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About 1,310 papers for “Regular polygon”

Regular polygon grid:

Wenbin Zhang (1840726), Yuejun Jin (21030765) · Figshare · 2025

(a) Administrative region; (b) Square; (c) Hexagon.

Cited by 0Open access

Regular polygon detection

Barnes, N, Loy, G, Shaw, D et al. · Figshare · 2005

This paper describes a new robust regular polygon detec-tor. The regular polygon transform is posed as a mixture of regular polygons in a five dimensional space. Given the edge structure of an image, we derive the a posteriori prob-ability for a mixture of regular polygons, and thus the prob-ability density function for the appearance of a mixture of regular polygons. Likely regular polygons can be isolated quickly by discretising and collapsing the search space into three dimensions. The remaining dimensions may be effi-ciently recovered subsequently using maximum likelihood at the locations of the most likely polygons in the subspace. This leads to an efficient algorithm. Also, the a posteriori formulation facilitates inclusion of additional a priori infor-mation leading to real-time application to road sign detec-tion. The use of edge orientation information also reduces noise compared to existing approaches such as the gener-alised Hough transform. Results are presented for images with noise to show stability. Also, the detector is applied to two separate applications: real-time road sign detection for on-line driver assistance; and, feature detection, recovering stable features in rectilinear environments. 1

Cited by 3Open access

Accelerating regular polygon beams

Shane Barwick · Optics Letters · 2010

Beams that possess high-intensity peaks that follow curved paths of propagation under linear diffraction have recently been shown to have a multitude of interesting uses. In this Letter, a family of phase-only masks is derived, and each mask gives rise to multiple accelerating intensity maxima. The curved paths of the peaks can be described by the vertices of a regular polygon that is centered on the optic axis and expands with propagation.

Cited by 33

Dot patterns suggesting regular polygon shapes

Van Geert, Eline, Wagemans, Johan · Figshare · 2023

Dot patterns suggesting regular polygon shapes. N indicates the structural complexity of the pattern as defined in Koenderink et al. (2018). These figures were created using the OCTA toolbox (Van Geert, Bossens, &amp; Wagemans, 2022), with the intention to resemble Figure 7 from Koenderink et al. (2018). <br> I created this figure for the paper titled "Prägnanz in visual perception" by Van Geert and Wagemans (submitted). Find the preprint version here: https://doi.org/10.31234/osf.io/pxdg4 <br> References: Koenderink, J., van Doorn, A., &amp; Pinna, B. (2018). Measures of Prägnanz? Gestalt Theory, 40, 7–28. https://doi.org/10.2478/gth-2018-0002 <br> Van Geert, E., Bossens, C., &amp; Wagemans, J. (2022). The Order &amp; Complexity Toolbox for Aesthetics (OCTA): A systematic approach to study the relations between order, complexity, and aesthetic appreciation. Behavior Research Methods. https://doi.org/10.3758/s13428-022-01900-w

Cited by 0Open access

Dot patterns suggesting regular polygon shapes

Van Geert, Eline, Wagemans, Johan · Figshare · 2023

Dot patterns suggesting regular polygon shapes. N indicates the structural complexity of the pattern as defined in Koenderink et al. (2018). These figures were created using the OCTA toolbox (Van Geert, Bossens, &amp; Wagemans, 2022), with the intention to resemble Figure 7 from Koenderink et al. (2018). <br> I created this figure for the paper titled "Prägnanz in visual perception" by Van Geert and Wagemans (submitted). Find the preprint version here: https://doi.org/10.31234/osf.io/pxdg4 <br> References: Koenderink, J., van Doorn, A., &amp; Pinna, B. (2018). Measures of Prägnanz? Gestalt Theory, 40, 7–28. https://doi.org/10.2478/gth-2018-0002 <br> Van Geert, E., Bossens, C., &amp; Wagemans, J. (2022). The Order &amp; Complexity Toolbox for Aesthetics (OCTA): A systematic approach to study the relations between order, complexity, and aesthetic appreciation. Behavior Research Methods. https://doi.org/10.3758/s13428-022-01900-w

Cited by 0Open access

A Robles-Kelly. Regular polygon detection

Nick Barnes, Gareth Loy, David Shaw et al. · 2005

This paper describes a new robust regular polygon detector. The regular polygon transform is posed as a mixture of regular polygons in a five dimensional space. Given the edge structure of an image, we derive the a posteriori probability for a mixture of regular polygons, and thus the probability density function for the appearance of a mixture of regular polygons. Likely regular polygons can be isolated quickly by discretising and collapsing the search space into three dimensions. The remaining dimensions may be efficiently recovered subsequently using maximum likelihood at the locations of the most likely polygons in the subspace. This leads to an efficient algorithm. Also the a posteriori formulation facilitates inclusion of additional a priori information leading to real-time application to road sign detection. The use of gradient information also reduces noise compared to existing approaches such as the generalised Hough transform. Results are presented for images with noise to show stability. The detector is also applied to two separate applications: real-time road sign detection for on-line driver assistance; and feature detection, recovering stable features in rectilinear environments. 1

Cited by 0

The Perceived Beauty of Regular Polygon Tessellations

Jay Friedenberg · Symmetry · 2019

Beauty judgments for regular polygon tessellations were examined in two experiments. In experiment 1 we tested the three regular and eight semi-regular tilings characterized by a single vertex. In experiment 2 we tested the 20 demi-regular tilings containing two vertices. Observers viewed the tessellations at different random orientations inside a circular aperture and rated them using a numeric 1–7 scale. The data from the first experiment show a peak in preference for tiles with two types of polygons and for five polygons around a vertex. Triangles were liked more than other geometric shapes. The results from the second experiment demonstrate a preference for tessellations with a greater number of different kinds of polygons in the overall pattern and for tiles with the greatest difference in the number of polygons between the two vertices. Ratings were higher for tiles with circular arrangements of elements and lower for those with linear arrangements. Symmetry group p6m was liked the most and groups cmm and pmm were liked the least. Taken as a whole the results suggest a preference for complexity and variety in terms of both vertex qualities and symmetric transformations. Observers were sensitive to both the underlying mathematical properties of the patterns as well as their emergent organization.

Cited by 7Open access

Vortex filament equation for a regular polygon

Francisco de la Hoz, Luis Vega · Nonlinearity · 2014

In this paper, we study the evolution of the localized induction approximation (LIA), also known as vortex filament 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 Gauß sum. We also study the fractal behavior of X(0, t), relating it with the so-called Riemann’s non-differentiable function, that, as proved by S. Jaffard, fits with the multifractal model of U. Frisch and G. Parisi, for fully developed turbulence. Keywords: vortex filament equation, Schrödinger map, generalized quadratic Gauß sums, pseudo-spectral methods, fractals

Cited by 45Open access

On monohedral tilings of a regular polygon

Bushra Basit, Zsolt Lángi · arXiv (Cornell University) · 2021

A tiling of a topological disc by topological discs is called monohedral if all tiles are congruent. Maltby (J. Combin. Theory Ser. A 66: 40-52, 1994) characterized the monohedral tilings of a square by three topological discs. Kurusa, Lángi and V\'ıgh (Mediterr. J. Math. 17: article number 156, 2020) characterized the monohedral tilings of a circular disc by three topological discs. The aim of this note is to connect these two results by characterizing the monohedral tilings of any regular $n$-gon with at most three tiles for any $n \geq 5$.

Cited by 0Open access

Deployable Arches Based on Regular Polygon Geometry

Torres Londoño, Natalia Paola, Peña Villamil, Diana Maritza · RECERCAT (Consorci de Serveis Universitaris de Catalunya) · 2017

This paper discusses a deployable-arch-structure design that is built using articulated bars, commonly called a scissor-system, and is based on the regular polygon geometry. \nThe deployed-arch shape can be determined by inscribing regular polygon geometry in a circle. \nIt is defined by the: a. number of bars required, b. position of the pivots, c. pivot-point distances, d. bar length, and e. open-geometry angle of the arches. The goal is a deployable half dome made up of semi-arches. Traditional arch construction depends on external structures to provide stability until the keystone is set, which then allows the supports to removed. Deployable structures avoid the need for these external supports greatly simplifying the assembly process and deployment time.

Cited by 0Open access

On monohedral tilings of a regular polygon

Bushra Basit, Zsolt Lángi · Aequationes Mathematicae · 2023

Abstract A tiling of a topological disc by topological discs is called monohedral if all tiles are congruent. Maltby (J Comb Theory Ser A 66:40–52, 1994) characterized the monohedral tilings of a square by three topological discs. Kurusa et al. (Mediterr J Math 17:156, 2020) characterized the monohedral tilings of a circular disc by three topological discs. The aim of this note is to connect these two results by characterizing the monohedral tilings of any regular n -gon with at most three tiles for any $$n \ge 5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:math> .

Cited by 0Open access

Iso-optic curve of a regular polygon

Szirmai, Jenő, Csima, Géza, Tóth, János · Acervo Digital da Universidade Estadual Paulista (Universidade Estadual Paulista) · 2013

Cited by 0