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How beta-skeletons lose their edges [article]

Andrew Adamatzky
2013 arXiv   pre-print
Two nodes in a β-skeleton are connected by an edge if their lune-based neighbourhood contains no other nodes. With increase of β some edges a skeleton are disappear.  ...  We study how a number of edges in β-skeleton depends on β. We speculate how this dependence can be used to discriminate between random and non-random planar sets.  ...  Curves e(n, β), calculated for circular arrangement of points with randomised centres and circles with randomised positions of nodes, show gradual decline in number of edges. arranged points of planar  ... 
arXiv:1312.7363v1 fatcat:u5ui6asb6bfwdcouysuhje7bla

How β-skeletons lose their edges

Andrew Adamatzky
2014 Information Sciences  
With increase of b some edges a skeleton are disappear. 26 We study how a number of edges in b-skeleton depends on b.  ...  Two nodes in a b-skeleton are connected by an edge if their lune-based neigh-25 bourhood contains no other nodes.  ...  Transformation of b-skeleton on planar points arranged in a rectangular array (a) with a single 'defective' node in 5th column and 4th row. , How b-skeletons lose their edges, Inform.  ... 
doi:10.1016/j.ins.2013.07.022 fatcat:utzane446vantm7bwksjarjs3y

2D Arrangement-based Hierarchical Spatial Partitioning

Murat Yirci, Mathieu Brédif, Julien Perret, Nicolas Paparoditis
2013 Proceedings of the Sixth ACM SIGSPATIAL International Workshop on Computational Transportation Science - IWCTS '13  
It proposes a hierarchical spatial surface partitioning, encoding the spatial partition with a 2D arrangement and structuring a generic hierarchy of semantic objects with a directed acyclic graph (DAG)  ...  For this purpose, three application-wise generic algorithms were integrated into our system called Streetmaker: two skeleton operators for centerline generation (straight skeleton and medial axis) and  ...  The authors also would like to thank the CGAL project for providing brilliant building blocks for geometric data structures and algorithms which we heavily utilized in our implementations.  ... 
doi:10.1145/2533828.2533843 dblp:conf/gis/YirciBPP13 fatcat:dyoy5wy6svd3zgkeagiysowhyu

Planar β-skeletons via point location in monotone subdivisions of subset of lunes [article]

Mirosław Kowaluk
2014 arXiv   pre-print
The method is based on point location in monotonic subdivisions of arrangements of curve segments.  ...  We present a new algorithm for lune-based β-skeletons for sets of n points in the plane, for β∈ (2,∞], the only case when optimal algorithms are not known.  ...  Thus, to construct a β-skeleton, we can use their definition to eliminate edges that do not belong to β-skeleton by comparing edges of Delaunay triangulation against all of the points in the input set.  ... 
arXiv:1411.5459v1 fatcat:t3lw7j7s35hvfclx3rgx5fyomq

Planar Matchings for Weighted Straight Skeletons

Therese Biedl, Stefan Huber, Peter Palfrader
2016 International journal of computational geometry and applications  
In this paper, we introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent.  ...  Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process.  ...  We would like to thank David Eppstein for the idea of interpreting the edge-pairing problem as a stable roommate problem.  ... 
doi:10.1142/s0218195916600050 fatcat:2mi5qwks6vccxdzz3wxmsfvbfe

Planar Matchings for Weighted Straight Skeletons [chapter]

Therese Biedl, Stefan Huber, Peter Palfrader
2014 Lecture Notes in Computer Science  
In this paper, we introduce planar matchings on directed pseudo-line arrangements, which yield a planar set of pseudo-line segments such that only matching-partners are adjacent.  ...  Using our new framework, we establish, for the first time, a complete, rigorous definition of weighted straight skeletons, which are based on a so-called wavefront propagation process.  ...  We would like to thank David Eppstein for the idea of interpreting the edge-pairing problem as a stable roommate problem.  ... 
doi:10.1007/978-3-319-13075-0_10 fatcat:2nmwqmfeuveidllhothwgh4od4

MultiPlane: A New Framework for Drawing Graphs in Three Dimensions [chapter]

Seok-Hee Hong
2006 Lecture Notes in Computer Science  
This paper presents a new framework for drawing graphs in three dimensions. In general, the new framework uses a divide and conquer approach.  ...  More specifically, the framework divides a graph into a set of smaller subgraphs, and then draws each subgraph in a 2D plane.  ...  Let v be a node in T and u be the parent node of v. The graph skeleton(u) has one common virtual edge with skeleton(v), which is called as a virtual edge of v.  ... 
doi:10.1007/11618058_49 fatcat:4753aqzzsvdmpm6k7633ovzjk4

On growing connected β -skeletons

Andrew Adamatzky
2013 Computational geometry  
A β-skeleton of a random planar set is usually a disconnected graph for β>2. With the increase of β, the number of edges in the β-skeleton of a random graph decreases.  ...  A β-skeleton, β≥ 1, is a planar proximity undirected graph of an Euclidean points set, where nodes are connected by an edge if their lune-based neighbourhood contains no other points of the given set.  ...  Examples are β-skeletons grown with ∆θ = 50 (Fig. 8ab) Possible applications in sciences Some aspects of a morphological dynamic of β-skeletons, controlled by β and ∆θ, resemble substrate-induced  ... 
doi:10.1016/j.comgeo.2012.11.009 fatcat:i67bu7573jcb7iemizm7mqyqnm

A Multi-Object Feature Selection Based Text Detection and Extraction Using Skeletonized Region Optical Character Recognition in-Text Images

K R. Sanjuna, K Dinakaran
2018 International Journal of Engineering & Technology  
This contributes the intra edge detection, segmentation along skeleton of object reflective. the impact of multi-objective region selection model (MSOR) is to recognize the exact character of style matches  ...  Information or content extraction from image is crucial task for obtaining text in natural scene images.  ...  To permit the detection of typescripts or text in images by utilizing the properties of shrewd edge boundary upgraded by multi include arrangement.  ... 
doi:10.14419/ijet.v7i3.6.16009 fatcat:lqaenfdnbnfpnmxp6xkoy6xjgu

Contour interpolation by straight skeletons

Gill Barequet, Michael T Goodrich, Aya Levi-Steiner, Dvir Steiner
2004 Graphical Models  
Then, the straight skeletons of the selected cells guide the triangulation of each face of the skeletons. Finally, the resulting triangles are lifted up in space to form an interpolating surface.  ...  This problem has applications to medical imaging, geographic information systems, etc.  ...  polygon's edge that defines the skeletal face.  ... 
doi:10.1016/j.gmod.2004.05.001 fatcat:5m6h6egi3vbkpid5tho5gl7hki

Motorcycle Graphs and Straight Skeletons

Siu-Wing Cheng, Antoine Vigneron
2007 Algorithmica  
In particular, we can compute the straight skeleton of a non-degenerate polygon with n vertices in O(n √ n log 2 n) expected time.  ...  Combining these results, we can compute the straight skeleton of a non-degenerate polygon with h holes and with n vertices, among which r are reflex vertices, in O(n √ h + 1 log 2 n + r √ r log r) expected  ...  As opposed to the widely used medial axis [13] (see Fig. 2 ), the straight skeleton has only straight line edges, which is useful when parabolic edges need to be avoided, either because the application  ... 
doi:10.1007/s00453-006-1229-7 fatcat:yaaof3353jd7xg7xapnezinaai

Straight Skeletons and Mitered Offsets of Nonconvex Polytopes

Franz Aurenhammer, Gernot Walzl
2016 Discrete & Computational Geometry  
We give a concise definition of mitered offset surfaces for nonconvex polytopes in R 3 , along with a proof of existence and a discussion of basic properties.  ...  For (weighted) straight skeletons of an n-facet polytope in R d , an upper bound of O ( n d ) on their combinatorial complexity is derived.  ...  distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in  ... 
doi:10.1007/s00454-016-9811-5 pmid:32355389 pmcid:PMC7175731 fatcat:nn3ljw7aejaktpdzibhckxe7me

Structural stabilities and electronic properties for planar Si compounds

Motoi Hirayama, Jun Nakamura, Akiko Natori
2006 e-Journal of Surface Science and Nanotechnology  
We have investigated atomic arrangements and electronic properties of two-dimensional Si compounds having the Si(111) skeletons with H and/or OH-radicals terminators, using first-principles calculations  ...  In such artificial compounds, a direct gap appears only at the thinnest Si thickness as well as the case of the planar siloxene. faces of Si(111)-1BL and the other has a Si-skeleton with a larger Si BL  ...  Acknowledgments This research is conducted as a program for the "Promotion of Leading Researchers" in Special Coordination Funds for Promoting Science and Technology by Ministry of Education, Culture,  ... 
doi:10.1380/ejssnt.2006.528 fatcat:dv7bo2atcnetpcgxhncwutkhgi

Adaptive Remeshing of Non-Manifold Surfaces [article]

Michael Zilske, Hans Lamecker, Stefan Zachow
2008 Eurographics State of the Art Reports  
We present a unified approach for consistent remeshing of arbitrary non-manifold triangle meshes with additional user-defined feature lines, which together form a feature skeleton.  ...  Our method is based on local operations only and produces meshes of high regularity and triangle quality while preserving the geometry as well as topology of the feature skeleton and the input mesh.  ...  Non-manifold vertices whose neighborhood can be arranged to form k pages which are joined at exactly two common edges, are called vertices with an open-book neighborhood (Fig. 1b) .  ... 
doi:10.2312/egs.20081013 fatcat:4g6amv3ypnga5pz3cp7ecnxpda

Page 2092 of Mathematical Reviews Vol. , Issue 87d [page]

1987 Mathematical Reviews  
We also give an O(n®) time algorithm if the desired polygon is maximized with respect to perimeter.” 87d:68098 Edelsbrunner, H. (A-TGRZ-I) 87d:68099 Edge-skeletons in arrangements with applications.  ...  Summary: “An edge-skeleton in an arrangement A(H) of a finite set of planes in E® is a connected collection of edges in A(H). We give a method that constructs a skeleton in O(,/nlogn) time per edge.  ... 
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