3D Polygon Research Articles

Digital Manufacturing System of Custom Wigs with Measurable 3D Images

Wigs are major important means for improving life quality of the increasing people suffered from hair loss through their image enhancements. For the production of custom made wigs, there requires a mold that reproduces the wearer’s head dimension and the shape of hair loss. The conventional method for this is to make a resin film that adheres to the wig wearer’s head using vinyl tape, and to make a wig pattern with drawing the shape of hair loss onto the film, and to produce a head mold with this pattern, and then to plant hair in a wig cap made based on this mold and wig pattern. This method requires highly skilled manual work, and generates a large amount of chemical waste during the manufacturing process, and takes a long manufacturing period. However, the digital automation of measuring head dimension and the shape of hair loss can replace or omit the production of wig patterns. In this study, a 3D head image capable of actual measurement was implemented by using a 3D polygon head shape measurement device and a camera, which makes a digital production system possible, which can replace the manual wig pattern production process for custom wigs.

An approach to apply the Jaya optimization algorithm to the nesting of irregular patterns

Abstract The problem of nesting frequently arises in the industrial environment, and it has a strong ecological and economic impact in the manufacturing processes. It basically consists of placing a set of pieces (polygons) on a material sheet, making sure that the pieces do not overlap and that they do not exceed the boundaries of the sheet. With regard to irregular 2D polygons, the problem is NP-complete. Therefore, different heuristics have been developed so as to cope with the problem. In this paper, the application of the Jaya metaheuristic algorithm to the nesting problem is proposed. This algorithm has been already applied to several engineering problems and has generally demonstrated better results than most metaheuristic algorithms. In this paper, the Jaya algorithm has been adapted to the specific features of the nesting problem so as to optimize the placement of pieces on a sheet, with the objective of minimizing material waste and computational time. The results of our experimentation demonstrate the algorithm's effectiveness in reducing the convex hull area across various datasets, showing potential in solving complex, irregular shape nesting problems. This research provides a new application of the Jaya algorithm and opens ways for future work in optimization techniques and parameter-free heuristic algorithms for nesting.

Generalization to d-dimensions of a fermionic path integral for exact enumeration of polygons on hypercubic lattices

The generating function for polygons on the square lattice has been known for many decades and is closely related to the path integral formulation of a free fermion model. On the cubic and hypercubic lattices the generating function is still unknown and the problem remains open. It has been conjectured that the three-dimensional (3D) and higher dimensional problems are not solvable—or, to be more precise, that there are no differentiably finite (D-finite) solutions. In this context, very recently a Berezin integral of an exponentiated Grassmann action was found for the polygon generating function on the cubic lattice, making explicit the connection between 3D polygons and a model of interacting fermions. Here we address the problem of how to generalize the 3D result to higher dimensions. We derive a Grassmann representation in terms of a Berezin integral for the generating function of polygons on d-dimensional hypercubic lattices. On the one hand, this new result admittedly brings us no closer to the problem of finding an explicit analytic expression for the desired generating function for polygons. On the other hand, however, the significant advance reported here precisely quantifies the remarkable mathematical difficulty of finding the explicit generating function. Indeed, the non-quadratic functional form of the Grassmann action that we derive here provides a very clear picture of the formidable mathematical obstruction that would need to be overcome. Specifically, in d dimensions, the Grassmann action contains terms of degree 2(d-1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2(d-1)$$\\end{document}, so the model describes interacting rather than free fermions. It is an open problem whether or not these models of interacting fermions can in principle be free fermionized through some still undiscovered algebraic method, but it is widely believed that this goal is mathematically impossible.

Development and validation of predictive models for skeletal malocclusion classification using airway and cephalometric landmarks

ObjectiveThis study aimed to develop a deep learning model to predict skeletal malocclusions with an acceptable level of accuracy using airway and cephalometric landmark values obtained from analyzing different CBCT images.BackgroundIn orthodontics, multitudinous studies have reported the correlation between orthodontic treatment and changes in the anatomy as well as the functioning of the airway. Typically, the values obtained from various measurements of cephalometric landmarks are used to determine skeletal class based on the interpretation an orthodontist experiences, which sometimes may not be accurate.MethodsSamples of skeletal anatomical data were retrospectively obtained and recorded in Digital Imaging and Communications in Medicine (DICOM) file format. The DICOM files were used to reconstruct 3D models using 3DSlicer (slicer.org) by thresholding airway regions to build up 3D polygon models of airway regions for each sample. The 3D models were measured for different landmarks that included measurements across the nasopharynx, the oropharynx, and the hypopharynx. Male and female subjects were combined as one data set to develop supervised learning models. These measurements were utilized to build 7 artificial intelligence-based supervised learning models.ResultsThe supervised learning model with the best accuracy was Random Forest, with a value of 0.74. All the other models were lower in terms of their accuracy. The recall scores for Class I, II, and III malocclusions were 0.71, 0.69, and 0.77, respectively, which represented the total number of actual positive cases predicted correctly, making the sensitivity of the model high.ConclusionIn this study, it is observed that the Random Forest model was the most accurate model for predicting the skeletal malocclusion based on various airway and cephalometric landmarks.

A macro BDM H-div mixed finite element on polygonal and polyhedral meshes

A BDM type of H(div) mixed finite element is constructed on polygonal and polyhedral meshes. The flux space is the H(div) subspace of the n-product ΠiPk(Ti)d space such that the divergence is a one-piece Pk−1 polynomial on the big polygon or polyhedron T. Here we assume the 2D polygon can be subdivided into triangles by connecting only one vertex with some vertices of the polygon. For the 3D polyhedron we assume it can be subdivided into tetrahedra, with no added vertex on subdividing its face-polygons, and with either no internal edge or one internal edge. Such mixed finite elements can be more economic on quadrilateral and hexahedral meshes, compared with the standard BDM mixed element on triangular and tetrahedral meshes. Numerical tests and comparisons with the triangular and tetrahedral BDM finite elements are provided.

MCTS with Refinement for Proposals Selection Games in Scene Understanding.

We propose a novel method applicable in many scene understanding problems that adapts the Monte Carlo Tree Search (MCTS) algorithm, originally designed to learn to play games of high-state complexity. From a generated pool of proposals, our method jointly selects and optimizes proposals that minimize the objective term. In our first application for floor plan reconstruction from point clouds, our method selects and refines the room proposals, modelled as 2D polygons, by optimizing on an objective function combining the fitness as predicted by a deep network and regularizing terms on the room shapes. We also introduce a novel differentiable method for rendering the polygonal shapes of these proposals. Our evaluations on the recent and challenging Structured3D and Floor-SP datasets show significant improvements over the state-of-the-art both in speed and quality of reconstructions, without imposing hard constraints nor assumptions on the floor plan configurations. In our second application, we extend our approach to reconstruct general 3D room layouts from a color image and obtain accurate room layouts. We also show that our differentiable renderer can easily be extended for rendering 3D planar polygons and polygon embeddings. Our method shows high performance on the Matterport3D-Layout dataset, without introducing hard constraints on room layout configurations.

A Survey of Methods for Converting Unstructured Data to CSG Models

The goal of this document is to survey existing methods for recovering or extracting CSG (Constructive Solid Geometry) representations from unstructured data such as 3D point-clouds or polygon meshes. We review and discuss related topics such as the segmentation and fitting of the input data. We cover techniques from solid modeling for the conversion of a polyhedron to a CSG expression and for the conversion of a B-rep to a CSG expression. We look at approaches coming from program synthesis, evolutionary techniques (such as genetic programming or genetic algorithm), and deep learning. Finally, we conclude our survey with a discussion of techniques for the generation of computer programs involving higher-level constructs, representations, and operations for representing solids.

Assessing differential land use impacts on soil quality: A method based on log-response ratios and polygonal projections

Soil quality indices (SQI) used for assessing soil degradation are often developed using additive scoring functions. However, these SQI may lack reference values for interpreting their outputs and the capacity to differentiate changes in specific variables. To overcome these limitations, this study introduces SQI using Log Response Ratios (LRR) as measures of size effects caused by land use in physical, chemical, and microbiological soil quality indicators. LRR vectors projected 2D polygons with condensed change measures along their perimeters. This method was tested in andosols within the southeastern region of Antioquia, Colombia. These soils were subjected to contrasting stages of degradation determined by the extent of A-horizon removal due to land use practices. This study shows that mining and agriculture have detrimental effects on soil organic carbon and water contents, and that size effects vary significantly between land uses (p < 0.05). Microbiological features also exhibit distinct size effects, such as populations of culturable mesophilic bacteria and fungi, microbial basal respiration, spore density of arbuscular mycorrhizal fungi (AMF), their diversity, and total glomalin-related soil proteins (p < 0.05). The SQI proposed exhibited a negative correlation with SQI computed from scoring additive functions either considering the entire dataset (R2 = 0.87) or a minimum dataset (R2 = 0.90). This approach underscores the utility of using LRR geometrical analysis to assess global soil quality differences among land uses (p < 0.01), offering a visual, quantifiable representation of the effects of each land use over specific soil quality indicators.

Metaverse as Tech for Good: Current Progress and Emerging Opportunities

Metaverse is an upcoming transformative technology that will impact our future society with immersive experiences. The recent surge in the adoption of new technologies and innovations in connectivity, interaction technology, and artificial realities can fundamentally change the digital world. The Metaverse concept is the most recent trend to encapsulate and define the potential new digital landscape. However, with the introduction of 5G with high speed and low latency advancements in the hardware and software with the graphics power to display millions of polygons in 3D and blockchain technology, this concept is no longer fiction. This transition from today’s Internet to a spatially embodied Internet is, at its core, a transition from 2D to 3D interactions taking place in multiple virtual universes. In recent years, augmented virtual reality has created possibilities in the private and professional spheres. The new Virtual Reality (VR) headsets and Augmented Reality (AR) glasses can provide immersion in the physical sense. Technology must offer realistic experiences for users to turn this concept into reality. This paper focuses on the potential use cases and benefits of the Metaverse as a tech for good. The research paper outlines the potential areas where a positive impact could occur, highlights recent progress, and discusses the issues around trust, ethics, and cognitive load.

Dissection Puzzles Composed of Multicolor Polyominoes

AbstractDissection puzzles leverage geometric dissections, wherein a set of puzzle pieces can be reassembled in various configurations to yield unique geometric figures. Mathematically, a dissection between two 2D polygons can always be established. Consequently, researchers and puzzle enthusiasts strive to design unique dissection puzzles using the fewest pieces feasible. In this study, we introduce novel dissection puzzles crafted with multi‐colored polyominoes. Diverging from the traditional aim of establishing geometric dissection between two 2D polygons with the minimal piece count, we seek to identify a common pool of polyomino pieces with colored faces that can be configured into multiple distinct shapes and appearances. Moreover, we offer a method to identify an optimized sequence for rearranging pieces from one form to another, thus minimizing the total relocation distance. This approach can guide users in puzzle assembly and lessen their physical exertion when manually reconfiguring pieces. It could potentially also decrease power consumption when pieces are reorganized using robotic assistance. We showcase the efficacy of our proposed approach through a wide range of shapes and appearances.

Creation of the Forearm 3D-Model with Veins from Transversal Ultrasonography Image Sequence.

This study developed an automatic detection algorithm of vessel and skin regions in a transversal ultrasonography image on the arm. We also developed an algorithm to generate a 3D model from detected areas to assist vein puncture. In the algorithm, the vessel's candidate regions in the ultrasonography image were detected using U-Net or Mask R-CNN, which are a kind of deep learning method for segmentation. Then vessel regions were selected among the candidates based on continuous properties in an image sequence. The skin regions were also detected. The 3D polygon data was created from paired pixels in sequential images. The experiments demonstrated that Mask R-CNN could correctly estimate the branch of vessel which were difficult to identify accurate region separately using U-Net, and achieved an overall IoU of 80%. The confirmation experiment of 3D model demonstrated that generated model have enough feasibility for assessment of appropriate veins and locations for puncture.Clinical relevance-The developed 3D model generation from ultrasonography images will be useful for support to identify the appropriate veins for puncture.

Image-based 3D modeling-to-simulation of single-wythe masonry structure via reverse descriptive geometry

This study aims to develop an innovative image-based 3D modeling-to-simulation framework that can efficiently assess the hazard vulnerability of single-wythe masonry structures. Using the novel concept of ‘reverse descriptive geometry’, the framework utilizes 2D masonry wall images to model a 3D single-wythe masonry structure, subsequently converting it into a 3D discrete element model for the vulnerability assessment. The methodology involves segmenting all bricks in the 2D images, identifying the brick geometries by tracing the boundaries, and approximating those into polygons using the splitting method. By incorporating the wall orientations, the simplified 2D polygons are introduced into 3D space and subsequently extruded to a specified thickness. The corners between the walls, i.e., adjoining wythes, are realistically modeled with a type of structural masonry bond. The digitally constructed 3D masonry geometry is enriched with physical properties such as brick mass and mortar strengths, enabling a seamless 3D discrete element simulation to gauge the hazard vulnerability. The proposed framework is successfully applied to Stylite Tower, a heritage single-wythe masonry structure in Jordan. The results demonstrate a remarkable geometric accuracy achieved and further illustrate the structure's potential vulnerability under seismic events, highlighting the efficiency and efficacy of the developed framework. This study introduces a streamlined procedure leveraging a single 2D image per wall for 3D modeling of a structure, thus highly efficient. A discrete element modeling is adopted instead of finite element methods based on a continuum theory. Therefore, this approach accurately captures the discontinuous nature of masonry structures, resulting in a high fidelity in simulation. Furthermore, this study adopts an impulse-based dynamic simulation method that is far more computationally efficient and tolerant to geometric errors than the conventional discrete element method. Therefore, the proposed framework presents a significant advancement in the vulnerability assessment of masonry structures, providing a novel, efficient, and reliable methodology for engineering practice.

TPNet: A novel mesh analysis method via topology preservation and perception enhancement

3D polygon mesh is an important and popular representation of 3D shapes in the field of computer graphics and computer-aided design. Recent works have introduced deep neural networks for mesh data analysis. However, it remains a great challenge for convolutional neural networks to learn mesh shape effectively due to the difficulty of deriving long-range information from the irregular data structure. Another tricky problem is how to explore a high effective representation of the input feature for mesh learning network. In this paper, we propose a novel 3D mesh learning method, named TPNet, which enhances the perception and learns long-range information by customizing dilated convolution for non-uniform mesh data. Specifically, we devise a faithful strategy that accurately locates the position where dilated convolutions can be adopted, despite the non-uniformity and irregularity of the mesh data. Furthermore, our method proposes a topology-preserved 7-dimension feature representation for mesh data and aggregates the features via stacks of convolution layers and dilated convolution layers. Extensive experiments demonstrate the effectiveness of our approach on 3D mesh learning tasks, where we show superior or at least comparable performance to the SOTA approaches.

CONSTRUCTIVE GEOMETRY IN IMPLEMENTATIONS OF MODERN 3D GRAPHICS

3D graphics are one of the crucial development trends of modern digital technologies. Engineering and manufacturing, architecture, design, cinematography, education, and the game industry are an incomplete list of industries where it is actively used. Specialists in 3D graphics are in high demand in the labor market. Their proper training presupposes high-quality knowledge of geometrical sciences, in particular – constructive geometry. Note that constructive geometry is an integral part of modern school mathematics education. That is why, even in the conditions of the school, the teacher should skillfully apply the demonstration capabilities of three-dimensional graphics. It will also encourage students of a comprehensive school to apply knowledge of constructive geometry in practice in the area of 3D modeling. This approach will make it possible to demonstrate the importance and interconnectedness of knowledge in geometry and computer science. Therefore, the article reveals the importance of interdisciplinary connections between the specified disciplines in the context of research, demonstration, and application aspects. In particular, the nuances of using the GeoGebra dynamic geometry complex for conducting computational experiments and creating spatial models based on tasks from a school spatial geometry course are described. After all, modern capabilities of software tools make it possible to demonstrate in real time all the transformations that took place during drawing modeling on the picture plane. The importance of the applied value of constructive geometry for 3D modeling reveals based on examples of solid and polygonal modeling of virtual spatial objects. In particular, the steps of creating a solid model of a pyramid, which is formed by cutting it off with a plane from a regular quadrangular pyramid, are illustrated by the basis of calculations and constructions, which are performed using techniques of constructive geometry. All stages are described and done using the TinkerCAD online modeling service tools. An example of using the Blender program for creating polygonal 3D models is also provided. In particular, the significant aspects of the part modeling process are presented in the example of a task from a drawing textbook. The importance of planimetric constructions in the process of performing high-precision polygonal modeling is also emphasized. The article contains many figures that illustrate the essential stages of modeling. The materials presented can be used to prepare lessons in either mathematics or computer science and can be used to conduct integrated classes that draw on both subjects. Possible prospects for further research on this topic are also presented.

Modeling the Area of Interest for a Mobile Sensory System

We live in the age of the 4th industrial revolution. The leading technologies of this revolution are Cloud computing, Big Data and the Internet of Things (IoT). The vast majority of IoT technologies are characterized by the fact that we collect data with the help of sensors using the Internet. The project MOVIR also implements such an IoT technology. The main goal of the project was the development of a sensor unit. Such sensor units form a network that protects a specific area. This network forms an autonomous electronic area or space protection system. To create this network, we need to define the place we want to protect and the placement of sensor units within this area. Our work is about the mathematical and digital definition of such an area and the placement of sensor units. One of our articles on air traffic control gave the idea of digital modeling the protected area. Here we define the area of interest using significant points. Points are given using GPS coordinates. With the help of a spatial coordinate system, these significant points and a projection, we define a coordinate system to define and model our protected area and the network of sensor units. Here, a digital raster terrain model where significant points are located is required as input data. The digital model of area is defined using a matrix whose elements indicate the height of points in space. The row and column indices of the matrix determine the details of the area. We can use several height layers to describe different obstacles. The accuracy of this theoretical mathematical terrain model depends on the description and details of the accuracy of the terrain. The mathematical model of the area of interest is a 3D polygon. The network of sensor units model is also a 3D polygon located within the area of interest.

Numerical analysis for impact resistance of nacre-like composites

Nacre is attracting attention in the field of bionic materials due to the lightweight and high-strength properties. Inspired by the micro layered structure of nacre, a 3D Voronoi polygons model of an AA7075-T651/toughened epoxy resin composite was established in Abaqus/Explicit. Cohesive elements are inserted between the tablets to simulate the organic matrix of nacre, and blunt bullets are used as research object of impact load. To investigate the interlocking failure mode of the nacre-like composites, the maximum of 40 layers were set in the tablet thickness direction. Based on the impact resistance process of the nacre-like composites, the mechanical mechanism and damage modes at different resistance stages was researched. In addition, the effects of tablet dimensions on energy dissipation and deformation characteristics are analyzed. The results show that increasing the number of layers and decreasing the tablets within the same layers can increase the energy absorption performance of composite. This is mainly due to the effective improvement of the interlayer interlocking mechanism, which increases the damage dissipation energy and frictional dissipation energy. The research has a reference value for the structural design and resistance mechanism analysis of nacre-like composites in the field of aerospace and insulation.

Three-dimensional electro-convective flows of dielectric liquids between concentric cylinders

This study numerically investigates the flow structures and bifurcations of three-dimensional (3D) electro-convection (EC) between concentric cylinders. The flow motion is driven by the volumetric Coulomb force exerting on the free ions introduced by a strong unipolar injection. Three different sets of cases with periodic or symmetric boundary conditions are carried out. The finite volume method is used to numerically resolve the model problem. The co-effect of 2D roll mode and 3D polygon mode at the initial period of the EC flow is identified. The EC flows are made up of different types of regular or irregular centrally downflowing polygonal cells and are characterized by the central charge density cores surrounded by the charge void regions. The symmetry, periodicity, and staggered distribution characteristics of polygonal cells are identified. The cell patterns of EC flow are strongly influenced by the computational domain and the electric Rayleigh number (T). The subcritical bifurcation of linear instability together with a hysteresis loop is observed. In addition, the stability of the triangular flow pattern is analyzed at a large range of T and found that the annular EC flow is more likely to be unstable in three dimensions than in two dimensions.

ПРАКТИЧНІ АСПЕКТИ ВИВЧЕННЯ ПОЛІГОНАЛЬНОГО 3D МОДЕЛЮВАННЯ

An article describes the practical aspects of studying polygonal modeling. To substantiate the topic's relevance, the author points out the importance of modernization in the education sphere. In particular, the using three-dimensional graphics and virtual and augmented reality technologies are one of the significant trends of today. That is why the studying of approaches to the creation and use of digital three-dimensional educational content is necessary for the training of future teachers and lecturers. The author considers the works of both Ukrainian and English-speaking researchers. His analysis of scientific research shows that scientists mainly describe the general issues of implementing 3D graphics, as well as VR and AR, in the educational process. However, they don't sufficiently reveal the topics that are related to the vital problematic moments of studying the process of creating 3D content. Usually, students master them very hard. These include polygonal three-dimensional modeling, animation, and rendering. That is why the author focuses his attention on one of such problematic points - the studying of polygonal modeling. In particular, he aimed to reveal practical aspects of learning based on the analysis of polygon modeling rules, which are directed at helping students to improve their skills in creating surfaces of virtual digital objects. In the main part of the article, the author notes the importance of observing the rules of high-quality construction of the polygon mesh on the object, which is modeled in the three-dimensional editor. Based on the analysis of the presented rules, he gives examples of educational tasks. They allow students to improve their skills in polygonal 3D modeling. The presented tasks can also be used by other teachers to create their system of practical tasks for studying 3D modeling. The article contains the necessary images of three-dimensional models that complement the text material. The models presented in the images are made in the freely distributed 3D graphics editor Blender. This choice is due to the fact that this program is used for teaching three-dimensional graphics both in the study of informatics in schools and institutions of higher and professional education. The conclusions summarize the presented material and point to further prospects for scientific research.

Multistability for a Reduced Nematic Liquid Crystal Model in the Exterior of 2D Polygons

We study nematic equilibria in an unbounded domain, with a two-dimensional regular polygonal hole with K edges, in a reduced Landau–de Gennes framework. This complements our previous work on the “interior problem” for nematic equilibria confined inside regular polygons (SIAM Journal on Applied Mathematics, 80(4):1678-1703, 2020). The two essential dimensionless model parameters are lambda -the ratio of the edge length of polygon hole to the nematic correlation length, and an additional degree of freedom, gamma ^*-the nematic director at infinity. In the lambda rightarrow 0 limit, the limiting profile has two interior point defects outside a generic polygon hole, except for a triangle and a square. For a square hole, the limiting profile has either no interior defects or two line defects depending on gamma ^*, and for a triangular hole, there is a unique interior point defect outside the hole. In the lambda rightarrow infty limit, there are at least left( {begin{array}{c}K 2end{array}}right) stable states and the multistability is enhanced by gamma ^*, compared to the interior problem. Our work offers new insights into how to tune the existence, location, and dimensionality of defects.

Anatomic variations in the frontal and occipital bones: a comparative study of neurocranial morphology

Developmental variations in the cranial vault arise during early ontogenesis due to premature or delayed suture closure, non-union between the normal ossification centers, and emergence of additional ossification centers. These variations cause abnormal calvarial partition and are often associated with modifications of the overall cranial configuration. This study aims to evaluate the impact of metopic suture persistence and the development of supernumerary bones in the occipital region on neurocranial morphology. A series of 245 crania of Bulgarian males was investigated. According to the presence or absence of developmental variations in the frontal and occipital bone they were divided into four series: control (n = 115); crania with a retained metopic suture (n = 32); crania with supernumerary bones in the occipital region (n = 67); and metopic crania with supernumerary bones in the occipital region (n = 31). Polygonal 3D models were generated, on which the 3D coordinates of 35 landmarks describing the neurocranium were collected. Geometric morphometric analyses were applied to compare the size and shape of the landmark configurations. Significant size differences were observed only in the frontal and occipital bone configurations between the metopic crania with occipital supernumerary bones and the non-metopic crania. Significant shape differences were found in all comparisons between the metopic and non-metopic groups for all configurations, except the occipital one. Metopism has a significant impact on overall neurocranial morphology, which is intensified by the presence of supernumerary bones in the occipital region.