. Moreover, we report that the energetically stable phase is the larger scale order (sqrt(19)*sqrt(19)), which is surprisingly in contradiction to the prior prediction (4*4). These findings are confirmed using two different kinetic pathways, i.e., direct growth at proper growth temperatures (T), and low-T growth followed by high-T annealing. Our results provide a comprehensive diagram of the "zoo" of CDW orders in ML 1T-NbTe2 for the first time and offer a new material platform for studying novel quantum phases in the 2D limit.

Feature-based parametric modeling is the de facto standard in CAD. Boundary representation-based direct modeling is another CAD paradigm developed recently. They have complementary advantages and limitations, thereby offering huge potential for improvement towards an integrated CAD modeling scheme. Most existing integration methods are developed by industry and typically treat direct edits as pseudo-features, where little can be said about seamless integration. This paper presents an alternative method for seamless parametric/direct integration, which allows parametric and direct edits to work in a unified way. The fundamental issues and challenges of parametric/direct integration are first explained. A framework is then proposed to handle those information inconsistencies, based on a detection-then-resolution strategy. Algorithms that can systematically detect and resolve all possible types of information inconsistencies are also given to implement the framework. With them, model validity can be maintained during the whole model editing process, and then the discrepancy between direct edits and parametric edits can be resolved. The effectiveness of the proposed approach has been shown with a series of case studies and comparisons, based on a preliminary prototype., Comment: 19pages

By substituting S into single-layer FeSe/SrTiO3, chemical pressure is applied to tune its paramagnetic state that is modeled as an incoherent superposition of spin-spiral states. The resulting electronic bands resemble an ordered checkerboard antiferromagnetic structure, consistent with angle-resolved photoemission spectroscopy measurements. Scanning tunneling spectroscopy reveals a gap evolving from U-shaped for FeSe to V-shaped for FeS with decreasing size, attributed to a d-wave superconducting state for which nodes emerge once the gap size is smaller than the effective spin-orbit coupling., Comment: need revision

The quality of tool paths is a dominant factor in CNC machining, determining its efficiency and accuracy. This paper provides a brief review (in Chinese) on tool path planning methods reported in the literature, focusing on their categorization, motivating problems/issues, and historical development. Some promising research trends have also been stressed, especially for the paradigm shift from tool path generation towards tool path optimization., Comment: in Chinese

In this paper, we revisit the long-standing problem of automatic reconstruction of 3D objects from single line drawings. Previous optimization-based methods can generate compact and accurate 3D models, but their success rates depend heavily on the ability to (i) identifying a sufficient set of true geometric constraints, and (ii) choosing a good initial value for the numerical optimization. In view of these challenges, we propose to train deep neural networks to detect pairwise relationships among geometric entities (i.e., edges) in the 3D object, and to predict initial depth value of the vertices. Our experiments on a large dataset of CAD models show that, by leveraging deep learning in a geometric constraint solving pipeline, the success rate of optimization-based 3D reconstruction can be significantly improved., Comment: Project page is at https://manycore-research.github.io/cstr

In parametric design, the geometric model is edited by changing relevant parameters in the parametric model, which is commonly done sequentially on multiple parameters. Without guidance on allowable parameter ranges that can guarantee the solvability of the geometric constraint system, the user could assign improper parameter values to the model's parameters, which would further lead to a failure in model updating. However, current commercial CAD systems provide little support for the proper parameter assignments. Although the existing methods can compute allowable ranges for individual parameters, they face difficulties in handling multi-parameter situations. In particular, these methods could miss some feasible parameter values and provide incomplete allowable parameter ranges. To solve this problem, an automatic approach is proposed in this paper to compute complete parameter ranges in multi-parameter editing. In the approach, a set of variable parameters are first selected to be sequentially edited by the user; before each editing operation, the one-dimensional ranges of the variable parameters are presented as guidance. To compute the one-dimensional ranges, each variable parameter is expressed as an equality-constrained function, and its one-dimensional allowable range is obtained by calculating the function range. To effectively obtain the function range which can hardly be calculated in a normal way, the function range problem is converted into a constrained optimization problem, and is then solved by Lagrange multiplier method and the Niching particle swarm optimization algorithm (the NichePSO). The effectiveness and efficiency of the proposed approach is verified by several experimental results.

In the history of computer-aided design (CAD), feature-based parametric modeling and boundary representation-based direct modeling are two of the most important CAD paradigms, developed respectively in the late 1980s and the late 2000s. They have complementary advantages and limitations, thereby offering huge potential for improvement towards an integrated CAD modeling scheme. Some believe that their integration will be the key characteristic of next generation CAD software. This paper provides a brief review on current parametric/direct integration approaches. Their basic ideas, advantages, and disadvantages will be discussed. The main result reads that existing integration approaches are far from being completed if seamless parametric/direct integration is desired. It is hoped that, by outlining what has already been made possible and what still remains problematic, more researchers will be attracted to work on this very important research topic of parametric/direct integration., Comment: 12 pages; 3 figures

This paper presents a comprehensive review of geometric constraint solving in parametric computer-aided design (CAD), with the major focus on its advances in the last 15 years. Geometric constraint solving can date back to the very first CAD prototype, Sketchpad, in the 1960s, but serious research studies were carried out only after parametric CAD was introduced in the late 1980s. In the following 30-year history of GCS research, two development stages may be identified: (1) the first 15 years (late 1980s - mid 2000s) were primarily devoted to geometric constraint decomposition for well-constrained systems or those with only structural constraint dependencies; and (2) the second 15 years (late 2000s - now) have seen research efforts shifted towards classification criteria and decomposition algorithms for general constraint systems (with and without non-structural constraint dependencies). Most existing reviews focused on the first 15 years. The problem researched in the second 15 years is, however, equally important, considering that a manually specified constraint system usually contains under- and over-constrained parts, and that such parts must be correctly detected and resolved before numerical solving can work. In this regard, this review paper covers both stages and will discusses what has already been made possible for handling general constraint systems, what developments can be expected in the near future, and which areas remain problematic., Comment: version 2. arXiv admin note: text overlap with arXiv:1904.00526

Variational design is a well-recognized CAD technique due to the increased design efficiency. It often presents as a parametric family of CAD models. Although effective, this way of working cannot handle design requirements that go beyond parametric changes. Such design requirements are not uncommon today due to the increasing popularity of product customization. In particular, there is often a need for designing a new model out of an existing structural family of models, which share a structural pattern but have individually varied detail features. To facilitate such design requirements, a new method is presented in this paper. The idea is to express the underlying structural pattern in terms of a submodel composed of the maximum common design features of the family, and then to build a single master model by attaching to the submodel all detail design features in the family. This master model is a representative model for the family and contains all the features. By removing unwanted detail features and adding new features, the master model can be easily adapted into a new design, while keeping aligned with the family, structurally. Effectiveness of this method has been validated by a series of case studies and comparisons of increasing complexity., Comment: 12 pages, 11 figures, journal paper

The adatom arrays on surfaces offer an ideal playground to explore the mechanisms of chemical bonding via changes in the local electronic tunneling spectra. While this information is readily available in hyperspectral scanning tunneling spectroscopy data, its analysis has been considerably impeded by a lack of suitable analytical tools. Here we develop a machine learning based workflow combining supervised feature identification in the spatial domain and un-supervised clustering in the energy domain to reveal the details of structure-dependent changes of the electronic structure in adatom arrays on the Co3Sn2S2 cleaved surface. This approach, in combination with first-principles calculations, provides insight for using artificial neural networks to detect adatoms and classifies each based on their local neighborhood comprised of other adatoms. These structurally classified adatoms are further spectrally deconvolved. The unexpected inhomogeneity of electronic structures among adatoms in similar configurations is unveiled using this method, suggesting there is not a single atomic species of adatoms, but rather multiple types of adatoms on the Co3Sn2S2 surface. This is further supported by a slight contrast difference in the images (or slight size variation) of the topography of the adatoms.

Lattice structures have been widely used in various applications of additive manufacturing due to its superior physical properties. If modeled by triangular meshes, a lattice structure with huge number of struts would consume massive memory. This hinders the use of lattice structures in large-scale applications (e.g., to design the interior structure of a solid with spatially graded material properties). To solve this issue, we propose a memory-efficient method for the modeling and slicing of adaptive lattice structures. A lattice structure is represented by a weighted graph where the edge weights store the struts' radii. When slicing the structure, its solid model is locally evaluated through convolution surfaces and in a streaming manner. As such, only limited memory is needed to generate the toolpaths of fabrication. Also, the use of convolution surfaces leads to natural blending at intersections of struts, which can avoid the stress concentration at these regions. We also present a computational framework for optimizing supporting structures and adapting lattice structures with prescribed density distributions. The presented methods have been validated by a series of case studies with large number (up to 100M) of struts to demonstrate its applicability to large-scale lattice structures.

Atomic structures and adatom geometries of surfaces encode information about the thermodynamics and kinetics of the processes that lead to their formation, and which can be captured by a generative physical model. Here we develop a workflow based on a machine learning-based analysis of scanning tunneling microscopy images to reconstruct the atomic and adatom positions, and a Bayesian optimization procedure to minimize statistical distance between the chosen physical models and experimental observations. We optimize the parameters of a 2- and 3-parameter Ising model describing surface ordering and use the derived generative model to make predictions across the parameter space. For concentration dependence, we compare the predicted morphologies at different adatom concentrations with the dissimilar regions on the sample surfaces that serendipitously had different adatom concentrations. The proposed workflow is universal and can be used to reconstruct the thermodynamic models and associated uncertainties from the experimental observations of materials microstructures. The code used in the manuscript is available at https://github.com/saimani5/Adatom_interactions.

This paper presents a new method to generate tool paths for machining freeform surfaces represented either as parametric surfaces or as triangular meshes. This method allows for the optimal tradeoff between the preferred feed direction field and the constant scallop height, and yields a minimized overall path length. The optimality is achieved by formulating tool path planning as a Poisson problem that minimizes a simple, quadratic energy. This Poisson formulation considers all tool paths at once, without resorting to any heuristic sampling or initial tool path choosing as in existing methods, and is thus a globally optimal solution. Finding the optimal tool paths amounts to solving a well-conditioned sparse linear system, which is computationally convenient and efficient. Tool paths are represented with an implicit scheme that can completely avoid the challenging topological issues of path singularities and self-intersections seen in previous methods. The presented method has been validated with a series of examples and comparisons., Comment: under review

This paper presents a new method to generate iso-scallop tool paths for triangular mesh surfaces. With the popularity of 3D scanning techniques, scanning-derived mesh surfaces have seen a significant increase in their application to machining. Quite often, such mesh surfaces exhibit defects such as noises, which differentiate them from the good-quality mesh surfaces previous research work focuses on. To generate tool paths for such poor-quality mesh surfaces, the primary challenge lies in robustness against the defects. In this work, a robust tool path generation method is proposed for poor-quality mesh surfaces. In addition to robustness, the method is quite efficient, providing the benefit of faster iterations and improved integration between scanning and machining. The fundamental principle of the method is to convert the tool path generation problem to the heat diffusion problem that has robust and efficient algorithms available. The effectiveness of the method will be demonstrated by a series of case studies and comparisons., Comment: 10 pages, 9 figures, Under journal review

The electronic structure inhomogeneities in Co, Ni, and Cr doped BaFe2As2 122 single crystals are compared using scanning tunneling microscopy/spectroscopy (STM/S) at the nanoscale within three bulk property regions in the phase diagram: a pure superconducting (SC) dome region (Co-122), a coexisting SC and antiferromagnetic (AFM) region (Ni-122), and a non-SC region (Cr-122). Machine learning is utilized to categorize the various nanometer scale inhomogeneous electronic states, described here as in-gap, L-shape and S-shape states immersed into the SC matrix for Ni-and Co-doped 122, and L-shape and S-shape states into the metallic matrix for Cr-doped 122. Although the relative percentages of in-gap, L-shape and S-shape states vary in the three samples, the total volume fraction of the three electronic states is quite similar. This is coincident with the number of electrons (Ni0.04 and Co0.08) and holes (Cr0.04) doped into the 122 compound. By combining the volume fractions of the three states, the local density of states (LDOS), magnetic field dependent behavior and global properties in these three samples, the in-gap state is confirmed as a magnetic impurity state from the Co or Ni dopants. In addition, the L-shape state is identified as a spin density wave (SDW) which competes with the SC phase, and the S-shape state is found to be another form of magnetic order which constructively cooperates with the SC phase, rather than competing with it. The comparison of the vortex structures indicates that the inhomogeneous electronic states serve as pinning centers for stabilizing the vortex lattice.