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Approximating Euclidean circles by neighbourhood sequences in a hexagonal grid

Benedek Nagy, Robin Strand
2011 Theoretical Computer Science  
The grid is coordinatized by three coordinates in a symmetric way. Digital circles are classified based on digital distances using neighbourhood sequences.  ...  Therefore the non-compactness ratio is used to measure the quality of approximation of the Euclidean circles. The best approximating neighbourhood sequence is presented.  ...  Acknowledgements The private communication with Professor Attila Kuba about the idea of approximating the Euclidean distance by two neighbourhood sequences simultaneously is gratefully acknowledged.  ... 
doi:10.1016/j.tcs.2010.10.028 fatcat:wlxce64kwbaz3akpslrs7m22ie

BRISKS: Binary Features for Spherical Images on a Geodesic Grid

Hao Guan, William A. P. Smith
2017 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
We discretise images on a spherical geodesic grid formed by recursive subdivision of a triangular mesh.  ...  This leads to a multiscale pixel grid comprising mainly hexagonal pixels that lends itself naturally to a spherical image pyramid representation.  ...  In the radius 2 case, corners centred on pentagonal pixels have p Figure 7 : An example of a pixel passing the hexagonal 7-12 AST. circles containing 10 pixels and we test for sequences of length 6.  ... 
doi:10.1109/cvpr.2017.519 dblp:conf/cvpr/GuanS17 fatcat:xrbeufvzond6vcye3r6zbrjxye

Isoperimetrically optimal polygons in the triangular grid with Jordan-type neighbourhood on the boundary

Benedek Nagy, Krisztina Barczi
2013 International Journal of Computer Mathematics  
Apart from the extension of these sections, entirely new results are provided in Section 5.  ...  The work is supported by the TÁMOP 4.2.1/B-09/1/KONV-2010-0007 project.  ...  The optimal hexagons approximate the regular hexagons (or in case, the perimeter is divisible by 6, they are the regular hexagons).  ... 
doi:10.1080/00207160.2012.737914 fatcat:coi5nbwfpbe6lpwdbihx2u5ofq

Rectangular and hexagonal grids used for observation, experiment and simulation in ecology

Colin P.D. Birch, Sander P. Oom, Jonathan A. Beecham
2007 Ecological Modelling  
The nearest neighbourhood in a hexagonal grid is simpler and less ambiguous than in a rectangular grid.  ...  A survey of recent uses of grids in Ecological Modelling suggested that hexagonal grids are rarely used, even in applications for which they are more suitable than rectangular grids, e.g. connectivity  ...  In these experiments, a hexagonal lattice planting arrangement is expanded away from the apex of a triangle or the centre of a circle, so that the spacing between plants is increased by a set proportion  ... 
doi:10.1016/j.ecolmodel.2007.03.041 fatcat:v4ldowekize27j4amefehxiifq


Valentin E. Brimkov, Reneta P. Barneva, Petra Wiederhold
2011 Theoretical Computer Science  
As a result of a rigorous reviewing process, typically by three referees per paper, 11 works were eventually accepted for publication.  ...  They also show that any cycle of the integer grid contains an inscribed square with integer vertices. Finally, they provide an O(n 2 ) algorithm to find inscribed squares in simple digital curves.  ...  In the paper ''Approximating Euclidean Circles by Neighbourhood Sequences in a Hexagonal Grid'', the authors Benedek Nagy and Robin Strand classify digital circles in a hexagonal grid.  ... 
doi:10.1016/j.tcs.2010.12.001 fatcat:gakq33in7zghtphdoei3zztgaa

Protein Folding in the Hexagonal Prism Lattice with Diagonals [article]

Dipan Lal Shaw, M. Sohel Rahman, A. S. M. Sohidull Islam, Shuvasish Karmaker
2014 arXiv   pre-print
Since, it is a problem of great potential complexity many simplified energy model have been proposed in literature on basis of interaction of amino acid residue in protein.  ...  In this paper, we proposed hexagonal prism lattice with diagonal that can overcome the problems of other lattice structure, e.g., parity problem.  ...  On the other hand, one vertex of hand hexagonal prism lattice with diagonal have 20 neighbour which property leads us to find better approximation ratio.  ... 
arXiv:1407.4650v1 fatcat:g2xszgkxb5fszpfkn7vfshhera

Broadcasting Automata and Patterns on Z^2 [article]

Thomas Nickson, Igor Potapov
2014 arXiv   pre-print
In this chapter we aim to study the geometrical shapes of informational waves on integer grid generated in broadcasting automata model as well as their potential use for metric approximation in a discrete  ...  The waves generated by activating processes in a digital environment can be used for designing a vari- ety of wave algorithms.  ...  Also studied in neighbourhood sequences is the possible resultant shapes which are categorised and examined for their various properties such as their use in approximation of euclidean distances where  ... 
arXiv:1410.0573v1 fatcat:wtlwc3s4onaiti4jdjterip64m

The Eccentricity Transform (of a Digital Shape) [chapter]

Walter G. Kropatsch, Adrian Ion, Yll Haxhimusa, Thomas Flanitzer
2006 Lecture Notes in Computer Science  
For a connected region of a digital image it is defined through its neighbourhood graph and the given metric.  ...  Eccentricity measures the shortest length of the paths from a given vertex v to reach any other vertex w of a connected graph.  ...  These distance transforms are easy to compute by scanning the image twice [12, 11] , although they are not a good approximation of the Euclidean distance.  ... 
doi:10.1007/11907350_37 fatcat:mzppmzjppjfozjif3xzou4x67i

Protein folding in HP model on hexagonal lattices with diagonals

Dipan Shaw, ASM Shohidull Islam, M Sohel Rahman, Masud Hasan
2014 BMC Bioinformatics  
Our first algorithm is a 5 3 -approximation algorithm, which is based on the strategy of partitioning the entire protein sequence into two pieces.  ...  Three dimensional structure prediction of a protein from its amino acid sequence, known as protein folding, is one of the most studied computational problem in bioinformatics and computational biology.  ...  A significant part of the costs have been borne by the authors.  ... 
doi:10.1186/1471-2105-15-s2-s7 pmid:24564789 pmcid:PMC4016602 fatcat:d7d26kil5rbstojuon7fnbtv54


1986 Le Journal de Physique Colloques  
Abstract -Daisies, and composite flowers, exhibit an ordered arrangement of florets (phyllotaxis) generated by a simple algorithm.  ...  Article published online by EDP Sciences and available at http://dx.  ...  The numerical work on the Daisy has been done in collaboration with A. Lissowski and R. Occelli [4], who obtained Fig.1 [12] . Fig.5 is due to GBhler and Rhyner.  ... 
doi:10.1051/jphyscol:1986331 fatcat:3pv4mkx3irhz7gkujtk5scbafi

Efficient multi-task allocation and path planning for unmanned surface vehicle in support of ocean operations

Yuanchang Liu, Richard Bucknall
2018 Neurocomputing  
The new algorithm is able to fast and effectively generate a sequence for executing multiple tasks in a cluttered maritime environment involving numerous obstacles.  ...  In terms of the multi-task allocation, a novel algorithm based upon a self-organising map (SOM) has been designed and developed.  ...  Acknowledgements This work is supported by the ACCeSS group. The Atlantic Centre for the innovative design and Control of Small Ships (ACCeSS) is an ONR-NNRNE programme with Grant no.  ... 
doi:10.1016/j.neucom.2017.09.088 fatcat:zaisgbxilranlieoww2aq7uaui

On geodesics of phyllotaxis

Roland Bacher
2014 Confluentes Mathematici (CM)  
This work has been partially supported by the LabEx PERSYVAL-Lab (ANR-11-LABX-0025). The author is a member of the project-team GALOIS supported by this LabEx.  ...  Acknowledgements I would like to thank David Speyer who started my interest in phyllotaxis by proposing ϕ θ (N) as an interesting configuration to consider in relation with Question 3307 of Mathoverflow  ...  They are illustrated by the square tiling obtained by covering the Euclidean plane with unit-squares centered at all points of Z 2 and by the honeycomb-tiling consisting of regular hexagons.  ... 
doi:10.5802/cml.10 fatcat:png6p3forfhkhjnzhoklys3jna

Introducing quantum Ricci curvature

N. Klitgaard, R. Loll
2018 Physical Review D  
Motivated by the search for geometric observables in nonperturbative quantum gravity, we define a notion of coarse-grained Ricci curvature.  ...  We test the prescription on a variety of regular and random piecewise flat spaces, mostly in two dimensions.  ...  neighbourhoods and in a quantum-gravitational context.  ... 
doi:10.1103/physrevd.97.046008 fatcat:hnf5dxnr7zbi3l5hqeevjkfrei

Phyllotaxis: a non-conventional crystalline solution to packing efficiency in situations with radial symmetry

J.-F. Sadoc, N. Rivier, J. Charvolin
2012 Acta Crystallographica Section A Foundations of Crystallography  
Phyllotaxis, the search for the most homogeneous and dense organizations of small discs inside a large circular domain, was first developed to analyse arrangements of leaves or florets in plants.  ...  The purpose of this paper is to describe a phyllotactic organization of points through its Voronoi cells and Delaunay triangulation and to refer to the concept of defects developed in condensed matter  ...  This will be discussed in a further article on phyllotaxis in non-Euclidean geometry.  ... 
doi:10.1107/s0108767312018910 fatcat:omrcwtnedbag3ky7mwuqsztu7i

Invariant Grids: Method of Complexity Reduction in Reaction Networks

Alexander Gorban, Iliya Karlin, Andrei Zinovyev
2004 ComPlexUs  
In this paper we present a discrete analog of this object: an invariant grid.  ...  The invariant grid is introduced independently from the invariant manifold notion and can serve to represent the dynamic system behaviour as well as to approximate the invariant manifold after refi nement  ...  Acknowledgements The project is partially supported by Swiss Na-  ... 
doi:10.1159/000093684 fatcat:qj4nbovrxnep5mt545maixcrqu
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