Representation Of Geometry Research Articles

Determination of forest canopy cover of different sized stands with diverse structure using ALS data: case study of the Białowieża Forest (Poland)

ABSTRACT The need for objective methods to determine tree canopy cover (CC) across large numbers of stands has led to the development of techniques that utilise airborne laser scanning (ALS) data, which provides a reproducible and detailed representation of canopy geometry. We developed a method for determining CC area and evaluated the estimation accuracy for stands of different sizes, structure and composition. This method is based on tree crown geometries obtained from ALS data, and verified with field measurements using data for 3245 stands of the Białowieża Forest District in Poland. In relatively large stands (3–5 ha), the theoretical error of prediction decreased from 0.13 to 0.10 with increasing stand area. In stands larger than 10 ha, however, the error in estimating CC was less than ±0.10. Although every estimation method comes with its own assumptions and errors, the presented method eliminates the subjectivity in observer bias prevalent in traditional field-based ocular assessments and provides a more transparent and methodologically uniform approach for estimating CC in forests.

Study of Parameters Influencing Wrinkles in the Deep Drawing of Fiber-Based Materials Using Automatic Image Detection

The evaluation of wrinkles in deep-drawn fiber-based materials is crucial for the assessment of product quality and the optimization of manufacturing processes. Wrinkling is a common phenomenon in the deep-drawing process and is caused by tangential compressive stresses on the flanges of the blank. This phenomenon is particularly prevalent for fiber-based materials with high tensile depths and can seriously affect the appearance and mechanical properties of the final product. The objective of this study is to identify the key process parameters affecting wrinkling and to deepen the understanding of their roles and interactions using wrinkle data for deep-drawn paper products. Image analysis techniques are employed, supported by a specially constructed darkroom platform to ensure uniform light intensity for capturing photographs. An automated program is developed for the detection and evaluation of wrinkle characteristics and distribution, which allows the free choice of the region to be detected and the representation of the wrinkle geometry not limited by the number. To enhance the precision of this program, the ellipticity is initially rectified for products without flanges, specifically cup-shaped deep-drawn products. The ellipticity is caused by the pronounced springback effect of the paperboard. The approach is employed to investigate the impact of material properties, blank holder force, drawing depth, drawing clearance, and punch speed on wrinkling formation after the deep-drawing process. The findings reveal that the blank holder force and drawing clearance are critical factors in wrinkle formation, with higher blank holder force generally leading to increased wrinkle numbers.

TriHuman: A Real-time and Controllable Tri-plane Representation for Detailed Human Geometry and Appearance Synthesis

Creating controllable, photorealistic, and geometrically detailed digital doubles of real humans solely from video data is a key challenge in Computer Graphics and Vision, especially when real-time performance is required. Recent methods attach a neural radiance field (NeRF) to an articulated structure, e.g., a body model or a skeleton, to map points into a pose canonical space while conditioning the NeRF on the skeletal pose. These approaches typically parameterize the neural field with a multi-layer perceptron (MLP) leading to a slow runtime. To address this drawback, we propose TriHuman a novel human-tailored, deformable, and efficient tri-plane representation, which achieves real-time performance, state-of-the-art pose-controllable geometry synthesis as well as photorealistic rendering quality. At the core, we non-rigidly warp global ray samples into our undeformed tri-plane texture space, which effectively addresses the problem of global points being mapped to the same tri-plane locations. We then show how such a tri-plane feature representation can be conditioned on the skeletal motion to account for dynamic appearance and geometry changes. Our results demonstrate a clear step toward higher quality in terms of geometry and appearance modeling of humans as well as runtime performance.

Linear Algebra :Eigen Value and Eigen Vectors and Their Applications

Abstract: Linear algebra is the branch of mathematics that concerned with the study of vectors,vector spaces(linear spaces), linear maps(linear transformations') and system of linear equations. Linear space is the central theme in modern mathematics that is widely used in both abstract algebra and functional analysis.Linear algebra also has a concrete representation in analytical geometry and in generalized operator theory. It has extensive applications in natural sciences as well as social sciences. Here in this paper we are presenting a study on linear algebra and associated linear equations, also the eigen values and eigen vectors as a subtopic and few applications of it.the work basically focuses n eigen values and eigen vectors their useful properties including some applications of it.

Improving a 1D Hydraulic Model to Include Bridges as Internal Boundary Conditions

The paper describes the implementation of internal boundary conditions in the 1D ORSADEM hydraulic model to simulate the effect of a hydraulic in-line structure. The proposed model introduces a simplified representation of the bridge geometry by imposing an equivalent narrowing, computed according to the opening size and characteristics, combined with the mass and energy balance at the structure. The model is then applied to a series of experimental tests concerning the propagation of shock waves through different types of bridges, representing different flow conditions, from free surface flow to overflow. The tests are also simulated with the original 1D ORSADEM model, including the standard head losses and the cross-section narrowing due to the presence of a structure. The comparison with the experimental measurements shows that the proposed model can simulate the shock wave flow through the bridges with a higher accuracy than the standard formulation. These findings highlight the possibility of properly evaluating the backwater effect at bridges even with a simple 1D model if the physical narrowing of the cross-section is modeled.

Modeling Realistic Geometries in Human Intrathoracic Airways.

Geometrical models of the airways offer a comprehensive perspective on the complex interplay between lung structure and function. Originating from mathematical frameworks, these models have evolved to include detailed lung imagery, a crucial enhancement that aids in the early detection of morphological changes in the airways, which are often the first indicators of diseases. The accurate representation of airway geometry is crucial in research areas such as biomechanical modeling, acoustics, and particle deposition prediction. This review chronicles the evolution of these models, from their inception in the 1960s based on ideal mathematical constructs, to the introduction of advanced imaging techniques like computerized tomography (CT) and, to a lesser degree, magnetic resonance imaging (MRI). The advent of these techniques, coupled with the surge in data processing capabilities, has revolutionized the anatomical modeling of the bronchial tree. The limitations and challenges in both mathematical and image-based modeling are discussed, along with their applications. The foundation of image-based modeling is discussed, and recent segmentation strategies from CT and MRI scans and their clinical implications are also examined. By providing a chronological review of these models, this work offers insights into the evolution and potential future of airway geometry modeling, setting the stage for advancements in diagnosing and treating lung diseases. This review offers a novel perspective by highlighting how advancements in imaging techniques and data processing capabilities have significantly enhanced the accuracy and applicability of airway geometry models in both clinical and research settings. These advancements provide unique opportunities for developing patient-specific models.

A parallel coupling framework for DEM-MBD: Model verification and application

Bulk material handling equipment can be numerically studied using the DEM-MBD method, where the particulate dynamics are solved by DEM (Discrete Element Method) and the motion characteristics of the mechanical components are modeled by MBD (Multi-Body Dynamics). In this work, a two-way coupling framework is proposed for the co-simulation of our self-developed DEM solver (DEMSLab) with the commercial MBD software (RecurDyn) using a parallel staggered coupling approach. To verify the proposed coupling method, the simulation result of a torsional spring damper system is compared with the corresponding analytical solution. After that, to assess the feasibility of this method in industrial-scale applications, a series of simulations involving a wheel loader is carried out. Different simulation conditions are adopted to reveal their impact on computational efficiency and simulation accuracy. These conditions include the mesh representation of the equipment geometry, the MBD time step size, and the coupling interval. An improved mesh simplification algorithm is proposed and used to reasonably simplify the surface mesh of the wheel loader, thus lowering the computational intensity of particle-wall interactions in DEM. The comparison results indicate that the computational time can be largely saved while the simulation accuracy remains considerably high. The MBD step size and coupling interval are crucial for numerical stability and should be selected carefully.

Free and forced vibration analysis of piezolaminated plates via an isogeometric layerwise finite element

Isogeometric layerwise finite element (L-IGA) formulation is a recent state-of-the-art approach integrating Non-Uniform Rational B-spline (NURBS) basis functions into the quasi-static solution process of piezolaminated composite plates. This study extends the application of the L-IGA framework to encompass free, forced vibration, and displacement control analyses of laminated composite plates with straight/curvilinear fibers and piezoelectric layers. To this end, the NURBS basis functions, utilized in geometry definition, are employed to solve electromechanically coupled differential equations following Hamilton’s variational principle. The adoption of high-order continuous NURBS shape functions throughout the IGA discretization span both in-plane and through-thickness laminate dimensions. This effectively facilitates precise geometry representation directly from Computer-Aided Design (CAD). Besides, such a discretization accelerates the convergence of displacement and electric potential solution fields toward exact results. Various benchmark problems have been solved to verify the robustness and high accuracy of the proposed dynamic L-IGA method. These include comparative analyses between L-IGA dynamic solutions (i.e. employing the Newmark-Beta method), analytical solutions, and ANSYS-Solid 226 finite element results. All the results are compared across various span-to-thickness ratios, mechanical-potential loading scenarios, and fiber orientation angles. Remarkably, the L-IGA method attains almost excellently accurate time response of various fields (displacement, stress, electric potential) and modal results, with considerably fewer mesh elements than Solid 226 solutions. Overall, such an outcome reveals the high potential and practical merits of the proposed L-IGA formulation as a proficient finite element approach for the dynamic analysis of piezolaminated plates.

Moving Morphable Components Using Strain-Based Beam Geometry Description for Topology Optimization

In the moving-morphable-component topology optimization, morphable components are introduced as a geometrical model mapped onto the background finite elements, and their shape parameters are utilized as design variables for topology optimization. Whereas a complex curved geometry ensuring C1 continuity can be generated using existing curved components, the component curvatures cannot be selected as design variables in the existing methods; thus geometric constraints associated with curvatures cannot also be directly imposed. To address this issue, this study proposes a curvature-based morphable component by introducing the curvilinear geometry representation in the strain-based beam formulation. Since the proposed component is parameterized by curvatures using the curvilinear equation, the component curvatures can be utilized as the design variables. This allows for directly imposing curvature constraints on structural members, thereby accounting for the manufacturability of an optimal topology. It is demonstrated that a symmetric placement of the design variables using the midpoint curvilinear coordinate system is critical in ensuring convergence of the proposed curvature-based component optimization. The symmetric curvature component is further extended to account for multiple curvatures within a single component while ensuring C1 continuity. Several examples are presented to demonstrate the benefits of the proposed multicurvature component for topology optimization.

Shape optimization of non-matching isogeometric shells with moving intersections

While shape optimization using isogeometric shells exhibits appealing features by integrating design geometries and analysis models, challenges arise when addressing computer-aided design (CAD) geometries comprised of multiple non-uniform rational B-splines (NURBS) patches, which are common in practice. The intractability stems from surface intersections within these CAD models. In this paper, we develop an approach for shape optimization of non-matching isogeometric shells incorporating intersection movement. Separately parametrized NURBS surfaces are modeled using Kirchhoff–Love shell theory and coupled using a penalty-based formulation. The optimization scheme allows shell patches to move without preserving relative location with other members during the shape optimization. This flexibility is achieved through an implicit state function, and analytical sensitivities are derived for the relative movement of shell patches. The introduction of differentiable intersections expands the design space and overcomes challenges associated with large mesh distortion, particularly when optimal shapes involve significant movement of patch intersections in physical space. Throughout optimization iterations, all members within the shell structures maintain the NURBS geometry representation, enabling efficient integration of analysis and design models. The optimization approach leverages the multilevel design concept by selecting a refined model for accurate analysis from a coarse design model while maintaining the same geometry. We adopt several example problems to verify the effectiveness of the proposed scheme and demonstrate its applicability to the optimization of the internal stiffeners of an aircraft wing.

Interactive geometry editing of Neural Radiance Fields

Neural Radiance Fields (NeRF) have recently emerged as a promising approach for synthesizing highly realistic images from 3D scenes. This technology has shown impressive results in capturing intricate details and producing photorealistic renderings. However, one of the limitations of traditional NeRF approaches is the difficulty in editing and manipulating the geometry of the scene once it has been captured. This restriction hinders creative freedom and practical applicability.In this paper, we propose a method that enables interactive geometry editing for neural radiance fields manipulation. We use two proxy cages (inner cage and outer cage) to edit a scene. The inner cage defines the operation target, and the outer cage defines the adjustment space. Various operations apply to the two cages. After cage selection, operations on the inner cage lead to the desired transformation of the inner cage and adjustment of the outer cage. Users can edit the scene with translation, rotation, scaling, or combinations. The operations on the corners and edges of the cage are also supported. Our method does not need any explicit 3D geometry representations. The interactive geometry editing applies directly to the implicit neural radiance fields. Extensive experimental results demonstrate the effectiveness of our approach.

Interference of prototypical geometry representations in students’ construction of concepts and development of proofs

ABSTRACT This study investigates the impact of prototypical geometric representations on students’ ability to construct accurate geometric concepts and their subsequent performance in proving tasks related to those concepts. Ninety-one 11th-grade students participated in the study. We intentionally designed and utilized a questionnaire as the primary data-collection tool. We used the questionnaire items and findings as a basis for semi-structured interviews that we conducted with approximately 10% of the study participants. This allowed the integration of the quantitative and qualitative analyses, to provide a comprehensive understanding of the learning processes. Our analysis reveals that many Grade 11 students struggle with geometric concept formation due to an overreliance on prototypical examples, which in turn hinders their ability to construct proofs concerning the attributes of these concepts, highlighting the need for more diverse representations in geometry instruction.

Software for Bioprinting.

The bioprinting of heterogeneous organs is a crucial issue. To reach the complexity of such organs, there is a need for highly specialized software that will meet all requirements such as accuracy, complexity, and others. The primary objective of this review is to consider various software tools that are used in bioprinting and to reveal their capabilities. The sub-objective was to consider different approaches for the model creation using these software tools. Related articles on this topic were analyzed. Software tools are classified based on control tools, general computer-aided design (CAD) tools, tools to convert medical data to CAD formats, and a few highly specialized research-project tools. Different geometry representations are considered, and their advantages and disadvantages are considered applicable to heterogeneous volume modeling and bioprinting. The primary factor for the analysis is suitability of the software for heterogeneous volume modeling and bioprinting or multimaterial three-dimensional printing due to the commonality of these technologies. A shortage of specialized suitable software tools is revealed. There is a need to develop a new application area such as computer science for bioprinting which can contribute significantly in future research work.

Source shape estimation for neutron imaging systems using convolutional neural networks.

Neutron imaging systems are important diagnostic tools for characterizing the physics of inertial confinement fusion reactions at the National Ignition Facility (NIF). In particular, neutron images give diagnostic information on the size, symmetry, and shape of the fusion hot spot and surrounding cold fuel. Images are formed via collection of neutron flux from the source using a system of aperture arrays and scintillator-based detectors. Currently, reconstruction of fusion source geometry from the collected neutron images is accomplished by solving a computationally intensive maximum likelihood estimation problem via expectation maximization. In contrast, it is often useful to have simple representations of the overall source geometry that can be computed quickly. In this work, we develop convolutional neural networks (CNNs) to reconstruct the outer contours of simple source geometries. We compare the performance of the CNN for penumbral and pinhole data and provide experimental demonstrations of our methods on both non-noisy and noisy data.

Isogeometric method for a nonlocal degenerate parabolic problem

In this article, we apply NURBS-based isogeometric method to solve a nonlocal degenerate parabolic problem. The isogeometric method has advantages over classical finite element method in terms of exact geometry representation and higher order smooth basis functions. We consider the NURBS-based semi-discretization of the problem. The second-order Crank–Nicolson method is applied for the complete discretization of the problem. Error estimates of the semi-discrete and fully-discrete problems are derived. Few numerical examples are provided to verify the theoretical findings.

TensoSDF: Roughness-aware Tensorial Representation for Robust Geometry and Material Reconstruction

Reconstructing objects with realistic materials from multi-view images is problematic, since it is highly ill-posed. Although the neural reconstruction approaches have exhibited impressive reconstruction ability, they are designed for objects with specific materials (e.g., diffuse or specular materials). To this end, we propose a novel framework for robust geometry and material reconstruction, where the geometry is expressed with the implicit signed distance field (SDF) encoded by a tensorial representation, namely TensoSDF. At the core of our method is the roughness-aware incorporation of the radiance and reflectance fields, which enables a robust reconstruction of objects with arbitrary reflective materials. Furthermore, the tensorial representation enhances geometry details in the reconstructed surface and reduces the training time. Finally, we estimate the materials using an explicit mesh for efficient intersection computation and an implicit SDF for accurate representation. Consequently, our method can achieve more robust geometry reconstruction, outperform the previous works in terms of relighting quality, and reduce 50% training times and 70% inference time. Codes and datasets are available at https://github.com/Riga2/TensoSDF.

LightFormer: Light-Oriented Global Neural Rendering in Dynamic Scene

The generation of global illumination in real time has been a long-standing challenge in the graphics community, particularly in dynamic scenes with complex illumination. Recent neural rendering techniques have shown great promise by utilizing neural networks to represent the illumination of scenes and then decoding the final radiance. However, incorporating object parameters into the representation may limit their effectiveness in handling fully dynamic scenes. This work presents a neural rendering approach, dubbed LightFormer , that can generate realistic global illumination for fully dynamic scenes, including dynamic lighting, materials, cameras, and animated objects, in real time. Inspired by classic many-lights methods, the proposed approach focuses on the neural representation of light sources in the scene rather than the entire scene, leading to the overall better generalizability. The neural prediction is achieved by leveraging the virtual point lights and shading clues for each light. Specifically, two stages are explored. In the light encoding stage, each light generates a set of virtual point lights in the scene, which are then encoded into an implicit neural light representation, along with screen-space shading clues like visibility. In the light gathering stage, a pixel-light attention mechanism composites all light representations for each shading point. Given the geometry and material representation, in tandem with the composed light representations of all lights, a lightweight neural network predicts the final radiance. Experimental results demonstrate that the proposed LightFormer can yield reasonable and realistic global illumination in fully dynamic scenes with real-time performance.

Exploring the influence of pore shape on conductance and permeation

There are increasing numbers of ion channel structures featuring heteromeric subunit assembly, exemplified by synaptic α1βB glycine and α4β2 nicotinic receptors. These structures exhibit inherent pore asymmetry, but the relevance of this to function is unknown. Furthermore, molecular dynamics simulations performed on symmetrical homomeric channels often lead to thermal distortion whereby conformations of the resulting ensemble are also asymmetrical. When functionally annotating ion channels, researchers often rely on minimal constrictions determined via radius-profile calculations performed with computer programs, such as HOLE or CHAP, coupled with an assessment of pore hydrophobicity. However, such tools typically employ spherical probe particles, limiting their ability to accurately capture pore asymmetry. Here, we introduce an algorithm that employs ellipsoidal probe particles, enabling a more comprehensive representation of the pore geometry. Our analysis reveals that the use of nonspherical ellipsoids for pore characterization provides a more accurate and easily interpretable depiction of conductance. To quantify the implications of pore asymmetry on conductance, we systematically investigated carbon nanotubes with varying degrees of pore asymmetry as model systems. The conductance through these channels shows surprising effects that would otherwise not be predicted with spherical probes. The results have broad implications not only for the functional annotation of biological ion channels but also for the design of synthetic channel systems for use in areas such as water filtration. Furthermore, we make use of the more accurate characterization of channel pores to refine a physical conductance model to obtain a heuristic estimate for single-channel conductance. The code is freely available, obtainable as pip-installable python package and provided as a web service.

Text-to-building: experiments with AI-generated 3D geometry for building design and structure generation

The paper seeks to investigate novel potentials for building design and structure generation that arise at the intersection of computational design and AI-generated 3D geometries. Although the use of AI technologies is exponentially increasing inside the architectural discipline, the design of spatial building configurations using AI-generated 3D geometries is still limited in its applications and represents an ongoing field of investigation in advanced architectural research. In this regard, several questions still need to be answered: how can we design new building typologies from AI-generated 3D geometries? And how can we use these typologies to shape both the real and the virtual world?The paper proposes a new approach to architectural design where artificial intelligence is used as the starting point for design exploration, while computational design procedures are employed to convert AI-generated 3D geometries into building elements – such as columns, beams, horizontal and vertical surfaces. The paper starts with a general overview of the current use of artificial intelligence inside the architectural discipline, and then it moves towards the explanation of specific AI generative models for 3D geometry reconstruction and representation. Subsequently, the proposed working pipeline is analysed in more detail – from the creation of 3D geometries using generative AI models to the conversion of such geometries into building elements that can be further designed and optimised using computational design tools and methods. The results shown in the paper are achieved using Shap-E as the main AI model, though the proposed pipeline can be implemented with multiple AI models. The paper ends by showing some of the generated results, finally adding some considerations to the relationship between human and artificial creativity inside the architectural discipline.The work presented in the paper suggests that the use of computational design tools and methods combined with the tectonics of the latent space opens new opportunities for topological and typological explorations. In a time where traditional architectural typologies are moving towards stagnation due to their inability to satisfy new human needs and ways of living, exploring AI-based working pipelines related to architectural design allows the definition of new design solutions for the generation of new architectural spaces. In doing so, the serendipitous aspect of AI biases is used as an auxiliary force to inform design decisions, promoting the discovery of a new inbuilt dynamism between human and artificial creativity. In a time where AI is everywhere, understanding the measure of such dynamism represents a key aspect for the future of the architectural discipline.

Efficient graph representation in graph neural networks for stress predictions in stiffened panels

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network (GNN) is a particular type of neural network which processes data that can be represented as graphs. This allows for efficient representation of complex geometries that can change during the conceptual design of a structure or a product. In this study, we propose a novel graph embedding for the efficient representation of 3D stiffened panels by considering separate plate domains as vertices. This approach is considered using Graph Sampling and Aggregation (GraphSAGE) to predict stress distributions in stiffened panels with varying geometries. A comparison between a finite element-vertex graph representation is conducted to demonstrate the effectiveness of the proposed approach. A comprehensive parametric study is performed to examine the effect of structural variables on stress predictions. A wide range of geometries is considered, material nonlinearity, a few boundary conditions, together with uniform and patch loading at various positions. The study involves straight and curved panels with uni- and bi-directional stiffeners. The proposed unit-vertex representation of the panel requires only about 2% of GPU memory and about 4% of training time in comparison to a finite element-vertex embedding. The GraphSAGE model with the proposed unit-vertex representation accurately captures stress distribution across all panels, achieving an average prediction accuracy of 92.3% for the maximum von Mises stress. Our results demonstrate the immense potential of graph neural networks with the proposed graph embedding as a robust reduced-order model for 3D structures.