3D Polygon Research Articles

Three-Dimensional Modeling of Weed Plants Using Low-Cost Photogrammetry.

Sensing advances in plant phenotyping are of vital importance in basic and applied plant research. Plant phenotyping enables the modeling of complex shapes, which is useful, for example, in decision-making for agronomic management. In this sense, 3D processing algorithms for plant modeling is expanding rapidly with the emergence of new sensors and techniques designed to morphologically characterize. However, there are still some technical aspects to be improved, such as an accurate reconstruction of end-details. This study adapted low-cost techniques, Structure from Motion (SfM) and MultiView Stereo (MVS), to create 3D models for reconstructing plants of three weed species with contrasting shape and plant structures. Plant reconstruction was developed by applying SfM algorithms to an input set of digital images acquired sequentially following a track that was concentric and equidistant with respect to the plant axis and using three different angles, from a perpendicular to top view, which guaranteed the necessary overlap between images to obtain high precision 3D models. With this information, a dense point cloud was created using MVS, from which a 3D polygon mesh representing every plants’ shape and geometry was generated. These 3D models were validated with ground truth values (e.g., plant height, leaf area (LA) and plant dry biomass) using regression methods. The results showed, in general, a good consistency in the correlation equations between the estimated values in the models and the actual values measured in the weed plants. Indeed, 3D modeling using SfM algorithms proved to be a valuable methodology for weed phenotyping, since it accurately estimated the actual values of plant height and LA. Additionally, image processing using the SfM method was relatively fast. Consequently, our results indicate the potential of this budget system for plant reconstruction at high detail, which may be usable in several scenarios, including outdoor conditions. Future research should address other issues, such as the time-cost relationship and the need for detail in the different approaches.

Integrated computer-aided forensic case analysis, presentation, and documentation based on multimodal 3D data

Three-dimensional (3D) crime scene documentation using 3D scanners and medical imaging modalities like computed tomography (CT) and magnetic resonance imaging (MRI) are increasingly applied in forensic casework. Together with digital photography, these modalities enable comprehensive and non-invasive recording of forensically relevant information regarding injuries/pathologies inside the body and on its surface. Furthermore, it is possible to capture traces and items at crime scenes. Such digitally secured evidence has the potential to similarly increase case understanding by forensic experts and non-experts in court.Unlike photographs and 3D surface models, images from CT and MRI are not self-explanatory. Their interpretation and understanding requires radiological knowledge. Findings in tomography data must not only be revealed, but should also be jointly studied with all the 2D and 3D data available in order to clarify spatial interrelations and to optimally exploit the data at hand. This is technically challenging due to the heterogeneous data representations including volumetric data, polygonal 3D models, and images.This paper presents a novel computer-aided forensic toolbox providing tools to support the analysis, documentation, annotation, and illustration of forensic cases using heterogeneous digital data. Conjoint visualization of data from different modalities in their native form and efficient tools to visually extract and emphasize findings help experts to reveal unrecognized correlations and thereby enhance their case understanding. Moreover, the 3D case illustrations created for case analysis represent an efficient means to convey the insights gained from case analysis to forensic non-experts involved in court proceedings like jurists and laymen. The capability of the presented approach in the context of case analysis, its potential to speed up legal procedures and to ultimately enhance legal certainty is demonstrated by introducing a number of representative forensic cases.

To what extent can 3D model replicate dimensions of individual mitral valve prolapse?

Determining the complex geometry of mitral valve prolapse is often difficult. We constructed 3D models of six prolapsed mitral valves for surgical assessment, and evaluated how accurately the models could replicate individual valve dimensions. 3D polygon data were constructed based on an original segmentation method for computed tomography images. The model's replication performance was confirmed via dimensional comparison between the actual hearts during surgery and those models. The results revealed that the prolapsed segments matched in all cases; however, torn chordae were replicated in four cases. The mean height differences were 0.0mm (SD 1.6, range - 2 to + 2mm) for the anterolateral side, 0.0mm (SD 1.7, range - 2 to + 2mm) for the prolapsed leaflet center, and - 1.5mm (SD 0.6, range - 1 to - 2mm) for the posteromedial side. Regression analysis showed a strong and positive correlation, and Bland-Altman plots indicated quantitative similarity of the models to the actual hearts. We concluded that our 3D valve models could replicate the actual mitral valve prolapses within acceptable dimensional differences. Our concepts are useful for better 3D valve creation and better surgical planning with reliable 3D valve models.

Geometric and computer-aided spline hob modeling

The paper considers acquiring the spline hob geometric model. The objective of the research is the development of a mathematical model of spline hob for spline shaft machining. The structure of the spline hob is described taking into consideration the motion in parameters of the machine tool system of cutting edge positioning and orientation. Computer-aided study is performed with the use of CAD and on the basis of 3D modeling methods. Vector representation of cutting edge geometry is accepted as the principal method of spline hob mathematical model development. The paper defines the correlations described by parametric vector functions representing helical cutting edges designed for spline shaft machining with consideration for helical movement in two dimensions. An application for acquiring the 3D model of spline hob is developed on the basis of AutoLISP for AutoCAD environment. The application presents the opportunity for the use of the acquired model for milling process imitation. An example of evaluation, analytical representation and computer modeling of the proposed geometrical model is reviewed. In the mentioned example, a calculation of key spline hob parameters assuring the capability of hobbing a spline shaft of standard design is performed. The polygonal and solid spline hob 3D models are acquired by the use of imitational computer modeling.

Singular fibers of the bending flows on the moduli space of 3D polygons

In this paper, we prove that in the system of bending flows on the moduli space of polygons with fixed side lengths introduced by Kapovich and Millson, the singular fibers are isotropic homogeneous submanifolds. The proof covers the case where the system is defined by any maximal family of disjoint diagonals. We also take in account the case where the fixed side lengths are not generic. In this case, the phase space is an orbispace, and our result holds in the sense that singular fibers are isotropic orbispaces.

Computer parametric designing in Blender software for creating 3D paper models

In the contemporary conditions, the implementation of computer parametric design to facilitate the design of 3D paper models is successfully realized using modern technological tools such as the free software Blender. Through the convenient interface of the program, the modeling of the desired three-dimensional shapes is greatly facilitated. This also applies to the automated process of constructing a drawing of the resulting polygonal 3D models, which in the future are assembled into three-dimensional paper models. This paper describes in detail the process of fine-designing 3D paper models using specific exemplary primitive, text, and with relatively complex form.

Optimization of a Construction of the Milling Combine on the Basis of a Moon Rover by Means of Technology of Imitating Dynamic Modeling

The work presents the comparative analysis of the options of a design of the milling combine created on the basis of a moon rover by means of imitating calculations. The work is focused on the section "The federal space program of Russia for 2016-2025 - "Basic space researches" according to which the problem of creation of the milling combine for carrying out geological researches on a surface of other planets is actual. The research objective is optimization of a design of the milling combine created on the basis of a moon rover by means of technology of ultrahigh and polygonal dynamic 3D modeling. For achievement of a goal the technological chain which is conditionally divided into some main stages was used. Due to the insistence to resources and specifics of tasks imitating modeling was carried out by means of hardware-software complexes. Results in the form of models of the milling combine and a lunar surface are received. The interactive simulator functioning in modern full-scale technologies of virtual reality for training of future operators when performing missions to the Moon is created. The design shape conforming to requirements received by an iterative method of design can be applied in systems of information support at all stages of life cycle of a product. Carrying out such works is a necessary condition of providing prospects of use of systems of modeling, both for carrying out examinations, and in interests of the solution of perspective tasks of designing of space equipment.

Особенность отображения гиперповерхности четырехмерного пространства

Investigation of singularity related to a mapping by the orthogonal projection in a four-dimensional space of a hypersurface given by parametric equations is presented in this paper. On this investigation’s basis have been proposed in a united way three approaches to the hypersurface’s discriminant determination. Thus, have been defined conditions which the investigated hypersurface’s discriminant set and criminant are satisfied. Have been obtained dependencies settling the relationship between parameters of the hypersurface at its discriminant points. They are used to determine the singularity of the hypersurface mapping by analytical methods in general form. The complexity of this approach (the first one) is that an equation connecting the hypersurface’s parameters contains its differential characteristics, and often is the transcendental one in applications, that causes certain difficulties when solving it. Have been obtained dependences in carrying out of which the hypersurface’s discriminant has an edge of regression. A study of hypersurface sections by hyperplanes which are parallel to coordinate hyperplanes has been performed. The last ones contain a coordinate axis along which the hypersurface mapping is performed. It has been established that curves obtained in these sections have extreme points belonging to the hypersurface’s discriminant. Such property is used to calculate the points of the hypersurface’s discriminant by numerical methods without using the hypersurface’s differential characteristics, and it is a basis for the second approach to solving the problem posed. It has been also demonstrated the use of 3D modeling for study of hypersurface’s different sections, as well as its discriminant that represents the third approach to the study. All three approaches having a common basis can be used both independently and complement each other in determining the envelope for one-parameter family of surfaces. As an example has been considered a hypersurface formed by a family of spheres. Based on stated results have been obtained equations determining the hypersurface’s discriminant and this family’s corresponding envelope, as well as various sections. These equations have been used for creating of polygonal 3D models of the hypersurface’s discriminant, and some of the hypersurface’s sections.

Математичне моделювання геометрії місцевості

В роботі наведено методику побудови тривимірних моделей місцевості, яка застосовується для вирішення задач із побудови тактичних діаграм захищеності бойових машин легкої категорії ваги (БМ ЛКВ). Під час створеня математичних моделей місцевості запропоновано використовувати в якості вхідних даних інформацію супутника LIDAR (від англ. Light Identification, Detection and Ranging). На відміну від сучасних ГІС (геоінформаційних систем), де використовуються дані переважно у растрових чи векторних форматах, описана полігональна тривимірна модель місцевості дозволяє вирішувати задачі із розміщення моделі бойової машини на змодельованій поверхні місцевості. Таким чином розміщена модель БМ ЛКВ на тривимірній місцевості змінює орієнтацію у просторі, що впливає на розміри діаграми захищеності. Розроблена методика моделювання місцевості та отримані на її основі математичні моделі призначені для вирішення задач із побудови тактичних діаграм захищеності БМ ЛКВ та можуть застосовуватись як вироби подвійного призначення. Подальша робота з розвитку методики направлена на розширення бази даних та може застосовуватись для розв’язання задач природокористування, агрономії та лісництва. Ключові слова: математична модель місцевості, тривимірна модель місцевості, ландшафт, бойові машини легкої категорії ваги, захищеність, тактичні діаграми, ГІС, супутникові дані

The stochastic highlighting of polygon edges in the transparent visualization of large-scale polygon meshes: application to visualizing a high-energy elementary particle detector

ABSTRACTIn this paper, we propose a new stochastic algorithm that supports high-quality transparent visualization of line objects and apply it to polygon edges of complex three-dimensional (3D) polygon models. We also apply it to realizing transparent wireframe visualization that greatly improves comprehensibility of the conventional method. In our algorithm, the line opacity is recognized as the probability that a pixel on the image plane becomes the projected line colour. Our stochastic algorithm successfully makes a depth sort of rendering primitives, which often causes rendering artefacts and a wrong depth feel in conventional non-stochastic transparent rendering, unnecessary. We demonstrate our method using 3D models of the ATLAS detector, which is the world's largest high-energy elementary particle detector at CERN laboratory (EU) and a complex car engine. We also demonstrate the transparent wireframe visualization using the simulation data, which consist of many line objects, acquired for the ATLAS detector.

Manifold Construction Over Polyhedral Mesh

We present a smooth parametric surface construction method over polyhedral mesh with arbitrary topology based on manifold construction theory. The surface is automatically generated with any required smoothness, and it has an explicit form. As prior methods that build manifolds from meshes need some preprocess to get polyhedral meshes with special types of connectivity, such as quad mesh and triangle mesh, the preprocess will result in more charts. By a skillful use of a kind of bivariate spline function which defines on arbitrary shape of 2D polygon, we introduce an approach that directly works on the input mesh without such preprocess. For non-closed polyhedral mesh, we apply a global parameterization and directly divide it into several charts. As for closed polyhedral mesh, we propose to segment the mesh into a sequence of quadrilateral patches without any overlaps. As each patch is an non-closed polyhedral mesh, the non-closed surface construction method can be applied. And all the patches are smoothly stitched with a special process on the boundary charts which define on the boundary vertex of each patch. Thus, the final constructed surface can also achieve any required smoothness.

Bernstein copula modeling for 2D discrete fracture network simulations

In many naturally fractured reservoirs, fractures play a crucial role in their flow and transport properties. An approach that has recently gained popularity for modeling fracture systems is the Discrete Fracture Network (DFN) model. This approach consists in applying a stochastic boolean simulation method, also known as object simulation method, where fractures are represented as simplified geometric objects (line segments in 2D and polygons in 3D). One of the shortcomings of this approach is that it usually does not consider the dependence relationships that may exist between geometric properties of fractures (direction, length, aperture), that is, each property is simulated independently.In this work a method for modeling such dependencies by copula theory is introduced. In particular, a nonparametric model using Bernstein copulas for direction-length fracture dependency in 2D is presented.The application of this method is illustrated in an example which shows high agreement between data and simulation, both graphically and in its descriptive statistics, both marginally and jointly, and in the DFN as a whole.

Height-field construction using cross contours

We developed an interactive modeling tool for constructing a height field from the cross contours in a line drawing, added to provide an illusion of depth. Our approach places no specific constraints on the artist and can handle freely drawn shapes with partially structured or partially connected cross contours. In our system, the user first draws cross contours across the interior boundaries of the object. The system then extracts the intersection points of the contours and derives 2D polygons by connecting consecutive intersection points with straight lines. These 2D polygons are treated as the projection of a polygonal surface approximating the shape of the object. The 3D edge vectors and 3D normals of the approximated polygon surface are then estimated while considering the perceptions of the viewer and the goals of the designer. Based on the relative height values obtained from the 3D edge vectors and the co-planarities of the curve segments, a height field is generated in the image space that reasonably matches the cross contours of the input drawing. Experimental results demonstrated the ability of the system to generate height fields from a wide range of cross contours. We also showed that our system can be used to apply lighting effects to sketches and allows local shape deformation based on the constructed height field.

Area collapse algorithm computing new curve of 2D geometric objects

Abstract The processing of cartographic data demands human involvement. Up-to-date algorithms try to automate a part of this process. The goal is to obtain a digital model, or additional information about shape and topology of input geometric objects. A topological skeleton is one of the most important tools in the branch of science called shape analysis. It represents topological and geometrical characteristics of input data. Its plot depends on using algorithms such as medial axis, skeletonization, erosion, thinning, area collapse and many others. Area collapse, also known as dimension change, replaces input data with lower-dimensional geometric objects like, for example, a polygon with a polygonal chain, a line segment with a point. The goal of this paper is to introduce a new algorithm for the automatic calculation of polygonal chains representing a 2D polygon. The output is entirely contained within the area of the input polygon, and it has a linear plot without branches. The computational process is automatic and repeatable. The requirements of input data are discussed. The author analyzes results based on the method of computing ends of output polygonal chains. Additional methods to improve results are explored. The algorithm was tested on real-world cartographic data received from BDOT/GESUT databases, and on point clouds from laser scanning. An implementation for computing hatching of embankment is described.

HIERARCHICAL REGULARIZATION OF POLYGONS FOR PHOTOGRAMMETRIC POINT CLOUDS OF OBLIQUE IMAGES

Abstract. Despite the success of multi-view stereo (MVS) reconstruction from massive oblique images in city scale, only point clouds and triangulated meshes are available from existing MVS pipelines, which are topologically defect laden, free of semantical information and hard to edit and manipulate interactively in further applications. On the other hand, 2D polygons and polygonal models are still the industrial standard. However, extraction of the 2D polygons from MVS point clouds is still a non-trivial task, given the fact that the boundaries of the detected planes are zigzagged and regularities, such as parallel and orthogonal, cannot preserve. Aiming to solve these issues, this paper proposes a hierarchical polygon regularization method for the photogrammetric point clouds from existing MVS pipelines, which comprises of local and global levels. After boundary points extraction, e.g. using alpha shapes, the local level is used to consolidate the original points, by refining the orientation and position of the points using linear priors. The points are then grouped into local segments by forward searching. In the global level, regularities are enforced through a labeling process, which encourage the segments share the same label and the same label represents segments are parallel or orthogonal. This is formulated as Markov Random Field and solved efficiently. Preliminary results are made with point clouds from aerial oblique images and compared with two classical regularization methods, which have revealed that the proposed method are more powerful in abstracting a single building and is promising for further 3D polygonal model reconstruction and GIS applications.

Gross Anatomical Brain Region Approximation (GABRA): a new landmark‐based approach for estimating brain regions in dinosaurs and other archosaurs

Studying brain evolution in extinct taxa can be challenging due to a lack of close correspondence between the morphology of the endocranial cavity and that of the underlying brain. Cranial endocasts may be faithful brain proxies in certain groups (mammals, birds) due to relatively complete filling of the cavity with neural tissue in life. However, the brain does not fill the endocranial cavity in many adult non‐avian archosaurs, making their endocasts less reliable indicators of brain size and shape. As such, previous studies of relative brain size and evolution in archosaurs relied on untested assumptions about brain‐endocast fidelity. We propose a new approach known as Gross Anatomical Brain Region Approximation (GABRA), which involves importing a digital endocast, derived from CT scanning and 3D visualization software, into modeling software (Maya). In Maya, brain regions underlying the endocast are modeled as 3D polygons. Discernable osteological correlates for soft‐tissue structures (e.g., neurovascular canals, dural sinuses, fossae formed by the brain itself) present on the endocast serve as anatomical landmarks that inform the location and size of the modeled general brain regions (e.g., cerebral hemispheres, cerebellum, optic lobes, olfactory bulbs). Together, the anatomical landmarks form a set of explicit criteria used to assess endocasts and model brain regions. GABRA criteria and resulting brain models were validated in extant diapsids (lizards, snakes, alligators, birds) via literature review, gross dissection, CT scanning of iodine‐stained specimens, and MRI studies. Therefore, GABRA models produced for extinct archosaurs are credible. Credible GABRA models for extinct dinosaurs provided volumetric estimates for general brain regions, which, when summed, offer a whole‐brain estimate. Such data from several dinosaurs have permitted analyses using modern comparative methods of relative brain‐size evolution (e.g., encephalization quotient), with results indicating that brain sizes for many dinosaurs were previously underestimated. Additionally, analyses of GABRA data show a mix of concerted and mosaic patterns of brain evolution, wherein the pituitary and olfactory bulbs emerge as evolving independently from the rest of the brain. In sum, GABRA provides insight into how brains evolved across dinosaur lineages. Future studies will examine within‐lineage changes, offering greater insight into how and why dinosaur brains evolved.Support or Funding InformationFunding for this project was provided by the follow sources: the National Science Foundation, Jurassic Foundation, Sigma Xi Grant‐in‐Aid of Research, Ohio Center for Ecology and Evolutionary Studies, Ohio University Student Enhancement Award, Ohio University Original Work Grant.

Sexual Dimorphism in Bones of the Thenar and Hypothenar Aspects of the Hand

Osteoarthritis of the pollical carpometacarpal joint is significantly more prevalent in females than in males. Although a number of hypotheses to explain sex differences in the prevalence of thumb osteoarthritis have been proposed, one possibility is that it is a product of sexual dimorphism where female hands have smaller joint surfaces relative to muscle strength, which results in higher stresses on the joints. Although dimorphism of the skull and long bones has been extensively researched, there are few basic data on female‐versus‐male differences in the short and irregular bones. Therefore, it is unclear whether sexual dimorphism is a relevant avenue of investigation for determining the cause of such sex‐based differences in hand pathology. Because powerful precision gripping is dependent on the thenar and hypothenar muscles, the hand bones with muscle attachments or that are directly subjected to transarticular loading by these muscles are of particular interest. Therefore, we investigated four hand bones contributing to the first and fifth carpometacarpal articulations in a sample of humans of African and European descent, and it was predicted that females would have smaller overall bone volumes and areas, smaller individual joint surface areas, as well as different joint and muscle attachment shapes. The hamate, trapezium, first metacarpal (Mc1), and fifth metacarpal (Mc5) of each individual were laser scanned to generate 3D surface polygon models. Volume and surface area were calculated for each bone as a whole in addition to the areas of specific joint surfaces. The shape of the pollical carpometacarpal joint (proximal Mc1 and distal trapezium) was assessed with quadric fitting functions to determine their dorsovolar and radioulnar curvatures. For the hamate, the orientation of the triquetrohamate joint surface relative to the proximodistal axis was quantified, and for the hamulus (which provides attachments for the flexor digiti minimi brevis, opponens digiti minimi, and flexor carpi ulnaris) its length, width, breadth, and angle were measured. The results indicate that females tend to have bones that are significantly smaller in overall size with correspondingly smaller joint surfaces, and a hamulus that differs in both size and shape. Future work will diversify the sample and incorporate measurements of relative thenar and hypothenar muscle force potential to further evaluate the biomechanical consequences of skeletal dimorphism. Such an approach may allow us to better investigate more specific factors contributing to the increased osteoarthritis risk in the hands of females.Support or Funding InformationNational Science Foundation (BCS‐1539741, BCS‐1317047), Wenner‐Gren Foundation, Leakey Foundation

ACCURACY OF 3D (THREE-DIMENSIONAL) TERRAIN MODELS IN SIMULATIONS

The usage of realistic three-dimensional (3D) polygon terrain models with multiple levels of detail (LOD) is becoming widespread in popular applications like computer games or simulations, as it offers many advantages. These models, which represent an actual location in the world, are essential for the simulation-based training of military vehicles like planes, helicopters or tanks. Because training scenarios on this kind of simulations are used to observe or to hit a target on the modeled location. In addition to that, driving the behavior of terrestrial vehicles is influenced by the terrain properties like slopes, ramps, hitches, etc. because of the direct interaction with the ground. For this reason, the terrain models in the simulation scene should not only display the textures realistically, but also represent an accurate morphology; meaning the terrain altitudes should be modeled as correct as possible. Such terrain representations can be created by using Digital Terrain Model (DTM) for the geometry and satellite images for texturing. The geometry models are in the form of polygonal meshes through the triangulation methods. However, the accuracy is influenced by some parameters. Using insufficient (under-refined) triangles during the 3D modeling causes missing of some altitude vertices. That means these points will not be present in the model. Consequently, it can be thought that the number of triangles should be increased for a better geometrical fidelity. Nevertheless, it is not always correct as the usage of too much (over-refined) triangles can also cause errors, especially in terrains with almost vertical faces (like cliffs). In addition to that, the performance of the system deteriorates drastically through the increase in the number of triangles, as the computational complexity is also getting higher.

GTangle

Tangles are a form of structured pen-and-ink 2D art characterized by repeating, recursive patterns. We present a method to procedurally generate tangle drawings, seen as recursively split sets of arbitrary 2D polygons with holes, with anisotropic and non-stationary features. We formally model tangles with group grammars, an extension of set grammars, that explicitly handles the grouping of shapes necessary to represent tangle repetitions. We introduce a small set of expressive geometric and grouping operators, showing that they can respectively express complex tangles patterns and sub-pattern distributions, with relatively simple grammars. We also show how users can control tangle generation in an interactive and intuitive way. Throughout the paper, we show how group grammars can, in few tens of seconds, produce a wide variety of patterns that would take artists hours of tedious and time-consuming work. We then validated both the quality of the generated tangles and the efficiency of the control provided to the users with a user study, run with both expert and non-expert users.

StructureMorph: Creating Scholarly 3D Models for a Convergent, Digital Publishing Environment

Background: The StructureMorph project rests on the premise that future publishing platforms will converge multiple applications, such as geographic information systems (GIS) and game engines, and multiple paradigms of computing, such as desktop computing and high-performance computing. Convergent platforms will also present design challenges for scholars.Analysis: In this contribution, one response to these challenges is presented: the Complex Object. Complex Objects are 4D models that alter their shape and surface appearance in response to user interaction, and changes in world time. They also to mimic the behaviours of 2D polygons as configured in geographic information systems, graphically linking attribute data with spatial locales.Conclusion and implications: This article discusses the concept of the Complex Object and describes the software and workflow devised to support its creation.