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Journal articles on the topic 'Polygonal'

Author: Grafiati

Published: 4 June 2021

Last updated: 5 February 2022

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1

BRUCKSTEIN, ALFRED M., GUILLERMO SAPIRO, and DORON SHAKED. "EVOLUTIONS OF PLANAR POLYGONS." International Journal of Pattern Recognition and Artificial Intelligence 09, no. 06 (1995): 991–1014. http://dx.doi.org/10.1142/s0218001495000407.

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Evolutions of closed planar polygons are studied in this work. In the first part of the paper, the general theory of linear polygon evolutions is presented, and two specific problems are analyzed. The first one is a polygonal analog of a novel affine-invariant differential curve evolution, for which the convergence of planar curves to ellipses was proved. In the polygon case, convergence to polygonal approximation of ellipses, polygo nal ellipses, is proven. The second one is related to cyclic pursuit problems, and convergence, either to polygonal ellipses or to polygonal circles, is proven. I

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2

DEVILLERS, OLIVIER. "SIMULTANEOUS CONTAINMENT OF SEVERAL POLYGONS: ANALYSIS OF THE CONTACT CONFIGURATIONS." International Journal of Computational Geometry & Applications 03, no. 04 (1993): 429–42. http://dx.doi.org/10.1142/s0218195993000270.

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The main concern of this paper is the detection of double contact configurations for some polygons moving in translation in a polygonal environment. We first establish some general properties about such configurations and give conditions of existence of double contacts for two or three objects. For three convex polygons moving in a polygonal environment or three simple polygons moving in a rectangle there always exists a double contact. Two examples without possibility of double contacts are given, one with three polygons (not convex) moving in a polygonal environment, and one with four convex

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3

Teymourtash, A. R., and M. Mokhlesi. "Experimental investigation of stationary and rotational structures in non-circular hydraulic jumps." Journal of Fluid Mechanics 762 (December 3, 2014): 344–60. http://dx.doi.org/10.1017/jfm.2014.646.

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AbstractWhen a vertical liquid jet impacts on a solid horizontal surface, the first expectation is to have a circular hydraulic jump. However, in some conditions, for highly viscous fluids, the transition from supercritical to subcritical flow occurs with non-circular shapes such as polygons. Indeed, a quick rotational wave appears on the circular jump before the formation of a polygonal form, which may be related to the Rayleigh–Plateau instability. In this paper, stable polygonal jumps are studied to complete this research. The region of stability is defined for polygonal jumps, and the depe

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Mahaney, William C., and Michael G. Boyer. "Notes on the Morphology and Genesis of Mud Polygons on Mount Kenya, East Africa." Géographie physique et Quaternaire 42, no. 1 (2007): 89–96. http://dx.doi.org/10.7202/032712ar.

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ABSTRACTMud polygons forming in a valley train deposit in Teleki Valley on Mount Kenya were studied with respect to their physical, mineralogical, chemical and biological characteristics. Developing in fine-grained alluvium of postglacial age, those polygonal systems are composed of numerous, and nearly isomorphous units, that appear close to existing drainages in areas stripped of vegetation cover. Stream erosion and animal activity (particularly rodents and Mount Kenya hyrax, e.g. cony) appear to be primarily responsible for the loss of plant cover. Field tests show that periodic wetting and

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Levy, Joseph S., David R. Marchant, and James W. Head. "Distribution and origin of patterned ground on Mullins Valley debris-covered glacier, Antarctica: the roles of ice flow and sublimation." Antarctic Science 18, no. 3 (2006): 385–97. http://dx.doi.org/10.1017/s0954102006000435.

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We map polygonally patterned ground formed in sublimation tills that overlie debris-covered glaciers in Mullins Valley and central Beacon Valley, in southern Victoria Land, Antarctica, and distinguish five morphological zones. Where the Mullins Valley debris-covered glacier debouches into Beacon Valley, polygonal patterning transitions from radial (orthogonal) intersections to non-oriented (hexagonal) intersections, providing a time-series of polygon evolution within a single microclimate. We offer the following model for polygon formation and evolution in the Mullins Valley system. Near-verti

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Zlotnik, Vitaly A., Dylan R. Harp, Elchin E. Jafarov, and Charles J. Abolt. "A Model of Ice Wedge Polygon Drainage in Changing Arctic Terrain." Water 12, no. 12 (2020): 3376. http://dx.doi.org/10.3390/w12123376.

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As ice wedge degradation and the inundation of polygonal troughs become increasingly common processes across the Arctic, lateral export of water from polygonal soils may represent an important mechanism for the mobilization of dissolved organic carbon and other solutes. However, drainage from ice wedge polygons is poorly understood. We constructed a model which uses cross-sectional flow nets to define flow paths of meltwater through the active layer of an inundated low-centered polygon towards the trough. The model includes the effects of evaporation and simulates the depletion of ponded water

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Wang, Chao, та Zhongzi Wang. "The limit shapes of midpoint polygons in ℝ3". Journal of Knot Theory and Its Ramifications 28, № 10 (2019): 1950062. http://dx.doi.org/10.1142/s0218216519500627.

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For a polygon in the [Formula: see text]-dimensional Euclidean space, we give two kinds of normalizations of its [Formula: see text]th midpoint polygon by a homothetic transformation and an affine transformation, respectively. As [Formula: see text] goes to infinity, the normalizations will approach “regular” polygons inscribed in an ellipse and a generalized Lissajous curve, respectively, where the curves may be degenerate. The most interesting case is when [Formula: see text], where polygons with all its [Formula: see text]th midpoint polygons knotted are discovered and discussed. Such polyg

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8

Kartoziia, Andrei. "Assessment of the Ice Wedge Polygon Current State by Means of UAV Imagery Analysis (Samoylov Island, the Lena Delta)." Remote Sensing 11, no. 13 (2019): 1627. http://dx.doi.org/10.3390/rs11131627.

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Modern degradation of Arctic permafrost promotes changes in tundra landscapes and leads to degradation of ice wedge polygons, which are the most widespread landforms of Arctic wetlands. Status assessment of polygon degradation is important for various environmental studies. We have applied the geographic information systems’ (GIS) analysis of data from unmanned aerial vehicles (UAV) to accurately assess the status of ice wedge polygon degradation on Samoylov Island. We used several modern models of polygon degradation for revealing polygon types, which obviously correspond to different stages

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9

İlhan, Hacer, and Haşmet Gürçay. "Polygon Morphing and Its Application in Orebody Modeling." Mathematical Problems in Engineering 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/732365.

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Three different polygon morphing methods are examined. The first one is based on the utilization of the trimmed skeleton of the symmetric difference of the source and target polygons as an intermediate polygon. The second one reduces the problem to the problem of morphing compatible planar triangulations and utilizes the representation of planar triangulations as a matrix constructed using barycentric coordinates of the planar triangulation's vertices relative to their neighbors. The third and last one describes the polygon by the parametric curve representation based on estimated Fourier para

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10

Wales, Nathan A., Jesus D. Gomez-Velez, Brent D. Newman, et al. "Understanding the relative importance of vertical and horizontal flow in ice-wedge polygons." Hydrology and Earth System Sciences 24, no. 3 (2020): 1109–29. http://dx.doi.org/10.5194/hess-24-1109-2020.

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Abstract. Ice-wedge polygons are common Arctic landforms. The future of these landforms in a warming climate depends on the bidirectional feedback between the rate of ice-wedge degradation and changes in hydrological characteristics. This work aims to better understand the relative roles of vertical and horizontal water fluxes in the subsurface of polygonal landscapes, providing new insights and data to test and calibrate hydrological models. Field-scale investigations were conducted at an intensively instrumented location on the Barrow Environmental Observatory (BEO) near Utqiaġvik, AK, USA.

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11

TAN, XUEHOU. "EDGE GUARDS IN STRAIGHT WALKABLE POLYGONS." International Journal of Computational Geometry & Applications 09, no. 01 (1999): 63–79. http://dx.doi.org/10.1142/s0218195999000066.

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We study the art gallery problem restricted to edge guards and straight walkable polygons. An edge guard is the guard that patrols individual edges of the polygon. A simple polygon P is called straight walkable if there are two vertices s and t in P and we can move two points montonically on two polygonal chains of P from s to t, one clockwise and the other counterclockwise, such that two points are always mutually visible. For instance, monotone polygons and spiral polygons are straight walkable. We show that ⌊(n+2)/5⌋ edge guards are always sufficient to watch and n-vertex gallery of this ty

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Dai, Xingde, and Yuanan Diao. "THE MINIMUM OF KNOT ENERGY FUNCTIONS." Journal of Knot Theory and Its Ramifications 09, no. 06 (2000): 713–24. http://dx.doi.org/10.1142/s0218216500000402.

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In this paper we discuss some fundamental issues regarding knot energy functions. These include the existence of minimum values of energy functions of smooth knots and energy functions of polygonal knots within a knot type, the convergence of these minimum values in the case of polygonal knot energy and the convergence of the corresponding polygons where these minimum values are attained. When the polygonal knot energy is derived from a smooth knot energy, will the minimal polygonal knot energies converge to the infimum of the smooth knot energy? Do the corresponding polygons converge to a smo

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Eder, Günther, Martin Held, and Peter Palfrader. "Min-/Max-Volume Roofs Induced by Bisector Graphs of Polygonal Footprints of Buildings." International Journal of Computational Geometry & Applications 28, no. 04 (2018): 309–40. http://dx.doi.org/10.1142/s0218195918500097.

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Piecewise-linear terrains (“roofs”) over simple polygons were first studied by Aichholzer et al. (J. UCS 1995) in their work on straight skeletons of polygons. We show how to construct a roof over the polygonal footprint of a building that has minimum or maximum volume among all roofs that drain water. Our algorithm for computing such a roof extends the standard plane-sweep approach known from the theory of straight skeletons by additional events. For both types of roofs our algorithm runs in [Formula: see text] time for a simple polygon with [Formula: see text] vertices.

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14

Deguchi, Tetsuo, and Kyoichi Tsurusaki. "A Statistical Study of Random Knotting Using the Vassiliev Invariants." Journal of Knot Theory and Its Ramifications 03, no. 03 (1994): 321–53. http://dx.doi.org/10.1142/s0218216594000241.

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Employing the Vassiliev invariants as tools for determining knot types of polygons in 3 dimensions, we evaluate numerically the knotting probability PK(N) of the Gaussian random polygon being equivalent to a knot type K. For prime knots and composite knots we plot the knotting probability PK(N) against the number N of polygonal nodes. Taking the analogy with the asymptotic scaling behaviors of self-avoiding walks, we propose a formula of fitting curves to the numerical data. The curves fit well the graphs of the knotting probability PK(N) versus N. This agreement suggests to us that the scalin

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15

Mellon, Michael T., Christopher P. Mckay, and Jennifer L. Heldmann. "Polygonal ground in the McMurdo Dry Valleys of Antarctica and its relationship to ice-table depth and the recent Antarctic climate history." Antarctic Science 26, no. 4 (2013): 413–26. http://dx.doi.org/10.1017/s0954102013000710.

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AbstractThe occurrence of dry permafrost overlying ice-rich permafrost is unique to the Antarctic Dry Valleys on Earth and to the high latitudes of Mars. The stability and distribution of this ice are poorly understood and fundamental to understanding the Antarctic climate as far back as a few million years. Polygonal patterned ground is nearly ubiquitous in these regions and is integrally linked to the history of the icy permafrost and climate. We examined the morphology of polygonal ground in Beacon Valley and the Beacon Heights region of the Antarctic Dry Valleys, and show that polygon size

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16

Ladd, Mallory P., David T. Reeves, Suresh Poudel, Colleen M. Iversen, Stan D. Wullschleger, and Robert L. Hettich. "Untargeted Exometabolomics Provides a Powerful Approach to Investigate Biogeochemical Hotspots with Vegetation and Polygon Type in Arctic Tundra Soils." Soil Systems 5, no. 1 (2021): 10. http://dx.doi.org/10.3390/soilsystems5010010.

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Rising temperatures in the Arctic have led to the thawing of tundra soils, which is rapidly changing terrain, hydrology, and plant and microbial communities, causing hotspots of biogeochemical activity across the landscape. Despite this, little is known about how nutrient-rich low molecular weight dissolved organic matter (LMW DOM) varies within and across tundra ecosystems. Using a high-resolution nano-liquid chromatography-mass spectrometry (LC/MS) approach, we characterized the composition and availability of LMW DOM from high-centered polygons (HCP) and low-centered polygons (LCP) with Eri

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17

SIMON, JONATHAN K. "ENERGY FUNCTIONS FOR POLYGONAL KNOTS." Journal of Knot Theory and Its Ramifications 03, no. 03 (1994): 299–320. http://dx.doi.org/10.1142/s021821659400023x.

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We define a scale-invariant energy function for polygonal knots in ℜ3 based on the minimum distances between segments. The energy is bounded below by 2π. (minimum crossing number of the knot type). For each knot type, there exists an ideal number of segments, from which can be made an ideal conformation of the knot having minimum energy among all polygons realizing that knot type. Results leading to this include the following: The energy of an n-segment polygon is greater than n; if energy is bounded then ratios of edge lengths and angles are bounded away from zero; changing knot type requires

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18

Sun, Ying. "Research of the DWTT Fracture of X70 Pipeline Steel." Advanced Materials Research 535-537 (June 2012): 643–46. http://dx.doi.org/10.4028/www.scientific.net/amr.535-537.643.

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The DWTT fracture toughness of X70 pipeline steel with different content and grain size of polygonal ferrite was investigated. The results show that when the content of polygon ferrite is above 28%, the shear-area percentage of DWTT fracture begins to decrease instead of increase, while polygonal ferrite toughening effect weakens. It is the difference of the polygonal ferrite content that results in the difference of shear-area percentage of DWTT fracture.

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19

MARTINI, H., and V. SOLTAN. "MINIMUM NUMBER OF PIECES IN A CONVEX PARTITION OF A POLYGONAL DOMAIN." International Journal of Computational Geometry & Applications 09, no. 06 (1999): 599–614. http://dx.doi.org/10.1142/s0218195999000340.

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Let [Formula: see text] be a given nonempty family of directions in the plane. For a multiply connected polygonal domain P with polygonal holes, possibly degenerate, we determine the minimum number of convex polygons into which P is partitioned by linear cuts in the directions from [Formula: see text].

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20

BERN, MARSHALL, DAVID DOBKIN, and DAVID EPPSTEIN. "TRIANGULATING POLYGONS WITHOUT LARGE ANGLES." International Journal of Computational Geometry & Applications 05, no. 01n02 (1995): 171–92. http://dx.doi.org/10.1142/s0218195995000106.

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We show how to triangulate polygonal regions—adding extra vertices as necessary— with triangles of guaranteed quality. Using only O(n) triangles, we can guarantee that the smallest height (shortest dimension) of a triangle in a triangulation of an n-vertex polygon (with holes) is a constant fraction of the largest possible. Using O(n log n) triangles for simple polygons or O(n3/2) triangles for polygons with holes, we can guarantee that the largest angle is no greater than 150°. We can add the guarantee on smallest height to these no-large-angle results, without increasing the asymptotic compl

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21

Joswig, M. "Isotopy of Polygonal Domains for Generalized Polygons." European Journal of Combinatorics 19, no. 2 (1998): 151–58. http://dx.doi.org/10.1006/eujc.1997.0171.

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22

CHAN, W. S., and F. CHIN. "APPROXIMATION OF POLYGONAL CURVES WITH MINIMUM NUMBER OF LINE SEGMENTS OR MINIMUM ERROR." International Journal of Computational Geometry & Applications 06, no. 01 (1996): 59–77. http://dx.doi.org/10.1142/s0218195996000058.

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We improve the time complexities for solving the polygonal curve approximation problems formulated by Imai and Iri. The time complexity for approximating any polygonal curve of n vertices with minimum number of line segments can be improved from O(n2 log n) to O(n2). The time complexity for approximating any polygonal curve with minimum error can also be improved from O(n2 log 2n) to O(n2 log n). We further show that if the curve to be approximated forms part of a convex polygon, the two problems can be solved in O(n) and O(n2) time respectively for both open and closed polygonal curves.

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23

GUTKIN, EUGENE, and NICOLAI HAYDN. "Topological entropy of polygon exchange transformations and polygonal billiards." Ergodic Theory and Dynamical Systems 17, no. 4 (1997): 849–67. http://dx.doi.org/10.1017/s0143385797088044.

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We study the topological entropy of a class of transformations with mild singularities: the generalized polygon exchanges. This class contains, in particular, polygonal billiards. Our main result is a geometric estimate, from above, on the topological entropy of generalized polygon exchanges. One of the applications of our estimate is that the topological entropy of polygonal billiards is zero. This implies the subexponential growth of various geometric quantities associated with a polygon. Other applications are to the piecewise isometries in two dimensions, and to billiards in rational polyh

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RAWDON, ERIC J., and JOSEPH WORTHINGTON. "ERROR ANALYSIS OF THE MINIMUM DISTANCE ENERGY OF A POLYGONAL KNOT AND THE MÖBIUS ENERGY OF AN APPROXIMATING CURVE." Journal of Knot Theory and Its Ramifications 19, no. 08 (2010): 975–1000. http://dx.doi.org/10.1142/s0218216510008303.

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Energy minimizing smooth knot configurations have long been approximated by finding knotted polygons that minimize discretized versions of the given energy. However, for most knot energy functionals, the question remains open on whether the minimum polygonal energies are "close" to the minimum smooth energies. In this paper, we determine an explicit bound between the Minimum-Distance Energy of a polygon and the Möbius Energy of a piecewise-C2 knot inscribed in the polygon. This bound is written in terms of the ropelength and the number of edges and can be used to determine an upper bound for t

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RANDELL, RICHARD, JONATHAN SIMON, and JOSHUA TOKLE. "MÖBIUS TRANSFORMATIONS OF POLYGONS AND PARTITIONS OF 3-SPACE." Journal of Knot Theory and Its Ramifications 17, no. 11 (2008): 1401–13. http://dx.doi.org/10.1142/s0218216508006671.

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The image of a polygonal knot K under a spherical inversion of ℝ3 ∪ ∞ is a simple closed curve made of arcs of circles, perhaps some line segments, having the same knot type as the mirror image of K. But suppose we reconnect the vertices of the inverted polygon with straight lines, making a new polygon [Formula: see text]. This may be a different knot type. For example, a certain 7-segment figure-eight knot can be transformed to a figure-eight knot, a trefoil, or an unknot, by selecting different inverting spheres. Which knot types can be obtained from a given original polygon K under this pro

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26

Mellini, Marcello. "Chrysotile and polygonal serpentine from the Balangero serpentinite." Mineralogical Magazine 50, no. 356 (1986): 301–5. http://dx.doi.org/10.1180/minmag.1986.050.356.17.

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AbstractTransmission electron microscopy shows that normal chrysotile and polygonal serpentine occur together and in parallel association with balangeroite, within the slip-veins of the Balangero serpentinite. Chrysotile substitutes for balangeroite and it is later replaced by the polygonal serpentine.The chrysotile fibres are packed together according to a rod close-packing scheme, with defects. Lattice images of the polygonal serpentine confirm the structure model proposed by Middleton and Whittaker (1976), consisting of polygonally arranged fiat layers. This structural type is probably comm

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27

Keady, Grant. "Steady slip flow of Newtonian fluids through tangential polygonal microchannels." IMA Journal of Applied Mathematics 86, no. 3 (2021): 547–64. http://dx.doi.org/10.1093/imamat/hxab008.

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Abstract The concern in this paper is the problem of finding—or, at least, approximating—functions, defined within and on the boundary of a tangential polygon, functions whose Laplacian is $-1$ and which satisfy a homogeneous Robin boundary condition on the boundary. The parameter in the Robin condition is denoted by $\beta $. The integral of the solution over the interior, denoted by $Q$, is, in the context of flows in a microchannel, the volume flow rate. A variational estimate of the dependence of $Q$ on $\beta $ and the polygon’s geometry is studied. Classes of tangential polygons treated

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Kolodziej, J. A., and A. Uścilowska. "Regular Polygonal Shapes, and Boundary Collocation Method." International Journal of Mechanical Engineering Education 28, no. 2 (2000): 140–50. http://dx.doi.org/10.7227/ijmee.28.2.3.

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In this article, the application of boundary collocation method for solving of boundary value technical problems for domains with regular polygonal shapes is discussed. Two sample problems are considered: (a) steady laminar flow in regular polygonal conduits, and (b) temperature field for hollow prismatic cylinders bounded by isothermal inner circles and outer regular polygon.

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Lu, Y. Q., M. R. Yalamanchili, and J. D. Miller. "FT-IR Internal Reflection Spectroscopy Using Regular Polygonal Internal Reflection Elements." Applied Spectroscopy 52, no. 6 (1998): 851–54. http://dx.doi.org/10.1366/0003702981944382.

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Regular polygonal reactive internal reflection elements (IREs) have been designed and fabricated for Fourier transform infrared (FT-IR) internal reflection spectroscopy (IRS) to study adsorption phenomena at the IRE surface. The geometric and optical features of these polygonal IREs are described with respect to the use of the FT-IR/IRS adsorption density equation. An octagonal internal reflection element of fluorite (CaF2) was prepared with 3 mm sides, and adsorption at the polygon faces was examined by FT-IR/IRS. Adsorption densities thus determined at the surface of the polygonal IRE were f

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Gewali, Laxmi, and Joseph Scanlan. "Recognizing Sharp Features of 2-D Shapes." International Journal of Electronics and Telecommunications 56, no. 2 (2010): 153–56. http://dx.doi.org/10.2478/v10177-010-0020-5.

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Recognizing Sharp Features of 2-D Shapes We present an efficient algorithm for recognizing and extracting sharp-features from complex polygonal shapes. The algorithm executes in O(n2) time, where n is the number of vertices in the polygon. Sharp-feature extraction algorithms can be useful as a pre-processing step for measuring shape-similarity between polygonal shapes.

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Abolt, Charles J., Michael H. Young, Adam L. Atchley, and Cathy J. Wilson. "Brief communication: Rapid machine-learning-based extraction and measurement of ice wedge polygons in high-resolution digital elevation models." Cryosphere 13, no. 1 (2019): 237–45. http://dx.doi.org/10.5194/tc-13-237-2019.

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Abstract. We present a workflow for the rapid delineation and microtopographic characterization of ice wedge polygons within high-resolution digital elevation models. At the core of the workflow is a convolutional neural network used to detect pixels representing polygon boundaries. A watershed transformation is subsequently used to segment imagery into discrete polygons. Fast training times (<5 min) permit an iterative approach to improving skill as the routine is applied across broad landscapes. Results from study sites near Utqiaġvik (formerly Barrow) and Prudhoe Bay, Alaska, demonstrate

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Seneviratne, L. D., W.-S. Ko, and S. W. E. Earles. "Triangulation-based path planning for a mobile robot." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 211, no. 5 (1997): 365–71. http://dx.doi.org/10.1243/0954406971522114.

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A triangulation-based path planning algorithm for a mobile robot is presented. A circular robot operating in a planar polygonal environment cluttered with polygonal obstacles is considered. The free space of the robot consists of a polygonal region with polygonal holes. A method called bridge building is presented for triangulating a simple polygon with polygonal holes. The free working space of the robot is thus triangulated, resulting in an exact cell decomposition. This enables a triangulation graph to be constructed, representing the topological connectivity of the free space, from which s

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RAWDON, ERIC J., and JONATHAN K. SIMON. "POLYGONAL APPROXIMATION AND ENERGY OF SMOOTH KNOTS." Journal of Knot Theory and Its Ramifications 15, no. 04 (2006): 429–51. http://dx.doi.org/10.1142/s0218216506004543.

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We establish a fundamental connection between smooth and polygonal knot energies, showing that the Minimum Distance Energy for polygons inscribed in a smooth knot converges to the Möbius Energy of the smooth knot as the polygons converge to the smooth knot. For this to work, the polygons must converge in a "nice" way, and the energies must be correctly regularized. We determine an explicit error bound for the convergence.

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Schlicker, Steven J. "Numbers Simultaneously Polygonal and Centered Polygonal." Mathematics Magazine 84, no. 5 (2011): 339–50. http://dx.doi.org/10.4169/math.mag.84.5.339.

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SUN, YUNG-NIEN, and SHU-CHIEN HUANG. "GENETIC ALGORITHMS FOR ERROR-BOUNDED POLYGONAL APPROXIMATION." International Journal of Pattern Recognition and Artificial Intelligence 14, no. 03 (2000): 297–314. http://dx.doi.org/10.1142/s0218001400000209.

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A new polygonal approximation algorithm, employing the concept of genetic evolution, is presented. In the proposed method, a chromosome is used to represent a polygon by a binary string. Each bit, called a gene, represents a point on the given curve. Three genetic operators, including selection, crossover, and mutation, are designed to obtain the approximated polygon whose error is bounded by a given norm. Many experiments show that the convergence is guaranteed and the optimal or near-optimal solutions can be obtained. Compared with the Zhu–Seneviratne algorithm,24 the proposed algorithm succ

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Ferreira, Chelo, José L. López, Rafael Navarro, and Ester Pérez Sinusía. "Zernike-like systems in polygons and polygonal facets." Applied Optics 54, no. 21 (2015): 6575. http://dx.doi.org/10.1364/ao.54.006575.

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Zhang, Li-Yuan, Yue Li, Guang-Kui Xu, and Xi-Qiao Feng. "Enumeration–screening method for the design of simple polygonal tensegrities." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2228 (2019): 20180812. http://dx.doi.org/10.1098/rspa.2018.0812.

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Tensegrities, consisting of axially pre-compressed bars and pre-stretched strings, hold broad applications in the design of, for instance, architectures, soft robotics and metamaterials. In this paper, we propose an enumeration–screening method to design planar tensegrities of simple polygonal shapes. In such a polygonal tensegrity, the strings are joined pair-wise to form a simple polygon (a planar shape consisting of straight, non-intersecting line segments) and only one bar is added at each node. The total number of simple polygonal tensegrities designed by this scheme increases exponential

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Xu, Qiang, Jian Yun Chen, Jing Li, Gui Bing Zhang, Hong Yuan Yue, and Xian Zheng Yu. "Nonlinear analysis for the polygonal element." MATEC Web of Conferences 272 (2019): 01020. http://dx.doi.org/10.1051/matecconf/201927201020.

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As an important method for solving boundary value problems of differential equations, the finite element method (FEM) has been widely used in the fields of engineering and academic research. For two dimensional problems, the traditional finite element method mainly adopts triangular and quadrilateral elements, but the triangular element is constant strain element, its accuracy is low, the poor adaptability of quadrilateral element with complex geometry. The polygon element is more flexible and convenient in the discrete complex geometric model. Some interpolation functions of the polygon eleme

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Wang, Hui, and Qing-Hua Qin. "Voronoi Polygonal Hybrid Finite Elements with Boundary Integrals for Plane Isotropic Elastic Problems." International Journal of Applied Mechanics 09, no. 03 (2017): 1750031. http://dx.doi.org/10.1142/s1758825117500314.

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Polygonal finite elements with high level of geometric isotropy provide greater flexibility in mesh generation and material science involving topology change in material phase. In this study, a hybrid finite element model based on polygonal mesh is constructed by centroidal Voronoi tessellation for two-dimensional isotropic elastic problems and then is formulated with element boundary integrals only. For the present [Formula: see text]-sided polygonal finite element, two independent fields are introduced: (i) displacement and stress fields inside the element; (ii) frame displacement field alon

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Guptasarma, D., and B. Singh. "New scheme for computing the magnetic field resulting from a uniformly magnetized arbitrary polyhedron." GEOPHYSICS 64, no. 1 (1999): 70–74. http://dx.doi.org/10.1190/1.1444531.

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The magnetic field at any point outside a uniformly magnetized polyhedron of arbitrary shape is obtained by adding the fields resulting from the effective free magnetic poles on each of the polygonal surfaces of the polyhedron. For each polygonal surface, the components of the field at the point of observation are expressed in terms of new line integrals around the edges of the polygon and the solid angle subtended by the polygon at the point of observation. The line integrals are standard elementary forms. This new approach makes the numerical evaluation of the magnetic fields for such models

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SARKAR, BISWAJIT, LOKENDRA KUMAR SINGH, and DEBRANJAN SARKAR. "A GENETIC ALGORITHM-BASED APPROACH FOR DETECTION OF SIGNIFICANT VERTICES FOR POLYGONAL APPROXIMATION OF DIGITAL CURVES." International Journal of Image and Graphics 04, no. 02 (2004): 223–39. http://dx.doi.org/10.1142/s0219467804001385.

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A polygonal approximation captures the essential features of a digital planar curve and yields a compact representation. Those points of the digital curve that carry vital information about the shape of the curve form the vertices of the approximating polygon and are called significant vertices. In this paper, we present a genetic algorithm-based approach to locate a specified number of significant points, such that the approximation error between the original curve and its polygonal version obtained by joining the adjacent significant points is minimized. By using a priori knowledge about the

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Cresto Aleina, F., V. Brovkin, S. Muster, et al. "A stochastic model for the polygonal tundra based on Poisson–Voronoi diagrams." Earth System Dynamics 4, no. 2 (2013): 187–98. http://dx.doi.org/10.5194/esd-4-187-2013.

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Abstract. Subgrid processes occur in various ecosystems and landscapes but, because of their small scale, they are not represented or poorly parameterized in climate models. These local heterogeneities are often important or even fundamental for energy and carbon balances. This is especially true for northern peatlands and in particular for the polygonal tundra, where methane emissions are strongly influenced by spatial soil heterogeneities. We present a stochastic model for the surface topography of polygonal tundra using Poisson–Voronoi diagrams and we compare the results with available rece

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Cresto Aleina, F., V. Brovkin, S. Muster, et al. "A stochastic model for the polygonal tundra based on Poisson-Voronoi Diagrams." Earth System Dynamics Discussions 3, no. 1 (2012): 453–83. http://dx.doi.org/10.5194/esdd-3-453-2012.

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Abstract. Sub-grid processes occur in various ecosystems and landscapes but, because of their small scale, they are not represented or poorly parameterized in climate models. These local heterogeneities are often important or even fundamental for energy and carbon balances. This is especially true for northern peatlands and in particular for the polygonal tundra where methane emissions are strongly influenced by spatial soil heterogeneities. We present a stochastic model for the surface topography of polygonal tundra using Poisson-Voronoi Diagrams and we compare the results with available rece

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Esquivel, Wilson D., and Luciano E. Chiang. "Nonholonomic path planning among obstacles subject to curvature restrictions." Robotica 20, no. 1 (2002): 49–58. http://dx.doi.org/10.1017/s0263574701003630.

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This paper addresses the problem of finding a nonholonomic path subject to a curvature restriction, to be tracked by a wheeled autonomous navigation vehicle. This robot is able to navigate in a structured environment, with obstacles modeled as polygons, thus constituting a model based system. The path planning methodology begins with the conditioning of the polygonal environment by offsetting each polygon in order to avoid the possibility of collision with the mobile. Next, the modified polygonal environment is used to compute a preliminary shortest path (PA) between the two extreme positions

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Zhang, Wenlei, Mingxu Ma, Haiyan Li, Jiapeng Yu, and Zhenwei Zhang. "An interference discrimination method for assembly sequence planning and assembly simulation." Assembly Automation 40, no. 4 (2020): 541–52. http://dx.doi.org/10.1108/aa-04-2019-0080.

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Purpose The purpose of this paper is to discriminate fake interference caused by polygonal approximation so as to achieve accurate assembly sequence planning and assembly simulation. Design/methodology/approach An approximation zone model is proposed to formulate polygonal approximation. Fake interference is discriminated from hard interference by evaluating if polygonal models intersect within corresponding approximation zones. To reduce the computation, the surface-surface, surface-end face and end face-end face intersection test methods have been developed to evaluate the intersection and o

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Eder, Günther, Martin Held, Steinþór Jasonarson, Philipp Mayer, and Peter Palfrader. "Salzburg Database of Polygonal Data: Polygons and Their Generators." Data in Brief 31 (August 2020): 105984. http://dx.doi.org/10.1016/j.dib.2020.105984.

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Grabowski, Adam. "Polygonal Numbers." Formalized Mathematics 21, no. 2 (2013): 103–13. http://dx.doi.org/10.2478/forma-2013-0012.

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Summary In the article the formal characterization of triangular numbers (famous from [15] and words “EYPHKA! num = Δ+Δ+Δ”) [17] is given. Our primary aim was to formalize one of the items (#42) from Wiedijk’s Top 100 Mathematical Theorems list [33], namely that the sequence of sums of reciprocals of triangular numbers converges to 2. This Mizar representation was written in 2007. As the Mizar language evolved and attributes with arguments were implemented, we decided to extend these lines and we characterized polygonal numbers. We formalized centered polygonal numbers, the connection between

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Park, Sang C. "Polygonal extrusion." Visual Computer 19, no. 1 (2003): 38–49. http://dx.doi.org/10.1007/s00371-002-0170-2.

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De Bruyn, Bart. "Polygonal valuations." Discrete Mathematics 313, no. 1 (2013): 84–93. http://dx.doi.org/10.1016/j.disc.2012.09.012.

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Kaneko, Masanobu, and Katsuichi Tachibana. "When is a Polygonal Pyramid Number again Polygonal?" Rocky Mountain Journal of Mathematics 32, no. 1 (2002): 149–65. http://dx.doi.org/10.1216/rmjm/1030539614.

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