Showing papers on "Polygon published in 2014"

Asymptotics of random lozenge tilings via Gelfand–Tsetlin schemes

Abstract: A Gelfand–Tsetlin scheme of depth $$N$$ is a triangular array with $$m$$ integers at level $$m$$ , $$m=1,\ldots ,N$$ , subject to certain interlacing constraints. We study the ensemble of uniformly random Gelfand–Tsetlin schemes with arbitrary fixed $$N$$ th row. We obtain an explicit double contour integral expression for the determinantal correlation kernel of this ensemble (and also of its $$q$$ -deformation). This provides new tools for asymptotic analysis of uniformly random lozenge tilings of polygons on the triangular lattice; or, equivalently, of random stepped surfaces. We work with a class of polygons which allows arbitrarily large number of sides. We show that the local limit behavior of random tilings (as all dimensions of the polygon grow) is directed by ergodic translation invariant Gibbs measures. The slopes of these measures coincide with the ones of tangent planes to the corresponding limit shapes described by Kenyon and Okounkov (Acta Math 199(2):263–302, 2007). We also prove that at the edge of the limit shape, the asymptotic behavior of random tilings is given by the Airy process. In particular, our results cover the most investigated case of random boxed plane partitions (when the polygon is a hexagon).

Distributed Deployment Algorithms for Improved Coverage in a Network of Wireless Mobile Sensors

Abstract: In this paper, efficient sensor deployment strategies are developed to increase coverage in wireless mobile sensor networks. The sensors find coverage holes within their Voronoi polygons and then move in an appropriate direction to minimize them. Novel edge-based and vertex-based strategies are introduced, and their performances are compared with existing techniques. The proposed movement strategies are based on the distances of each sensor and the points inside its Voronoi polygon from the edges or vertices of the polygon. Simulations confirm the effectiveness of the proposed deployment algorithms and their superiority to the techniques reported in the literature.

Convex equipartitions via Equivariant Obstruction Theory

Abstract: We describe a regular cell complex model for the configuration space F(ℝ d , n). Based on this, we use Equivariant Obstruction Theory to prove the prime power case of the conjecture by Nandakumar and Ramana Rao that every polygon can be partitioned into n convex parts of equal area and perimeter.

Route detection in a trip-oriented message data communications system

Abstract: In an embodiment, a data processing method provides an improvement in personal tracking and comprises, using a server computer, obtaining a plurality of personal calendar records, wherein each of the calendar records comprises a location value specifying a geographical location of an event, and a start time value specifying a start time of an event at the location; using the server computer, obtaining a plurality of present location updates, wherein each of the present location updates comprises a geo-location value indicating a then-current location of a computing device; using the server computer, creating and storing polygon data that defines a polygon in geographical space that contains a final set of the plurality of location values; using the server computer, determining a street address that is contained in the polygon; creating and storing a database record that associates a particular calendar record with the street address.

Polygon-Shaped Slotted Dual-Band Antenna for Wearable Applications

Abstract: This letter presents the design of a wearable dual-band patch antenna for operating in the GSM-900 and 1800 bands. The proposed polygon patch antenna comprises a circular slot and vertical slits embedded on jeans substrate. This structure provides two paths for currents, making it viable for dual bands. The effect of patch length, slot radius, and slit length on the overall antenna performance is analyzed by performing a comprehensive parametric study. Further bending, crumpling, wetness, and on-body measurements have been performed to validate the structure. Specific absorption rate (SAR) values ranging between 0.00039-0.0035 W/Kg have been obtained for two different analyses.

Scaled boundary polygons with application to fracture analysis of functionally graded materials

Abstract: SUMMARY This study presents a framework for the development of polygon elements based on the scaled boundary FEM. Underpinning this study is the development of generalized scaled boundary shape functions valid for any n-sided polygon. These shape functions are continuous inside each polygon and across adjacent polygons. For uncracked polygons, the shape functions are linearly complete. For cracked polygons, the shape functions reproduce the square-root singularity and the higher-order terms in the Williams eigenfunction expansion. This allows the singular stress field in the vicinity of the crack tip to be represented accurately. Using these shape functions, a novel-scaled boundary polygon formulation that captures the heterogeneous material response observed in functionally graded materials is developed. The stiffness matrix in each polygon is derived from the principle of virtual work using the scaled boundary shape functions. The material heterogeneity is approximated in each polygon by a polynomial surface in scaled boundary coordinates. The intrinsic properties of the scaled boundary shape functions enable accurate computation of stress intensity factors in cracked functionally graded materials directly from their definitions. The new formulation is validated, and its salient features are demonstrated, using five numerical benchmarks. Copyright © 2014 John Wiley & Sons, Ltd.

A fast polygon inflation algorithm to compute the area of feasible solutions for three‐component systems. II: Theoretical foundation, inverse polygon inflation, and FAC‐PACK implementation

Abstract: The area of feasible solutions (AFS) of a multivariate curve resolution method is the continuum of feasible solutions under the given constraints. In the current paper the AFS is computed only on the condition of nonnegative solutions. This work is a continuation of a paper (J. Chemometrics 28:106-116, 2013) on the polygon inflation algorithm for AFS computations. In this second part various properties of the AFS are analyzed. First, its boundedness is proved, which is a necessary condition for its numerical computation. Second, it is shown that the origin is never contained in the area of feasible solutions. This fact is the basis for t he inverse polygon inflation algorithm, which allows to compute specific types of an AFS containing a hole. The numerical computation of the AFS is a complicated and computationally expensive process. The construction of proper objective functions for the AFS-optimization problem appears to be decisive. The paper contains a comparative analysis of two objective functions and describes the ideas of the new FAC-PACK toolbox for MatLab. This freely available toolbox contains a numerical implementation of the polygon inflation and of the inverse polygon inflation algorithm.

Influence of wheel polygonal wear on interior noise of high-speed trains

Abstract: This work presents a detailed investigation conducted into the relationships between wheel polygonal wear and wheel/rail noise, and the interior noise of high-speed trains through extensive experiments and numerical simulations. The field experiments include roundness measurement and characteristics analysis of the high-speed wheels in service, and analysis on the effect of re-profiling on the interior noise of the high-speed coach. The experimental analysis shows that wheel polygonal wear has a great impact on wheel/rail noise and interior noise. In the numerical simulation, the model of high-speed wheel/rail noise caused by the uneven wheel wear is developed by means of the high-speed wheel-track noise software (HWTNS). The calculation model of the interior noise of a high-speed coach is developed based on the hybrid of the finite element method and the statistic energy analysis (FE-SEA). The numerical simulation analyses the effect of the polygonal wear characteristics, such as roughness level, polygon order (or wavelength), and polygon phase, on wheel/rail noise and interior noise of a high-speed coach. The numerical results show that different polygon order with nearly the same roughness levels can cause different wheel/rail noises and interior noises. The polygon with a higher roughness level can cause a larger wheel/rail noise and a larger interior noise. The combination of different polygon phases can make a different wheel circle diameter difference due to wear, but its effect on the interior noise level is not great. This study can provide a basis for improving the criteria for high-speed wheel re-profiling of China’s high-speed trains.

Vortex Filament Equation for a Regular Polygon

Abstract: In this paper, we study the evolution of the localized induction approximation (LIA), also known as vortex lament equation, Xt = Xs^ Xss; for X(s; 0) a regular planar polygon. Using algebraic techniques, supported by full numerical simulations, we give strong evidence that X(s;t) is also a polygon at any rational time; moreover, it can be fully characterized, up to a rigid movement, by a generalized quadratic Gau sum. We also study the fractal behavior of X(0;t), relating it with the socalled Riemann’s non-dierentiable function, that, as proved by S. Jaard, ts with the multifractal model of U. Frisch and G. Parisi, for fully developed turbulence.

Detecting Weakly Simple Polygons

Abstract: A closed curve in the plane is weakly simple if it is the limit (in the Frechet metric) of a sequence of simple closed curves. We describe an algorithm to determine whether a closed walk of length n in a simple plane graph is weakly simple in O(n log n) time, improving an earlier O(n^3)-time algorithm of Cortese et al. [Discrete Math. 2009]. As an immediate corollary, we obtain the first efficient algorithm to determine whether an arbitrary n-vertex polygon is weakly simple; our algorithm runs in O(n^2 log n) time. We also describe algorithms that detect weak simplicity in O(n log n) time for two interesting classes of polygons. Finally, we discuss subtle errors in several previously published definitions of weak simplicity.

Freeze/thaw processes in complex permafrost landscapes of northern Siberia simulated using the TEM ecosystem model: impact of thermokarst ponds and lakes

Abstract: . Freeze/thaw (F/T) processes can be quite different under the various land surface types found in the complex tundra of the Arctic, such as polygonal tundra (wet center and dry rims), ponds, and thermokarst lakes. Proper simulation of these different processes is essential for accurate prediction of the release of greenhouse gases under a warming climate scenario. In this study we have incorporated the water layer into a dynamic organic soil version of the Terrestrial Ecosystem Model (DOS-TEM), having first verified and validated the model. Results showed that (1) the DOS-TEM was very efficient and its results compared well with analytical solutions for idealized cases, and (2) despite a number of limitations and uncertainties in the modeling, the simulations compared reasonably well with in situ measurements from polygon rims, polygon centers (with and without water), and lakes on Samoylov Island, Siberia, indicating the suitability of the DOS-TEM for simulating the various F/T processes. Sensitivity tests were performed on the effects of water depth and our results indicated that both water and snow cover are very important in the simulated thermal processes, for both polygon centers and lakes. We therefore concluded that the polygon rims and polygon centers (with various maximum water depths) should be considered separately, and that the dynamics of water depth in both polygons and lakes should be taken into account when simulating thermal processes for methane emission studies.

A QPTAS for maximum weight independent set of polygons with polylogarithmically many vertices

Abstract: The Maximum Weight Independent Set of Polygons (MWISP) problem is a fundamental problem in computational geometry. Given a set of weighted polygons in the two-dimensional plane, the goal is to find a set of pairwise non-overlapping polygons with maximum total weight. Due to its wide range of applications and connections to other problems, the MWISP problem and its special cases have been extensively studied both in the approximation algorithms and the computational geometry community. Despite a lot of research, its general case is not well-understood yet. Currently the best known polynomial time algorithm achieves an approximation ratio of ne, and it is not even clear whether the problem is APX-hard. We present a (1 + e)-approximation algorithm, assuming that each polygon in the input has at most a polylogarithmic number of vertices. Our algorithm has quasi-polynomial running time, i.e., it runs in time 2poly(log n, 1/e). In particular, our result implies that for this setting the problem is not APX-hard, unless NP ⊆ DTIME(2poly(log n)).We use a recently introduced framework for approximating maximum weight independent set in geometric intersection graphs. The framework has been used to construct a QPTAS in the much simpler case of axis-parallel rectangles. We extend it in two ways, to adapt it to our much more general setting. First, we show that its technical core can be reduced to the case when all input polygons are triangles. Secondly, we replace its key technical ingredient which is a method to partition the plane using only few edges such that the objects stemming from the optimal solution are evenly distributed among the resulting faces and each object is intersected only a few times. Our new procedure for this task is no more complicated than the original one and, importantly, it can handle the difficulties arising from the arbitrary angles of the input polygons. Note that already this obstacle makes the known analysis for the above framework fail. Also, in general it is not well understood how to handle this difficulty by efficient approximation algorithms.

Predictive modeling of geometric deviations of 3D printed products - A unified modeling approach for cylindrical and polygon shapes

Abstract: Geometric fidelity of 3D printed products is critical for Additive Manufacturing (AM) or 3D printing to be a direct manufacturing technology. Shape deviations of AM built products can be attributed to multiple variation sources such as substrate geometry defect, disturbance in process variables, and material phase change. Three strategies have been reported to improve geometric quality in AM: (1) control process variables x based on the observed disturbance of process variables Δx, (2) control process variables x based on the observed product deviation Δy, and (3) control input product geometry y based on the observed product deviation Δy. This study adopts the third strategy which changes the CAD design by optimally compensating the product deviations. To accomplish the goal an predictive model is desirable to forecast the quality of a wide class of product shapes, particularly considering the vast library of AM built products with complex geometry. Built upon our previous optimal compensation study of cylindrical products, this work aims at an unified modeling approach to predict the quality of both cylinder and polygon shapes. Experimental investigation of polygon shapes indicates the promise of predicting and compensating a wide class of products built through 3D printing technology.

Subsatellite polygon for studying hydrophysical processes in the Black Sea shelf-slope zone

Abstract: The first data on the creation of the subsatellite polygon on the Black Sea shelf and continental slope in the Gelendzhik area (designed in order to permanently monitor the state of the aquatic environment and biota) and the plans for maintaining and developing this polygon are presented. The autonomous measuring systems of the polygon in the composition of bottom stations with acoustic Doppler current profilers (ADCP), Aqualog robotic profilers, and thermo-chains on moored buoy stations should make it possible to regularly obtain hydrophysical, hydrochemical, and bio-optical data with a high spatial-time resolution and transmit these data to the coastal center on a real-time basis. These field data should be used to study the characteristics and formation mechanisms of the marine environment and biota variability, as well as the water-exchange processes in the shelf-deep basin system, ocean-atmosphere coupling, and many other processes. These data are used to calibrate the satellite measurements and verify the water circulation numerical simulation. It is assumed to use these data in order to warn about the hazardous natural phenomena and control the marine environment state and its variation under the action of anthropogenic and natural factors, including climatic trends. It is planned to use the polygon subsatellite monitoring methods and equipment in other coastal areas, including other Black Sea sectors, in order to create a unified system for monitoring the Black Sea shelf-slope zone.

Vectorial boundary-based sub-pixel mapping method for remote-sensing imagery

Abstract: This article presents a vectorial boundary-based sub-pixel mapping (VBSPM) method to obtain the land-cover distribution with finer spatial resolution in mixed pixels. With inheritance from the geometric SPM (GSPM), VBSPM first geometrically partitions a mixed pixel using polygons, and then utilizes a vectorial boundary extraction model (VBEM), rather than the rasterization method in GSPM, to determine the location and length of each edge in the polygon, while these edges are located at the boundary of and within the interior of the mixed pixel. Furthermore, VBSPM uses a decay function to manage the mixed pixels along the image boundary region due to the missing parts of their neighbours. Finally, a ray-crossing algorithm is employed to determine the land-cover class of each sub-pixel in terms of vectorial boundaries. The experiments with artificial and remotely sensed images have demonstrated that VBSPM can reduce the inconsistency between the boundaries of different land-cover classes, approximately calculating errors with an odd zoom factor, and achieve more accurate sub-pixel mapping results than the hard classification methods and GSPM.

Phase-regularized polygon computer-generated holograms

Abstract: The dark-line defect problem in the conventional polygon computer-generated hologram (CGH) is addressed. To resolve this problem, we clarify the physical origin of the defect and address the concept of phase-regularization. A novel synthesis algorithm for a phase-regularized polygon CGH for generating photorealistic defect-free holographic images is proposed. The optical reconstruction results of the phase-regularized polygon CGHs without the dark-line defects are presented.

Polygon-based approach for extracting multilane roads from OpenStreetMap urban road networks

Abstract: This study proposes a novel approach for extracting multilane roads from urban road networks in OpenStreetMap OSM data sets as functional high-level roads, thereby allowing comparative analyses to determine the differences between this functional hierarchy and other hierarchies. OSM road networks have high levels of detail and complex structures, but they also have large numbers of duplicated lines for the same road features, which leads to difficulties and low efficiency when extracting multilane roads using conventional methods based on the analysis and operations of line segments. To overcome these deficiencies, a polygon-based method is proposed that is based on shape analysis and Gestalt theory, which treats polygons surrounded by roads as operating elements. First, shape descriptors are calculated for each polygon in networks and are used for classification. Second, candidate multilane polygons are classified as seeds based on all the polygons used as shape descriptors by a support vector machine. Finally, based on the seed polygons, a region-growing method is proposed that connects and fills the multilane features according to Gestalt theory. An experiment using OSM data from different urban networks verified the validity of the proposed method. The method achieved good and effective extraction performance, regardless of the complexity and duplication of data sets. Thus, a comparative analysis with high-level roads extracted based on road type attributes and structural analysis was performed to demonstrate the differences between the constructed road levels and other hierarchies.

Corners and edges always scatter

Abstract: Consider time-harmonic acoustic scattering problems governed by the Helmholtz equation in two and three dimensions We prove that bounded penetrable obstacles with corners or edges scatter every incident wave nontrivially, provided the function of refractive index is real-analytic Moreover, if such a penetrable obstacle is a convex polyhedron or polygon, then its shape can be uniquely determined by the far-field pattern over all observation directions incited by a single incident wave Our arguments are elementary and rely on the expansion of solutions to the Helmholtz equation

Probability Theory of Random Polygons from the Quaternionic Viewpoint

Abstract: We build a new probability measure on closed space and plane polygons. The key construction is a map, given by Hausmann and Knutson, using the Hopf map on quaternions from the complex Stiefel manifold of 2-frames in n-space to the space of closed n-gons in 3-space of total length 2. Our probability measure on polygon space is defined by pushing forward Haar measure on the Stiefel manifold by this map. A similar construction yields a probability measure on plane polygons that comes from a real Stiefel manifold. The edgelengths of polygons sampled according to our measures obey beta distributions. This makes our polygon measures different from those usually studied, which have Gaussian or fixed edgelengths. One advantage of our measures is that we can explicitly compute expectations and moments for chord lengths and radii of gyration. Another is that direct sampling according to our measures is fast (linear in the number of edges) and easy to code. Some of our methods will be of independent interest in studying other probability measures on polygon spaces. We define an edge set ensemble (ESE) to be the set of polygons created by rearranging a given set of n edges. A key theorem gives a formula for the average over an ESE of the squared lengths of chords skipping k vertices in terms of k, n, and the edgelengths of the ensemble. This allows one to easily compute expected values of squared chord lengths and radii of gyration for any probability measure on polygon space invariant under rearrangements of edges. © 2014 Wiley Periodicals, Inc.

Vehicle Front Bumper with Utility Well

Abstract: A vehicle front bumper with a middle portion and end or lateral portions, the end or lateral portions each having a polygon shaped rearward and downward angled forward facing surface, at least one of which has a utility well perimeter opening.

Logistics service range determination method and device

Abstract: The invention discloses a logistics service range determination method and device. The logistics service range determination method comprises the following steps: extracting the address text of each logistics service site from historical logistics data; according to the address text of the service site, determining the position coordinate of the service site; for a service site set corresponding to any service provider, calculating the external polygon of the set according to the position coordinate of the service site; and according to the external polygon obtained by calculation, determining the service range of the corresponding service provider. According to the scheme, the service range is shown by the polygon so as to bring convenience for users to understand and memorize; in addition, for a given site, whether the site is positioned within the service range or not can be directly determined by judging the position relationship between the site and the external polygon; high processing efficiency is provided; and dependency on the completeness of historical address data is lowered.

Slicing and/or texturing for three-dimensional printing

Abstract: A method for slicing a three-dimensional model for printing of a corresponding object by a 3D printer, comprises: obtaining the envelope of the object as polygons, then for each region of a predefined work area within the slicing plane: identifying the closest polygon of said envelope that is positioned above said respective pixel; where no polygon is identified, then marking a corresponding region as a no-print region; if the direction vector of said closest above polygon has a positive component in the Z direction, then marking said corresponding region as a model region; and if the direction vector of said polygon has a negative component in the Z direction, then marking the region as a support region, and printing accordingly. An advantage of the above procedure is that the slicing, and in addition texture mapping, can be efficiently carried out on a graphics card or GPU.

Rational polygons as rotation sets of generic homeomorphisms of the two torus

Abstract: We prove the existence of an open and dense set D\subset? Homeo0(T2) (set of toral homeomorphisms homotopic to the identity) such that the rotation set of any element in D is a rational polygon. We also extend this result to the set of axiom A dif- feomorphisms in Homeo0(T2). Further we observe the existence of minimal sets whose rotation set is a non-trivial segment, for an open set in Homeo0(T2).

Semi-analytic texturing algorithm for polygon computer-generated holograms

Abstract: A texturing method for the semi-analytic polygon computer-generated hologram synthesis algorithm is studied. Through this, the full-potential and development direction of the semi-analytic polygon computer-generated holograms are discussed and compared to that of the conventional numerical algorithm of polygon computer-generated hologram generation based on the fast Fourier transform and bilinear interpolation. The theoretical hurdle of the semi-analytic texturing algorithm is manifested and an approach to resolve this problen. A key mathematical approximation in the angular spectrum computer-generated hologram computation, as well as the trade-offs between texturing effects and computational efficiencies are analyzed through numerical simulation. In this fundamental study, theoretical potential of the semi-analytic polygon computer-generated hologram algorithm is revealed and the ultimate goal of research into the algorithm clarified.