Number Of Polygons Research Articles

Use of simple polygonal chains in generating random simple polygons

The main motivation for generating random simple polygons is to produce test instances for geometric algorithms. In this paper three new algorithms are proposed to generate random simple polygons. A point set in a two dimensional plane is the input, and a simple polygon is the output of the problem. At first a new algorithm to convert any kind of simple polygonal chains into simple polygons is presented and the correctness of the algorithm is proved. Then three new algorithms are presented to produce random simple polygonal chains from the given point set. The first algorithm is capable of producing $$2^n$$ simple polygonal chains. The second algorithm works by the concept of divide and conquer and the third algorithm is the most complete and produces all the possible simple polygonal chains. The worst time complexities of these three chain generation algorithms are $$O(n^2)$$ , $$O(n^2)$$ and $$O(n^3)$$ respectively and the time complexity of the conversion algorithm is O(n*l), where $$1<l<n$$ . The polygon generation algorithm works in this way that first each simple polygonal chain generation algorithms are applied over the point set and then the generated chains are converted to simple polygons. The number of different simple polygons generated by each of three algorithms is compared with the well-known algorithms and the experimental results show that the third algorithm produces more polygons rather than the well-known 2-opt move algorithm. The first algorithm acts better than the second algorithm, where both act better than steady Growth.

Polygon Approximation Based Cognitive Information Delivery in Geo-location Database Oriented Spectrum Sharing

In geo-location database oriented spectrum sharing system, the entire geographic area is divided into meshes to classify, store and delivery the cognitive information. In this paper, we propose a flexible polygon mesh division scheme to reduce the number of meshes. Hence the cognitive information can be reduced correspondingly. Besides, polygon mesh can approximate the real environment and reduce the error of cognitive information because the edges of polygon are selected along the boundaries of the networks. We have designed the polygon approximation algorithm and have analyzed the relation between the error and the number of polygon`s edges. Finally, the simulation results are provided to verify the algorithm and analysis. The polygon mesh division scheme in this paper provides an efficient approach for cognitive information organization in database oriented spectrum sharing system.

Convex Polygons in Geometric Triangulations

We show that the maximum number of convex polygons in a triangulation ofnpoints in the plane isO(1.5029n). This improves an earlier bound ofO(1.6181n) established by van Kreveld, Löffler and Pach (2012), and almost matches the current best lower bound of Ω(1.5028n) due to the same authors. Given a planar straight-line graphGwithnvertices, we also show how to compute efficiently the number of convex polygons inG.

Railway side mapping of alien plant distributions in Mpumalanga, South Africa

Background: Alien plant invasions are among the major threats to natural and semi-natural ecosystems in South Africa on approximately 18 million hectares of land. Much of the available data are not suitable for planning of local scale management because it is presented at a quarter degree grid square scale, which makes accurate location and estimates of invaded areas difficult.Objectives: The aim was to identify the dominant alien plant species and quantify their areal extent along a 479 km railway corridor in the Mpumalanga province.Method: The extent of the invaded area was obtained by manual digitising of alien plant distribution and density from Satellite Pour l’Observation de la Terre 5 imagery and by further applying an Iterative Self-Organising Data Analysis technique of the unsupervised classification method. Species’ occurrences were located and identified in the field using a Global Positioning System.Results: The most dominant invaders in terms of the number of individual polygons and the infested area were Eucalyptus spp., Acacia spp., Populus alba L., Pinus patula Schltdl Cham., Salix babylonica L. and Caesalpinia decapetala (Roth) Alston. These species have also been previously classified as major invaders, although the Conservation of Agricultural Resources Act regulations permit their planting provided spreading to adjacent areas is avoided except for C. decapetala, which must be cleared under all circumstances.Conclusion: Knowledge of the species’ occurrence and their extent will assist landowners and relevant authorities to control the spread of alien plants, which impact rail safety, agricultural production, water availability and biodiversity.

KDet: Parallel Constant Time Collision Detection for Polygonal Objects

We define a novel geometric predicate and a class of objects that enables us to prove a linear bound on the number of intersecting polygon pairs for colliding 3D objects in that class. Our predicate is relevant both in theory and in practice: it is easy to check and it needs to consider only the geometric properties of the individual objects – it does not depend on the configuration of a given pair of objects. In addition, it characterizes a practically relevant class of objects: we checked our predicate on a large database of real-world 3D objects and the results show that it holds for all but the most pathological ones. Our proof is constructive in that it is the basis for a novel collision detection algorithm that realizes this linear complexity also in practice. Additionally, we present a parallelization of this algorithm with a worst-case running time that is independent of the number of polygons. Our algorithm is very well suited not only for rigid but also for deformable and even topology-changing objects, because it does not require any complex data structures or pre-processing. We have implemented our algorithm on the GPU and the results show that it is able to find in real-time all colliding polygons for pairs of deformable objects consisting of more than 200k triangles, including self-collisions.

FILM ANIMASI 3D JURNALIS SINDO

3-Dimension Sindo's Journalist Animation Movie tells about a journalist's deception. 3 Dimensional animated film using Low Poly technique. Low Poly is a computer graphics that has a small number of polygons. This modeling technique reduces the detail of a 3-dimensional model with the purpose of geometry efficiency that can lighten the system's workload while designing and when rendering. Software used in the making of this film is Blender 3D, Adobe Illustrator, Adobe PhotoShop, Adobe. Premiere, Corel Draw and Format Factory.Use visual concepts derived from verbal language that is processed into visual language, in concept there are some elements, such as creativity, aesthetics, efficiency, communicative, and others to be accepted by the target audience. Visual object processing requires the composition of design formats, layouts, typography, illustrations, and colors to make the visual messages and messages delivered easily accepted by target audiences. Key words : Animation Movie, 3 Dimension, Low Poly, Sindo

Rendering of specular curved objects in polygon-based computer holography.

A realistic rendering technique is presented for creating large-scale computer-generated holograms. The technique is based on the polygon-based method, but allows specular curved surfaces to be reconstructed without increasing the number of polygons. In this technique, specular flat surfaces are transformed into curved surfaces. This is achieved by controlling the direction of reflected light, using fragmentary plane waves. An actual large-scale computer-generated hologram is created, and is used to verify the validity and practicality of the technique.

A Novel Description approach based on sorted rectangles for scheduling information bearing in OFDMA systems

Dynamic time/frequency resource allocation has been widely employed in wireless OFDMA systems. In such mechanisms, sophisticated scheduling decisions need to be conveyed to users and may lead to considerable signaling overhead. In this paper, a new efficient approach, namely, Sorted-Rectangle Description (SRD) is proposed for describing the scheduling decision in an OFDMA frame. SRD first partitions a frame into minimum number of rectangular polygons, namely, rectangular bursts (RB), in which each RB contains the resource units belonging to the same assignment. We show that each RB-partitioned frame is sufficient to be fully reconstructed by the top-left coordinates of each RB in a specific sorted order. Sorting and reconstructing algorithms with linear time complexity in the total number of RBs are also proposed. Simulations based on a multi-user OFDMA system with full-buffer or periodic small-data traffic model are conducted to evaluate the performance of the proposed SRD method under two representative scenarios. The simulation results show that, for the full-buffer traffic model with a proportional fair (PF) scheduler, the proposed description approach can achieve significant reduction of the overhead ratio compared to that of the existing systems and is expected to lead to considerable increase of system throughput. Meanwhile, for the periodic small-data traffic model, it is shown that the proposed description approach can greatly reduce the rate of packet loss due to timeout or buffer overflow and thus provides significant improvement of the system capacity.

Jamming transition evinced by Voronoi Tesselation

We calculated the Voronoi tessellation (VT) of simulations of two-dimensional granular system disturbed by an intruder. The intruder is kept fixed within a rectangular box containing certain amount of grains. Making the box to move against the intruder we calculated the VT for several instants of this movement, analyzing geometrical properties of the Voronoi polygons in function of time. The dependence of stationary values of the polygon areas and number of sides in function of the packing fraction (ϕ ) of the granular media has shown that the system displays a possible jamming transition at critical point ϕc ≈ 80:5%.

INDENTATION OF FLAT-ENDED AND TAPERED INDENTERS WITH POLYGONAL CROSS-SECTIONS

Using the Boundary Element Method, we numerically study the indentation of prismatic and tapered indenters with polygonal cross-sections. The contact stiffness of punches with flat bases in the form of a triangle and a square as well as a number of higher-order polygons is determined. In particular, the classical results of King (1987) for indenters with triangle and square base shapes are revised and more precise numerical results are provided. For tapered indenters, the equivalent transformed profile used in the Method of Dimensionality Reduction (MDR) is determined. It is shown that the MDR-transformed profile of polygon-based indenters with power function side is given by the power function with the same power; it differs from the 3D profile only by a constant coefficient. These coefficients are listed in the paper for various types of indenters, in particular for pyramidal and paraboloid ones. The determined MDR-transformed profiles can be used for study of other contact problems such as tangential contact, normal contact with elastomers, and, in an approximate way, to adhesive contacts.

Disordered contact networks in jammed packings of frictionless disks

We analyse properties of contact networks formed in packings of soft frictionless disks near the unjamming transition. We construct polygonal tilings and triangulations of the contact network that partitions space into convex regions which are either covered or uncovered. This allows us to characterize the local spatial structure of the packing near the transition using well-defined geometric objects. We construct bounds on the number of polygons and triangulation vectors that appear in such packings. We study these networks using simulations of bidispersed disks interacting via a one-sided linear spring potential. We find that several underlying geometric distributions are reproducible and display self averaging properties. We find that the total covered area is a reliable real space parameter that can serve as a substitute for the packing fraction. We find that the unjamming transition occurs at a fraction of covered area . We determine scaling exponents of the excess covered area as the energy of the system approaches zero , and the coordination number approaches its isostatic value . We find and , representing new structural critical exponents. We use the distribution functions of local areas to study the underlying geometric disorder in the packings. We find that a finite fraction of order persists as the transition is approached.

Vectorization of classified remote sensing raster data to establish topological relations among polygons

Vector and raster are two types of spatial data structures used in a geographic information system (GIS). With the development of GIS and remote sensing (RS) technologies, how to rapidly convert raster to vector data and establish topological relations among vectorized polygons is becoming a bottleneck in data integration between GIS and RS. Based on the previous work, an improved vectorization method is proposed to vectorize classified RS raster data quickly and automatically establish topological relations. In accordance with the connection information of arcs and nodes and both-sides polygonal attributes of arcs, the next arc can be searched directly by attribute matching when constructing polygons, thereby improving search efficiency. Moreover, our method addressed the problems of self-intersecting polygons, shared-boundary, and multi-nested islands and gave corresponding solutions, which can establish the topological relations of an entire image quickly. Two experiments, one for comparison between before and after vectorization of two different classified RS raster maps, and the other for comparison with several methods, are carried out to test the accuracy and efficiency of our method. Results show that the method solves the self-intersecting polygons, shared-boundary, and multi-nested islands problems. In addition, its vectorization speed is more than double that of commercial software ArcGIS, and the advantage of our method becomes more obvious as the number of polygons increases. Thus, our method can vectorize large and complex classified RS raster data with sufficient efficiency for practical use and establish topological relations among vectorized polygons.

Principles of the Complete Voronoi Diagram Localization

This paper explores the rationale behind the Complete Voronoi Diagram (CVD) Localization, which is a computational geometry approach to the wireless network localization. Our work consists mainly of three parts. The first part focuses on the analysis of CVD's mathematical properties. We characterize CVD's central tendency as the mirror-image distribution and provide mathematical formula for its probability density function. We also provide a closed formula for the relationship between CVD's vertices, chords, and faces, the average chord length, and the average edge number of a CVD polygon. And, the expressions for the average overall and local positioning error are also provided. Based upon these findings, we show that the convergence speed for a CVD based localization scheme is quadratic, and the optimal time and space complexities are Θ( n 2) and Θ( n ), respectively. The second part proposes a novel approach, called Polling, which utilizes the concept of the Error Region, to further improve the accuracy. Polling, in theory, enables us to make use of the topology information with the quantity up to O( n 4) provided by CVD for localization, while a conventional CVD scheme can use only O(1) such information. The third part, through simulations, shows how to use the quasi Analog-to-Digital Conversion (qADC) strategy to handle signal errors. Combined with Polling and qADC, a CVD scheme can provide a simple, robust, and powerful solution to the wireless network localization. Some of our findings and methods may also contribute to the field of computational geometry its own.

Study on the Head Mounted Display (HMD)-Based VR Contents and Producing Method

Background/Objectives: Year 2016 has been presented as the starting year of Virtual Reality (VR). However, there has been little study on VR content production techniques . Methods/Statistical Analysis: The purpose of this study was to examine various VR content production techniques and present the direction for development of VR contents. For methodology, the study classified production techniques for 15 contents in 3 areas, i.e., 5 contents of 360° life-size shooting, 5 contents based on 3D low polygon, and 5 contents of 360° animation which were differentiated in terms of production techniques and contents among 109 VR contents registered on March 3, 2016 which were on VR platforms provided by Oculus Rift. Furthermore, the study presented production methods applying concerned techniques and their characteristics. Findings: The results of this study showed that VR contents could be defined as real-size image, 2 and 3D low-polygon VR contents, and 360° animation, depending on production characteristics. First, 360° life-size shooting technique was suitable for special locations and situations such as performance, movies, etc., but did not enable presentation such as lighting, etc. Furthermore, 360° life-size is shooting required special technology and much time for the latter part works such as stitching, special effects, etc., in connection with production technique. Second, 3D low polygon-based VR contents enabled simulation with excellent sense of presence and immersion based on 0.02 second latency by reducing the number of 3D polygons from 30,000 to 50,000. However, it had the disadvantage of degraded reality of images. Third, 360° animation production technique enabled various presentations and enhanced image quality, but had limitation that it enabled only fragmentary interaction and simulation. Improvements/Applications: Future VR content would need to be developed in such a way that efficiency and synergic effects can be maximized by combining the advantages of various production techniques, depending on the purpose and needs of VR contents, rather than applying single production technique.

Low-altitude remote sensing and GIS-based analysis of cropmarks: classification of past thermal-contraction-crack polygons in central western Poland

The examination of low-altitude aerial photographs reveals the presence of more than 400 polygonal nets in central western Poland. Polygons range from 5 to almost 70m in diameter. Based on the polygons' diameter and intersection angles, we identified seven main types of nets geometry. Based on ground verification, we interpreted them as past thermal-contraction-cracks, filled mostly with sand (i.e. sand-wedge casts). As favourable weather conditions and a proper land cover (i.e. cultivated land) are necessary for identifying polygonal nets, the observed number of polygons is probably much underestimated.The broad occurrence of former thermal-contraction-cracks' polygons indicates that continuous permafrost was widespread in central western Poland after the termination of the Last Glacial Maximum (LGM). Preliminary dating of the cracks' infilling as well as polygon geometry suggest that thermal-contraction-cracking occurred in several different phases and that a time frame of a few thousand years is sufficient to form complex, mature nets.

VALIDATION OF THE ASTER GLOBAL DIGITAL ELEVATION MODEL VERSION 3 OVER THE CONTERMINOUS UNITED STATES

The ASTER Global Digital Elevation Model Version 3 (GDEM v3) was evaluated over the conterminous United States in a manner similar to the validation conducted for the original GDEM Version 1 (v1) in 2009 and GDEM Version 2 (v2) in 2011. The absolute vertical accuracy of GDEM v3 was calculated by comparison with more than 23,000 independent reference geodetic ground control points from the U.S. National Geodetic Survey. The root mean square error (RMSE) measured for GDEM v3 is 8.52 meters. This compares with the RMSE of 8.68 meters for GDEM v2. Another important descriptor of vertical accuracy is the mean error, or bias, which indicates if a DEM has an overall vertical offset from true ground level. The GDEM v3 mean error of &amp;minus;1.20 meters reflects an overall negative bias in GDEM v3. The absolute vertical accuracy assessment results, both mean error and RMSE, were segmented by land cover type to provide insight into how GDEM v3 performs in various land surface conditions. While the RMSE varies little across cover types (6.92 to 9.25 meters), the mean error (bias) does appear to be affected by land cover type, ranging from &amp;minus;2.99 to +4.16 meters across 14 land cover classes. These results indicate that in areas where built or natural aboveground features are present, GDEM v3 is measuring elevations above the ground level, a condition noted in assessments of previous GDEM versions (v1 and v2) and an expected condition given the type of stereo-optical image data collected by ASTER. GDEM v3 was also evaluated by differencing with the Shuttle Radar Topography Mission (SRTM) dataset. In many forested areas, GDEM v3 has elevations that are higher in the canopy than SRTM. The overall validation effort also included an evaluation of the GDEM v3 water mask. In general, the number of distinct water polygons in GDEM v3 is much lower than the number in a reference land cover dataset, but the total areas compare much more closely.

VALIDATION OF THE ASTER GLOBAL DIGITAL ELEVATION MODEL VERSION 3 OVER THE CONTERMINOUS UNITED STATES

Abstract. The ASTER Global Digital Elevation Model Version 3 (GDEM v3) was evaluated over the conterminous United States in a manner similar to the validation conducted for the original GDEM Version 1 (v1) in 2009 and GDEM Version 2 (v2) in 2011. The absolute vertical accuracy of GDEM v3 was calculated by comparison with more than 23,000 independent reference geodetic ground control points from the U.S. National Geodetic Survey. The root mean square error (RMSE) measured for GDEM v3 is 8.52 meters. This compares with the RMSE of 8.68 meters for GDEM v2. Another important descriptor of vertical accuracy is the mean error, or bias, which indicates if a DEM has an overall vertical offset from true ground level. The GDEM v3 mean error of −1.20 meters reflects an overall negative bias in GDEM v3. The absolute vertical accuracy assessment results, both mean error and RMSE, were segmented by land cover type to provide insight into how GDEM v3 performs in various land surface conditions. While the RMSE varies little across cover types (6.92 to 9.25 meters), the mean error (bias) does appear to be affected by land cover type, ranging from −2.99 to +4.16 meters across 14 land cover classes. These results indicate that in areas where built or natural aboveground features are present, GDEM v3 is measuring elevations above the ground level, a condition noted in assessments of previous GDEM versions (v1 and v2) and an expected condition given the type of stereo-optical image data collected by ASTER. GDEM v3 was also evaluated by differencing with the Shuttle Radar Topography Mission (SRTM) dataset. In many forested areas, GDEM v3 has elevations that are higher in the canopy than SRTM. The overall validation effort also included an evaluation of the GDEM v3 water mask. In general, the number of distinct water polygons in GDEM v3 is much lower than the number in a reference land cover dataset, but the total areas compare much more closely.

A stochastic scaled boundary finite element method

By extending the existing scaled boundary finite element method (SBFEM) into the random field problem, a stochastic scaled boundary finite element method (SSBFEM) is developed in this paper to predict the structural responses with randomly distributed material properties. The analyzed domain is discretized into a number of polygons modeled as sub-domains of the SBFEM so that the non-homogeneous material properties are possible to be considered in establishment of the constitutive equation. The random field represented by the Karhunen–Loève (KL) expansion is then directly incorporated into both the equilibrium equation of the SBFEM and its sensitivity analysis formulation. The perturbation method is employed to calculate the statistical moments of the structural responses and a semi-analytical sensitivity analysis method is used to efficiently calculate the gradients involved. Particularly, the proposed method is successfully applied to the stochastic fracture analysis with spatially varying random material properties. Four numerical examples are investigated to demonstrate the validity of the proposed method.

Soil map of the Russian Arctic on a 1 : 1 M scale: Contents and compilation methods

A new soil map of the Russian Arctic on a scale of 1 : 1 M shows the soil cover in the north of Eurasia and on the islands of the Arctic Ocean to the north of 68° N. This map has been developed in a geoinformation system in the vector format with the wide use of remote sensing data. The delineated soil polygons show dominant and accompanying soils and the structure of soil cover patterns with indication of soil associations and soil complexes, the character of parent materials, and the topographic conditions. The map of the soil-geographic zoning of the Russian Arctic developed on the basis of the soil map differs from its earlier analogues in a greater degree of detail. The soil map of the Russian Arctic on a scale of 1 : 1 M displays the most detailed information on the soil cover patterns and can be used for solving various problems related to the exploration and development of this territory. Soil names from the new classification system of Russian soils [10] have been introduced into the legend of the map. New soil information and the use of remote sensing data have made it possible to enlarge the number of soil polygons shown on the map and to correct their boundaries in comparison with previous soil maps of the Russian Arctic.

Circle Numbers of Regular Convex Polygons

The circle number function is extended here to regular convex polygons. To this end, the radius of the polygonal circle is defined as the Minkowski functional of the circumscribed polygonal disc, and the arc-length of the polygonal circle is measured in a generalized Minkowski space having the rotated polar body as the unit disc.