3D Geometry Research Articles

Comprehensive Geometric Parameterization and Computationally Efficient 3D Shape Matching Optimization of Realistic Stents

Abstract Flexible and compact shape representation schemes are essential for design optimization problems. Current shape representation schemes for coronary stent designs concern predominantly idealized or independent ring (IR) designs, which are outdated and only consider a small number of core design variables (such as strut width, height, and thickness) and ignore clinically critical design characteristics such as the number of connectors. No reports exist on the geometry parameterization of the latest helical stents (HS) that have more complex geometric designs than IR stents. Here, we present two new shape parameterization schemes to fully capture the 3D designs of contemporary IR and double-helix HS stents. We developed a 3D stent geometry builder based on 17 (IR) and 18 (HS) design variables, including strut width, thickness, height, number of connectors and rings, stent length, and strut centerline shape. The shape of the strut centerline was derived via a combination of NURBS, PARSEC, quarter circle, and straight line segments. Shape matching for complex 3D geometries, such as the contemporary stents within limited function evaluations, is not trivial and requires efficient parameterization and optimization algorithms. We used shape matching optimization with a limited function evaluation budget to test the proposed parameterization and two surrogate-assisted optimization algorithms relying on predictor believer and an expected improvement maximization formulation. The performance of these algorithms is objectively compared with a gradient-based optimization method to highlight their strengths. Our work paves the way for more realistic, full-fledged stent design optimization with structural and hemodynamic objectives in the future.

DEGAN: Detail-Enhanced Generative Adversarial Network for Monocular Depth-Based 3D Reconstruction

Although deep networks-based 3D reconstruction methods can recover the 3D geometry given few inputs, they may produce unfaithful reconstruction when predicting occluded parts of 3D objects. To address the issue, we propose Detail-Enhanced Generative Adversarial Network (DEGAN) which consists of Encoder–Decoder-Based Generator (EDGen) and Voxel-Point Embedding Network-Based Discriminator (VPDis) for 3D reconstruction from a monocular depth image of an object. Firstly, EDGen decodes the features from the 2.5D voxel grid representation of an input depth image and generates the 3D occupancy grid under GAN losses and a sampling point loss. The sampling loss can improve the accuracy of predicted points with high uncertainty. VPDis helps reconstruct the details under voxel and point adversarial losses, respectively. Experimental results show that DEGAN not only outperforms several state-of-the-art methods on both public ModelNet and ShapeNet datasets but also predicts more reliable occluded/missing parts of 3D objects.

Biobased coatings for architectural timber applied using the robotic 3D printing technique

Materials applied for coating architectural timber are often environmentally harmful. This study examines a sustainable alternative – a coating from microfibrillated cellulose hydrogel applied for the first time on architectural timber using robotic 3D printing. The proposed solution is evaluated through architectural design and robotic 3D printing experiments, with patterned coating designs deposed onto eight architectural mockups. Through qualitative and quantitative analyses of coating features preproduction and postproduction, fundamental aspects affecting coating design are identified, namely, the 3D printing path geometry and layout, substrate type, and precoating material. These aspects are correlated with the final architectural coating qualities at the mesoscale and macroscale by characterizing dimensional stability, geometric features, and color appearance. The best coating effects are observed for pine substrates precoated with hydroxyethyl cellulose. By delivering new knowledge on biobased architectural coatings, this study contributes to the global effort of phasing out fossil-based materials in the built environment.

Zero‐curvature subconformal structures and dispersionless integrability in dimension five

AbstractWe extend the recent paradigm “Integrability via Geometry” from dimensions 3 and 4 to higher dimensions, relating dispersionless integrability of partial differential equations to curvature constraints of the background geometry. We observe that in higher dimensions on any solution manifold, the symbol defines a vector distribution equipped with a subconformal structure, and the integrability imposes a certain compatibility between them. In dimension 5, we express dispersionless integrability via the vanishing of a certain curvature of this subconformal structure. We also obtain a “master equation” governing all second‐order dispersionless integrable equations in 5D, and count their functional dimension. It turns out that the obtained background geometry is parabolic of the type . We provide its Cartan‐theoretic description and compute the harmonic curvature components via the Kostant theorem. Then, we relate it to 3D projective and 4D conformal geometries via twistor theory, discuss symmetry reductions and nested Lax sequences, as well as give another interpretation of dispersionless integrability in 5D through Levi‐degenerate CR structures in 7D.

Abstract 4114497: Shape Variations in Right Ventricular 3D Geometry are associated with adverse outcomes in Hypoplastic Left Heart Syndrome Patients: A Fontan Outcomes Registry using CMR Examination (FORCE) Study

Introduction: Right ventricular (RV) function is critical to the long-term health of patients with hypoplastic left heart syndrome (HLHS). However, conventional measurements do not consider the range of RV morphology that may impact RV function and lead to adverse outcomes. In this study, we determined associations between RV shape and clinical outcomes of HLHS using statistical shape modeling (SSM) and a large cardiac magnetic resonance (CMR) multicenter registry. Methods: Three hundred and twenty-eight studies from unique HLHS patients in the F ontan O utcomes R egistry using C MR E xaminations (FORCE) were post-processed by a core lab at one institution, including volumetry and strain analysis. 3D end-diastolic models of RV were reconstructed using Mimics (Materialise). SSM was performed via Shapeworks Studio (NIH/NIGMS CIBC) to derive mean template and quantified shape variations (shape mode) representing deviation from the mean. RV shape relationship with mortality/heart transplant was assessed using bivariable/multivariable analyses with stepwise model selection. Results: The mean template from all 328 patients resembled a circumferentially dilated RV with loss of concavity in septal wall (Fig A). Several generalized variants were identified (Fig B), particularly p1 – a sigmoidal / “apical bulge” variant where the RV apex dilates and "wraps” around the hypoplastic left ventricle (Fig C). Twenty-eight patients (8.5%) experienced mortality/heart transplant at 2.5±2.4 years after CMR. On bivariable analysis, p1 was associated with mortality/heart transplant, along with larger indexed RV end-diastolic volume/mass and reduced global circumferential strain. On multivariable analysis, p1 and indexed RV mass were associated with mortality/heart transplant (Table). Conclusions: Statistical Shape Modeling can define the “usual” RV shape of HLHS. A sigmoidal shape variant is associated with adverse outcomes. SSM may provide patient-specific metrics to define RV dysfunction in HLHS.

Useless Math – The Complex Untold Story

If you don't understand mathematics, ask yourself if I'm right, because others don't understand mathematics either. By useless mathematics we mean incomplete mathematical spaces of a classical 3D+t variety that are inadequate for generating well-defined definitions and hypotheses as well as time-dependent partial differential equations. The current classical discrete 3D+t space PDE, in which time is an external controller and not integrated into the 3D geometric space, cannot be integrated digitally. This space is logically incomplete and misleading in the production of definitions and hypotheses as well as in the resolution itself of time- dependent PDEs. No wonder these definitions/assumptions are ugly and result in weak or intractable mathematics, leading to all kinds of misunderstandings, from horrible notations to undisciplined length of theorems containing a considerable amount of black magic and ending with a gray nature of the mathematical result obtained. In this article we present some of the most catastrophic inaccurate assumptions existing in current classical mathematics, resulting from the use of 3D+t manifold space to specify initial conditions, boundary conditions and the source/sink term. Fortunately, these inaccurate assumptions that start with an ugly space for boundary conditions, initial conditions and source/sink term can be spotted and analyzed via 4D unitary numerical statistical theory called Cairo techniques in the format of transition chains of matrix B to complete what is missing. In other words, we present how to spot some of the ugliest mathematical conclusions of classical 3D geometry plus t as an external control numerical space, and then show how to correct them via the 4D unit space of statistical transition matrix chains. By complex and untold history, we mean that useless and misleading mathematics dominated scientific research and education throughout the 20th century, so much so that the accumulated legacy of misconceptions became a huge, complex mountain, almost impossible to eliminate. Fortunately, the numerical theory of Cairo techniques and the Laplacian theorem constitute an advanced and exhaustive form of the energy continuity equation and thus can create new logical mathematics. This is also the case of the famous Schrödinger time- dependent PDE.  The Laplacian theorem is one of the most important products created by the numerical statistical theory called Cairo techniques. In previous articles we introduced and briefly explained the so-called Laplacian theorem in the 4D x-t unit space, while in this article we highlight its importance and how it can generate new mathematics in more detail. The Laplacian partial differential equation that interests us is the one having a well-defined exclusive form and living in an isolated sample spatial control volume surrounded by a closed surface (A) and subject to Dirichlet boundary conditions. This very particular case of Laplacian PDE is always treated mathematically in a classical D^4 variety which is lazy and misleading. Finally, this article collects, studies, identifies and analyzes the dozen most common current useless mathematical events and presents an effective and adequate alternative.

IShapEditing: Intelligent Shape Editing with Diffusion Models

AbstractRecent advancements in generative models have enabled image editing very effective with impressive results. By extending this progress to 3D geometry models, we introduce iShapEditing, a novel framework for 3D shape editing which is applicable to both generated and real shapes. Users manipulate shapes by dragging handle points to corresponding targets, offering an intuitive and intelligent editing interface. Leveraging the Triplane Diffusion model and robust intermediate feature correspondence, our framework utilizes classifier guidance to adjust noise representations during sampling process, ensuring alignment with user expectations while preserving plausibility. For real shapes, we employ shape predictions at each time step alongside a DDPM‐based inversion algorithm to derive their latent codes, facilitating seamless editing. iShapEditing provides effective and intelligent control over shapes without the need for additional model training or fine‐tuning. Experimental examples demonstrate the effectiveness and superiority of our method in terms of editing accuracy and plausibility.

DeepJEB: 3D Deep Learning-based Synthetic Jet Engine Bracket Dataset

Abstract Recent advances in artificial intelligence (AI) have impacted various fields, including mechanical engineering. However, the development of diverse, high-quality datasets for structural analysis remains a challenge. Traditional datasets, like the jet engine bracket dataset, are limited by small sample sizes, hindering the creation of robust surrogate models. This study introduces the Deep- JEB dataset, generated through deep generative models and automated simulation pipelines, to address these limitations. DeepJEB offers comprehensive 3D geometries and corresponding structural analysis data. Key experiments validated its effectiveness, showing significant improvements in surrogate model performance. Models trained on DeepJEB achieved up to a 23% increase in the coefficient of determination and over a 70% reduction in mean absolute percentage error (MAPE) compared to those trained on traditional datasets. These results underscore the superior generalization capabilities of DeepJEB. By supporting advanced modeling techniques, such as graph neural networks (GNNs) and convolutional neural networks (CNNs), DeepJEB enables more accurate predictions in structural performance. The DeepJEB dataset is publicly accessible at: https://www.narnia.ai/dataset.

Three-Dimensional Hullform Reconstruction from Two-Dimensional Drawings Based on Image Processing Techniques

Abstract Repair shipyards sometimes need three-dimensional geometry for repairs and retrofits. However, they often create models manually from two-dimensional drawings provided by ship owners. In this case, human error leads to inaccuracies, making the process time-consuming and laborious. Therefore, there is a need for research on efficient three-dimensional hullform reconstruction from two-dimensional drawings. This study proposed a method to automatically extract points from two-dimensional lines and visualize them in three dimensions. The proposed method consists of three steps. The first step is a point extraction through image processing, which uses a starting point search algorithm to access overlapping or intersection lines and extracts the points on the lines in the drawing by searching for paths between the starting point and the end point entered by the user. The second step is the transformation of the extracted data, which transforms the points based on pixel coordinate into 3D points through coordinate transformation and scaling by utilizing the stored line data and three-dimensional coordinate information. The last step is to visualize the transformed data as a real three-dimensional model with point visualization. This study demonstrates that the proposed method can be effectively utilized by detecting two-dimensional lines and reconstructing the hullform in three dimensions.

Reliability of Extraoral Scanners in Capturing 3D Geometry for Dental Prostheses: A Systematic Review

Reliability of Extraoral Scanners in Capturing 3D Geometry for Dental Prostheses: A Systematic Review

Evaluating process parameters of SLS part of polyamide-12 recycled powder using RSM

Abstract Selective laser sintering (SLS) is a highly flexible rapid prototyping (RP) technology which can use a wide range of powdered materials to generate high quality complex geometries directly from digital models. The SLS process uses a laser to sinter selected areas of powdered materials to produce solid objects layer by layer, according to the 2D data obtained from CT scan or MRI imaging techniques. This paper presents research work for evaluating the effect of process parameters on impact toughness and surface roughness of the part manufactured on Farsoon SS402P SLS from recycled ageing FS 3300PA which is PA-12 based powder and standard operating parameters using Response Surface Methodology (RSM) design of experiments. Impact tests have been performed as per the ASTM D6110 standard using recommendations from ISO 179-2. According to the results, effect of process parameters are successfully analyzed by employing impact toughness and surface roughness tests. Based on the results of the ANOVA analysis, impact toughness increases with increasing laser power (4.467 j/cm2 at 72.5 watts). Similarly, it is also clear from the results that the region with the lowest laser power, high layer thickness, and 90-degree orientation had the lowest surface roughness (3.46 μm).

Geometric decomposition and algorithmic model of main gate muqarnas of Ankara Cenabi Ahmet Pasha Mosque

Cenabi Ahmet Pasha Mosque (Cenab-ı Ahmet Paşa Mosque) is known to be the only work that resembles the style of Architect Sinan in Ankara. In this study, it is aimed to examine the two-dimensional muqarnas scheme of the mosque's main gate and to determine through algorithmic modeling the combination of muqarnas cells in the third dimension. By the photogrammetry method, the grid and star forms used in the muqarnas plan scheme are revealed. The geometric characteristic of the muqarnas in two dimensions is determined. Cell types of the muqarnas and their geometric configurations are obtained. It is demonstrated that there is a radial grid in the plan of the Cenabi Ahmet Pasha Mosque main gate muqarnas, and that the three-dimensional structure of the muqarnas consisting of six layers includes almond cell, triangle cell, deltoid cell, intermediate triangle cell, intermediate deltoid cell, biped cell and triped cell. Additionally, an algorithmic model based on the creation of cell unit system is proposed for the creation of the muqarnas geometry in 3D.

Diffusion-based generative drug-like molecular editing with chemical natural language

Recently, diffusion models have emerged as a promising paradigm for molecular design and optimization. However, most diffusion-based molecular generative models focus on modeling 2D graphs or 3D geometries, with limited research on molecular sequence diffusion models. The International Union of Pure and Applied Chemistry (IUPAC) names are more akin to chemical natural language than the Simplified Molecular Input Line Entry System (SMILES) for organic compounds. In this work, we apply an IUPAC-guided conditional diffusion model to facilitate molecular editing from chemical natural language to chemical language (SMILES) and explore whether the pre-trained generative performance of diffusion models can be transferred to chemical natural language. We propose DiffIUPAC, a controllable molecular editing diffusion model that converts IUPAC names to SMILES strings. Evaluation results demonstrate that our model outperforms existing methods and successfully captures the semantic rules of both chemical languages. Chemical space and scaffold analysis show that the model can generate similar compounds with diverse scaffolds within the specified constraints. Additionally, to illustrate the model's applicability in drug design, we conducted case studies in functional group editing, analogue design and linker design.

Computational multiphysics modeling of radioactive aerosol deposition in diverse human respiratory tract geometries

The evaluation of aerosol exposure relies on generic mathematical models that assume uniform particle deposition profiles over the human respiratory tract and do not account for subject-specific characteristics. Here we introduce a hybrid-automated computational workflow that generates personalized particle deposition profiles in 3D reconstructed human airways from computed tomography scans using Computational Fluid and Particle Dynamics simulations. This is the first large-scale study to consider realistic airways variability, where 380 lower and 40 upper human respiratory tract 3D geometries are reconstructed and parameterized. The data is clustered into nine groups using random forest regression. Computational fluid and particle dynamics simulations are conducted on these representative geometries using a realistic heavy-breathing respiratory cycle and radioactive iodine-131 as a source term. Monte Carlo radiation transport simulations are performed to obtain detailed energy deposition maps. Our findings emphasize the importance of personalized studies, as minor respiratory tract variations notably influence deposition patterns rather than global parameters of the lower airways, observing more than 30% variance in the mass deposition fraction.

Thoracic Aortic Three-Dimensional Geometry.

Aortic structure impacts cardiovascular health through multiple mechanisms. Aortic structural degeneration occurs with aging, increasing left ventricular afterload and promoting increased arterial pulsatility and target organ damage. Despite the impact of aortic structure on cardiovascular health, three-dimensional (3D) aortic geometry has not been comprehensively characterized in large populations. We segmented the complete thoracic aorta using a deep learning architecture and used morphological image operations to extract multiple aortic geometric phenotypes (AGPs, including diameter, length, curvature, and tortuosity) across various subsegments of the thoracic aorta. We deployed our segmentation approach on imaging scans from 54,241 participants in the UK Biobank and 8,456 participants in the Penn Medicine Biobank. Our method provides a fully automated approach towards quantifying the three-dimensional structural parameters of the aorta. This approach expands the available phenotypes in two large representative biobanks and will allow large-scale studies to elucidate the biology and clinical consequences of aortic degeneration related to aging and disease states.

Joint Observation of a Series of Magnetic Holes by Tianwen-1 and MAVEN on Mars

Magnetic holes (MHs) are transient magnetic structures responsible for energy conversion in space plasma. Using single-spacecraft measurements from Mars Atmosphere and Volatile EvolutioN (MAVEN), the existence of MHs on Mars has been confirmed. However, due to the limitations of single-spacecraft observations, significant uncertainty also arises on the identification of the spatial scale and 3D geometry of MHs. In this study, we report a series of MHs successively detected by Tianwen-1 near the high-latitude magnetopause and by the MAVEN spacecraft near the subsolar magnetopause. The large separation between Tianwen-1 and MAVEN (∼4 R M) suggests these MHs are macroscale structures extending along the axial direction. Additionally, we observe whistler waves generated by electron perpendicular anisotropy in one of the macroscale MHs. This study is the first joint observation of Martian MHs, shedding light on the research of transient magnetic structures on Mars.

Machine Vision to Provide Quantitative Analysis of Meltpool Stability for a Coaxial Wire Directed Energy Deposition Process.

Wire-based additive manufacturing (AM) is at the forefront of complex metal fabrication because of its scalability for large components, potential for high deposition rates, and ease of use. A common goal of wire directed energy deposition (DED) is preserving a stable process throughout deposition. If too little energy is put into the deposition, the wire will stub into the substrate and begin oscillating, creating turbulence within the meltpool. If too much energy exists, the wire will overheat, causing surface tension to take over and create liquid drips as opposed to a solid bead. This paper proposes a computer vision technique to work as both a state detection and event detection system for wire stability. The model utilizes intensity variations along with frame-to-frame difference calculations to determine process stability. Because the proposed model does not rely on machine learning techniques, it is possible for an individual to interpret and adjust as they see fit. The first part of this paper describes creation and implementation of the model. The model's capability was then evaluated using a 1D laser power experiment, which generated a wide range of stability states across varying powers. The model's accuracy was evaluated through 3D geometry data gathered from the experimentally deposited beads. The model proved to be both capable and accurate and has potential to be used as a real-time control system with future work.

Oriblock: The origami-blocks based on hinged dissection

Traditional origami, a well-known art of paper-folding, does not account for material thickness. Subsequently, several thickness-accommodation techniques have been developed, considering the non-negligible thickness of materials, which enables the application of origami to a wide range of mechanisms. Although these techniques prevent self-intersections and preserve kinematics after accommodating panel thickness, they are limited by their reliance on initial zero-thickness origami patterns in two dimensions. To address this issue, this study proposes a novel technique, the volume-accommodation technique in three-dimensional space, which allocates non-coplanar origami creases based on solid geometry to allow a greater variety of shape-changing motions. Typical solid geometries, such as a pyramid and a prism, are selected as examples to demonstrate the design procedures. Closure equations of the obtained oriblock are used to analyze the kinematic properties. Additionally, Bennett and Myard Linkages are derived from oriblocks based on their kinematic equivalence to strengthen their connections. As a result, this new type of origami can offer a variety of mechanisms for designers and facilitate potential applications in origami-inspired metamaterials and robotics.

Multi-functional additively constructed honeycomb walls for housing and sheltering

Honeycomb designs have become increasingly popular in additive manufacturing due to their great mechanical properties. The honeycomb infill pattern has allowed the creation of lightweight objects without sacrificing the strength of solid objects. Honeycombs have been utilized in different applications, including architecture, aerospace, and automotive. However, there is a lack of honeycomb designs within the construction industry. With the growth of concrete additive construction, there is an opportunity to introduce honeycomb designs into construction practices. This paper proposes a methodology for manufacturing multi-functional walls through additive construction. The methodology includes several key steps, from material development and quality control testing to wall assembly and experimental investigation. Two multi-functional wall segments were additively constructed, reaching a height of 1180 mm, a width of 610 mm, and a thickness of 90 mm. These measurements led to the manufacturing of seven distinct cellular sections per wall, comprising three main, two intermediate, and two end cellular units. In addition, a columnar unit was additively constructed for corner connection, featuring two vertical octagonal cells with end brackets. A preliminary wall system made up of honeycomb wall segments was assembled using various additional materials such as sealant, clamping systems, and insulative materials. Furthermore, an additional wall segment with end connections was designed and manufactured to test its load-carrying capacity. The wall segment performed well compared to wooden stud walls and showed sufficient load-carrying capacity. Unlike traditional un-reinforced concrete structures, which are brittle and experience small plastic deformations before failing, the honeycomb wall structure experienced large plastic deformation before failure due to the use of insulation foam and silicon rubber. The preliminary testing showed that the honeycomb wall system could be an alternative to traditional housing construction, especially for shelters.

Research on wheel–rail impact dynamics due to combined rail weld irregularities and polygonal wheel effects considering 3D contact geometry

The geometric irregularities of rail welds and polygonal wheels are common defects observed in high-speed railways, leading to the generation of high-frequency impact forces and vibrations in the wheel–rail contact system. This research establishes a novel vehicle-track coupled dynamic model that incorporates a 3D wheel–rail contact model using meshing grid and conjugate gradient methods to study the high-magnitude wheel–rail impact forces caused by rail weld irregularities and polygonal wheel combinations. The primary objective of this study is to develop a precise 3D contact model that incorporates the actual geometry of wheel and rail surface irregularities into the calculation of vehicle-track dynamic interactions. The study evaluates the effects of 3D rail weld irregularities and polygonal wheels on wheel–rail dynamic interaction by comparing results with those obtained from a conventional vehicle-track coupled model that considers a 2D contact model. The results show that the lengths and depths of polygonal wheels and rail weld irregularities, as well as vehicle speeds, significantly increase the wheel/rail dynamic impact forces. The results also indicate that the widening of irregularities not only significantly affects the wheel–rail contact force but also has an important influence on the contact stiffness.