Polygonal Surface Research Articles

PCO: Precision-Controllable Offset Surfaces with Sharp Features

Surface offsetting is a crucial operation in digital geometry processing and computer-aided design, where an offset is defined as an iso-value surface of the distance field. A challenge emerges as even smooth surfaces can exhibit sharp features in their offsets due to the non-differentiable characteristics of the underlying distance field. Prevailing approaches to the offsetting problem involve approximating the distance field and then extracting the iso-surface. However, even with dual contouring (DC), there is a risk of degrading sharp feature points/lines due to the inaccurate discretization of the distance field. This issue is exacerbated when the input is a piecewise-linear triangle mesh. This study is inspired by the observation that a triangle-based distance field, unlike the complex distance field rooted at the entire surface, remains smooth across the entire 3D space except at the triangle itself. With a polygonal surface comprising n triangles, the final distance field for accommodating the offset surface is determined by minimizing these n triangle-based distance fields. In implementation, our approach starts by tetrahedralizing the space around the offset surface, enabling a tetrahedron-wise linear approximation for each triangle-based distance field. The final offset surface within a tetrahedral range can be traced by slicing the tetrahedron with planes. As illustrated in the teaser figure, a key advantage of our algorithm is its ability to precisely preserve sharp features. Furthermore, this paper addresses the problem of simplifying the offset surface's complexity while preserving sharp features, formulating it as a maximal-clique problem.

Acoustic Radiation Patterns of Different Polygon Piston Surfaces

Transducers are used in acoustic remote sensing and several other modern applications. The radiating surface geometry of a single acoustic transducer affects its beam pattern and has a cumulative effect on the overall performance of an array configuration. In addition, the transducers with polygon radiating surfaces provide more compact structure in an array than the circular pistons due to their flat surface edges. However, until now, the radiation patterns of acoustic polygonal pistons have not been exclusively studied and documented. In this study, the directional factors of acoustic pistons with polygonal surfaces of three to ten sides were derived analytically from the first principle using the Rayleigh integral. These directional factors were used to synthesise and characterise the radiation patterns of the piston sources in comparison with the baffled circular piston of an equivalent surface area. The rectangular, the triangular, and the rest of the polygons have the same performance with the circular piston when the surface diameter is not higher than 0.5λ, 0.28λ and 0.43λ, respectively. The main lobe of the acoustic emissions from the square is very close to that of the circular piston whose diameter is greater than a wavelength while that of the rectangle is wider. The results show that the radiating surface perimeter and symmetry are the two most critical factors affecting the beam characteristics of a piston source rather than the surface area or the number of sides. The theoretical results were validated using the finite element method with an excellent compliance.

Autonomous design framework for deploying building integrated photovoltaics

The advancements in perovskite solar cells present promising prospects for the widespread deployment of Building-Integrated Photovoltaics (BIPVs). Finding an efficient and accurate approach is essential to provide deployment strategies for decision support. This study develops an autonomous decision-making design framework for BIPV, including data collection, 3D modeling, and deployment strategy. For data collection, an open-source unmanned aerial vehicle platform is produced to execute an innovation explore-then-exploit algorithm for viewpoints generation and path planning. Subsequently, point cloud models of buildings are generated using a unique deep learning-based multi-view stereo network and then converted into polygonal surface models. Moreover, a novel Grasshopper plugin component is developed to assess the economic performance of various BIPV layouts by life cycle cost analysis. Based on the analysis results, potential BIPV deployment strategies are provided to support the decision-making process. The effectiveness of the framework is validated through its application in an industrial building in Hong Kong, demonstrating a 7.6 % discrepancy in the average annual solar radiation access value. Finally, two BIPV deployment strategies are proposed for the building. This study has significant implications for the design and deployment of PV systems in urban environments, representing an important step towards supporting the transition to sustainable and low-carbon cities.

The relationship between facial directional asymmetry, handedness, chewing side preference, and eyedness

We aimed to describe facial directional asymmetry (DA) in individuals with different manifestations of laterality. Due to the overlap between brain and face development, a relationship between the manifestation of brain laterality and DA is hypothesised. These findings could clarify the relationship between the brain and facial phenotype and help to plan facial or oral motor rehabilitation. The DA of 163 healthy individuals was assessed by two complementary 3D methods: landmark and polygonal surface analysis using colour-coded maps. Handedness was assessed using the Edinburgh Handedness Inventory, while chewing side and eye preferences were self-reported. The results showed a similar DA pattern regardless of sex and laterality (the right-sided protrusion of the forehead, nose, lips, and chin) and a slightly curved C-shape of the midline in landmark analysis. A relationship between lateralized behaviours and DA was found only in males, in females the DA pattern was more homogenous. Right-handed individuals and right-side chewers showed a protrusion of the right hemiface. Males, left-handed and left-side chewers, manifested a protrusion of the left lateral hemiface. We suggest that these specific differences in males may be due to their typically higher level of brain asymmetry. No apparent relationship was found between eyedness and DA.

Controlling the surface oxidation state of halogenated Cu-based catalyst for electrochemical reduction of carbon dioxide to ethylene

The electrochemical CO2 reduction reaction (CO2RR) has attracted significant attention as strategy for achieving carbon neutrality. Among the candidate materials for the CO2RR, Cu-based electrocatalysts can potentially produce various high-value carbon products. However, the diversity of their products obtained via CO2RR induces low selectivity and hinders the acquisition of a specific product with a high yield. Herein, we suggest the strategies for enhancing ethylene production via CO2RR by reconstructing the oxidation states of the Cu-based catalysts. The introduced chemical oxidation and following halogenation contributes to modulate the electron structures and oxidation states of the electrodeposited polygonal Cu catalyst surface. In particular, the chemical oxidation step induces the coexistence of Cu0 and Cu+ on the catalyst surface which stabilize the CO2 adsorption onto the catalyst surface, and the halogenation maintains the Cu0/Cu+ ratio of the catalyst surface during the CO2RR. As a result, controlling the oxidation states of Cu-based catalyst improves the ethylene production selectivity up to 47.0 % of Faradaic efficiency. Furthermore, we employ a membrane electrode assembly-based electrolyzer for CO2RR which is used for commercialization, and achieve high ethylene production with a partial current density of 124.7 mA cm–2.

Laplacian2Mesh: Laplacian-Based Mesh Understanding.

Geometric deep learning has sparked a rising interest in computer graphics to perform shape understanding tasks, such as shape classification and semantic segmentation. When the input is a polygonal surface, one has to suffer from the irregular mesh structure. Motivated by the geometric spectral theory, we introduce Laplacian2Mesh, a novel and flexible convolutional neural network (CNN) framework for coping with irregular triangle meshes (vertices may have any valence). By mapping the input mesh surface to the multi-dimensional Laplacian-Beltrami space, Laplacian2Mesh enables one to perform shape analysis tasks directly using the mature CNNs, without the need to deal with the irregular connectivity of the mesh structure. We further define a mesh pooling operation such that the receptive field of the network can be expanded while retaining the original vertex set as well as the connections between them. Besides, we introduce a channel-wise self-attention block to learn the individual importance of feature ingredients. Laplacian2Mesh not only decouples the geometry from the irregular connectivity of the mesh structure but also better captures the global features that are central to shape classification and segmentation. Extensive tests on various datasets demonstrate the effectiveness and efficiency of Laplacian2Mesh, particularly in terms of the capability of being vulnerable to noise to fulfill various learning tasks.

Spatio-Temporal Hierarchical Data Structure Based on Sparse Voxel Octrees for Representation of the Geometry of Time-Variable Three-Dimensional Scenes

Abstract The paper deals with the problematics of representation of the geometry of three-dimensional scenes in computer graphics using domain-specific hierarchical data structures based on octant trees or directed acyclic graphs as the means of space saving binary representation of this information. Several hierarchical data structures were introduced in this field in past decades. In this paper we are moving this problematic to the field of the representation of three-dimensional scenes which are rather dynamic in time, so their geometry is changing on the regular basis. We are investigating the influence of this time-variability on the size of the related hierarchical data structure on binary level. We are comparing the approach in which each time step is considered as the stand-alone static three-dimensional scene and therefore is represented by its own hierarchical data structure with the approach when this time-variable scene is considered as the four dimensional space and spatio-temporal sparse voxel octree hierarchical data structure is used for the representation of the geometry of this scene. We tested both approaches on three different scenes which were obtained by voxelization into two different resolutions of polygonal surface models represented originally as the mesh of triangles in Wavefront Object file format. Results of the tests show that spatio-temporal sparse voxel octree is better solution, when we obtained from 1.73 to 2.08 more compact binary representation, in comparison to the solution when time frames were encoded separately as the set of sparse voxel octrees.

Quasi-3D slope stability analysis of waste dump based on double wedge failure

The double wedges sliding along the weak layer of the foundation can be observed on the slope of the waste dump and the sliding body is divided into the active wedge and passive wedge by the weak foundation and the failure surfaces of the waste dump. Because the conventional limit equilibrium slice method cannot reflect the polygonal slip surface of the slope of the waste dump with weak foundation, this study proposed a double wedge calculation method for the slope of the waste dump with weak foundation. The limit equilibrium analysis is performed on double wedges by considering the direction and values of the interaction force between double wedges to obtain the safety factor of the slope of the waste dump. Meanwhile, the quasi-3D double wedges stability analysis method of the waste dump slope with weak foundation is proposed by considering the influence of the geometry and sliding direction of the slope surface on the slope stability. The safety factor of the inverted dump slope is 0.82, the volume of the sliding body is 6.43 million m3, and the main sliding direction is 20° south by east. The shear strain rate cloud diagram of the section is ‘y’ type distribution, and the sliding body is divided into two independent blocks. The safety factor of the sliding body section obtained by the double wedge method is between 0.76 and 0.92, and the closer to the boundary of the sliding body, the greater the safety factor of the section. The quasi-three-dimensional safety factor obtained by theoretical analysis is 0.817. The results show that the calculation results of quasi-3D double wedge are basically consistent with the calculation results of strength reduction method, while the proposed method is simpler. It can be used as a quick method to evaluate slope stability in engineering practice.

Hybrid 3D Reconstruction of Indoor Scenes Integrating Object Recognition

Indoor 3D reconstruction is particularly challenging due to complex scene structures involving object occlusion and overlap. This paper presents a hybrid indoor reconstruction method that segments the room point cloud into internal and external components, and then reconstructs the room shape and the indoor objects in different ways. We segment the room point cloud into internal and external points based on the assumption that the room shapes are composed of some large external planar structures. For the external, we seek for an appropriate combination of intersecting faces to obtain a lightweight polygonal surface model. For the internal, we define a set of features extracted from the internal points and train a classification model based on random forests to recognize and separate indoor objects. Then, the corresponding computer aided design (CAD) models are placed in the target positions of the indoor objects, converting the reconstruction into a model fitting problem. Finally, the indoor objects and room shapes are combined to generate a complete 3D indoor model. The effectiveness of this method is evaluated on point clouds from different indoor scenes with an average fitting error of about 0.11 m, and the performance is validated by extensive comparisons with state-of-the-art methods.

A Novel Radial Basis Function Description of a Smooth Implicit Surface for Musculoskeletal Modelling

As musculoskeletal illnesses continue to increase, practical computerised muscle modelling is crucial. This paper addresses this concern by proposing a mathematical model for a dynamic 3D geometrical surface representation of muscles using a Radial Basis Function (RBF) approximation technique. The objective is to obtain a smoother surface while minimising data use, contrasting it from classical polygonal (e.g. triangular) surface mesh models or volumetric (e.g. tetrahedral) mesh models. The paper uses RBF implicit surface description to describe static surface generation and dynamic surface deformations based on its spatial curvature preservation during the deformation. The novel method is tested on multiple data sets, and the experiments show promising results according to the introduced metrics.

Line-Based 3D Building Abstraction and Polygonal Surface Reconstruction From Images.

Textureless objects, repetitive patterns and limited computational resources pose significant challenges to man-made structure reconstruction from images, because feature-points-based reconstruction methods usually fail due to the lack of distinct texture or ambiguous point matches. Meanwhile multi-view stereo approaches also suffer from high computational complexity. In this article, we present a new framework to reconstruct 3D surfaces for buildings from multi-view images by leveraging another fundamental geometric primitive: line segments. To this end, we first propose a new multi-resolution line segment detector to extract 2D line segments from each image. Then, we construct a 3D line cloud by introducing an improved Line3D++ algorithm to match 2D line segments from different images. Finally, we reconstruct a complete and manifold surface mesh from 3D line segments by formulating a Bayesian probabilistic modeling problem, which accurately generates a set of underlying planes. This output model is simple and has low performance requirements for hardware devices. Experimental results demonstrate the validity of the proposed approach and its ability to generate abstract and compact surface meshes from the 3D line cloud with low computational costs.

Boulder Diversity in the Nightingale Region of Asteroid (101955) Bennu and Predictions for Physical Properties of the OSIRIS‐REx Sample

AbstractThe sample of asteroid (101955) Bennu was collected from the Nightingale sample site by the Origins, Spectral Interpretation, Resource Identification, and Security–Regolith Explorer spacecraft and arrived on Earth on 24 September 2023. To better understand Bennu's parent body, we identified boulders over 2 m in diameter around the Nightingale region and analyzed normal albedo, morphology, and surface roughness. We found that boulders can be separated into two groups based on albedo, and four groups using morphology including angularity, texture, and the presence or absence of clasts, layers, and bright spots: Type A is rounded, rugged, and clastic, with the highest root‐mean square deviation roughness; Type B is sub‐angular with intermediate roughness and polygonal surface fractures; Type C is angular, has distinct fractures, and the lowest roughness; and Type D is sub‐angular with intermediate roughness and bright spots. Unsupervised clustering algorithms showed that our Type A‐D classification represents the diversity in the morphology and albedo data. Using documented contacts between boulder groups, we conclude that boulders on Bennu originated on a single, heterogeneous parent body that experienced vertical mixing via impacts prior to or during its disruption. The boulder morphologies on Bennu bear striking resemblance to those on asteroid Ryugu, potentially suggesting a shared origin. Finally, from analyses of sample collection images, we predict that the sample will be heterogeneous in morphology, brightness, and degree of aqueous alteration and dominated by darker Type A and B material. These predictions are supported by initial analyses of the Ryugu sample.

Size and shape of human mandible: Sex differences and influence of age on sex estimation accuracy

The degree of sexual dimorphism expressed by human bones is of primary importance for the development of accurate methods for sex estimation. The objective of the present study was to investigate sex differences in shape and size of the mandible using geometric morphometric methods. The study also aimed to examine the impact of age on the sex classification ability of the size and shape of the mandible. Computed tomography images of 190 Bulgarians (98 males and 92 females) were used in the study. Polygonal surface models of the skulls were generated and used for digitizing 45 landmarks located on the mandible. The raw three-dimensional coordinates of the landmarks were processed via generalized Procrustes superimposition. The sex differences in mandibular size and shape were evaluated for statistical significance. Multivariate regression was applied for correction of the allometric effect. Principal component analysis, discriminant analysis, and canonical variate analysis were also used in the study. Mandibular size differed significantly between males and females and achieved a sex classification accuracy of 87%. The significance of the sex differences in mandibular shape depended on the type of shape variables used in the analysis. The shape variables provided different classification accuracy: 78% using the Procrustes coordinates and 53% using the regression residuals. The male and female mandibles differed significantly in size and shape, including the allometric component. Mandibular size is a more effective sex indicator than shape. Age has an ambiguous effect on the classification accuracy of the size and shape variables of the mandible.

Approaching Intradural Lesions of the Anterior Foramen Magnum and Craniocervical Junction: Anatomical Comparison of the Open Posterolateral and Anterior Extended Endonasal Endoscopic Approaches

Lesions of the foramen magnum (FM) and craniocervical junction area are traditionally managed surgically through anterior, anterolateral, and posterolateral skull-base approaches. This anatomical study aimed to compare the usefulness of a modified extended endoscopic approach, the so-called far-medial endonasal approach (FMEA), versus the traditional posterolateral far-lateral approach (FLA). Ten fixed silicon-injected heads specimens were used in the Skull Base ENT-Neurosurgery Laboratory of the University Hospital of Strasbourg, France. A total of 20 FLAs and 10 FMEAs were realized. A high-resolution computed tomography scan was performed for quantitative analysis of the different approaches. The analysis aimed to estimate the extent of surgical exposure and freedom of movement (maneuverability) through the operating channel using a polygonal surface model to obtain a morphometric estimation of the area of interest (surface and volume) on postdissection computed tomography scans using Slicer 3D software. FMEA allows for a more direct route to the anterior FM, with wider brainstem exposure compared with the FLA and an excellent visualization of all anterior midline structures. The limitations of the FMEA include the deep and narrow surgical corridor and difficulty in reaching lesions located laterally over the jugular foramen and hypoglossal canal. The FMEA and FLA are both effective surgical routes to reach FM and craniocervical junction lesions. Modern skull base surgeons should have a good command of both because they appear complementary. This anatomical study provides the tools for comprehensive preoperative evaluations and selection of the most appropriate surgical approach.

Deep learning of curvature features for shape completion

The paper presents a novel solution to the issue of incomplete regions in 3D meshes obtained through digitization. Traditional methods for estimating the surface of missing geometry and topology often yield unrealistic outcomes for intricate surfaces. To overcome this limitation, the paper proposes a neural network-based approach that generates points in areas where geometric information is lacking. The method employs 2D inpainting techniques on color images obtained from the original mesh parameterization and curvature values. The network used in this approach can reconstruct the curvature image, which then serves as a reference for generating a polygonal surface that closely resembles the predicted one. The paper’s experiments show that the proposed method effectively fills complex holes in 3D surfaces with a high degree of naturalness and detail. This paper improves the previous work in terms of a more in-depth explanation of the different stages of the approach as well as an extended results section with exhaustive experiments.

Patterns of influence of different landslide boundaries and their spatial shapes on the uncertainty of landslide susceptibility prediction

Some landslide susceptibility modeling uses idealized landslide points or buffer circles as landslide boundaries, adding uncertainty to the susceptibility modeling. However, landslide boundaries and their spatial shapes are typically presented as irregular polygonal surfaces, such as semicircles and bumps. To study the influence of different landslide boundaries on modeling uncertainty, 370 landslides and 11 environmental factors in Ruijin were chosen in order to establish landslide boundaries and their frequency ratio correlations with environmental factors. Then, these borders were formed, utilizing, respectively, landslide points, buffer circles, and precisely encoded and drawn polygons. Then, models like Point, Circle, and Polygon-based DBN and RF were built using deep belief network (DBN) and random forest (RF). Finally, the distribution pattern of the susceptibility index and its variability were used, along with the receiver operating characteristic (ROC) accuracy, to analyze the modeling uncertainty. The results indicate that: (1) while correct landslide polygon borders are more successful in ensuring modeling accuracy and dependability, using landslide points or buffer circles as boundaries can increase modeling uncertainty. (2) but the. (3) in the absence of precise landslide borders, the landslide susceptibility results derived by employing points and buffer circles as landslide barriers can reflect the spatial distribution pattern of landslide likelihood in the studied area as a whole.

CellRemorph: A Toolkit for Transforming, Selecting, and Slicing 3D Cell Structures on the Road to Morphologically Detailed Astrocyte Simulations

Understanding functions of astrocytes can be greatly enhanced by building and simulating computational models that capture their morphological details. Novel computational tools enable utilization of existing morphological data of astrocytes and building models that have appropriate level of details for specific simulation purposes. In addition to analyzing existing computational tools for constructing, transforming, and assessing astrocyte morphologies, we present here the CellRemorph toolkit implemented as an add-on for Blender, a 3D modeling platform increasingly recognized for its utility for manipulating 3D biological data. To our knowledge, CellRemorph is the first toolkit for transforming astrocyte morphologies from polygonal surface meshes into adjustable surface point clouds and vice versa, precisely selecting nanoprocesses, and slicing morphologies into segments with equal surface areas or volumes. CellRemorph is an open-source toolkit under the GNU General Public License and easily accessible via an intuitive graphical user interface. CellRemorph will be a valuable addition to other Blender add-ons, providing novel functionality that facilitates the creation of realistic astrocyte morphologies for different types of morphologically detailed simulations elucidating the role of astrocytes both in health and disease.

Polygonal contact model revisited: notes on usage and improved implementation

The polygonal contact model is an established contact algorithm for multibody dynamics based on polygonal surfaces. Some guidance for its practical use is presented. In particular, assignment and discretization of the surface meshes are discussed with regard to correct results and optimal efficiency. Moreover, notes on stiffness and damping parameters are given.An improved implementation of the polygonal contact model is introduced. The new algorithm goes without quite complicated intersection construction steps. As a consequence, it is less complex, more robust and usually more efficient than the classic implementation.Application examples of varied complexity demonstrate both notes on usage and improved implementation of the polygonal contact model.

Area Calculation using Measure (iPad and iPhone App)

Mobile applications are rapidly growing in importance and can be used for various purposes. They are now widely used in education. One of the educational purposes for which mobile applications can be used is to calculate the exact result of surface area. This research aims to study the relationships between behavioral factors and the perceived usefulness of using the Measure mobile application in calculating polygonal surfaces. Also, the purpose of the research is to investigate the performance, satisfaction, and perceived behavior of the students while using this application. The methodology of the study is the observation method. The sample of the study includes 50 students from the primary and lower secondary school "Heronjtë e Lumës" Vërmica /Prizren, and from the primary and lower secondary school "Zef Lush Marku" Velezha/Prizren from the Republic of Kosovo. For data collection, the observation list with three sections of 10 indicators is the main instrument. The results of this study show that the use of the Measure mobile application in learning mathematics for students using the application helped to increase student achievement and success. Also, the application was considered satisfactory and promoted a significant increase in students' knowledge, being appropriate for its intended use.

Experimental assessment of the informativity of signs in the analysis of 2d images of bone objects in forensic examination.

This article describes the software implementation of the system for extracting and evaluating information features from 2D images of bone fractures and bone objects for classifying fractures and identifying the alleged instrument that caused the injury. As parameters, the textural characteristics of Haralick, local binary patterns of pixels for 2D images, Gabor filters, Laws energy texture characteristics for 2D images are considered. The analysis carried out on basis of information content estimation to select the features that are most suitable for solving the problem of bone fractures classification. The results will be used for development of methods for complex forensic examination of complex polygonal surfaces of solid objects for automated system for analyzing digital images.