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How beta-skeletons lose their edges
[article]

2013
*
arXiv
*
pre-print

Two nodes

arXiv:1312.7363v1
fatcat:u5ui6asb6bfwdcouysuhje7bla
*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 ...##
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How β-skeletons lose their edges

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. ...

##
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2D Arrangement-based Hierarchical Spatial Partitioning

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

doi:10.1145/2533828.2533843
dblp:conf/gis/YirciBPP13
fatcat:dyoy5wy6svd3zgkeagiysowhyu
*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. ...##
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Planar β-skeletons via point location in monotone subdivisions of subset of lunes
[article]

2014
*
arXiv
*
pre-print

The method is based on point location

arXiv:1411.5459v1
fatcat:t3lw7j7s35hvfclx3rgx5fyomq
*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. ...##
###
Planar Matchings for Weighted Straight Skeletons

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. ...

##
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Planar Matchings for Weighted Straight Skeletons
[chapter]

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. ...

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

2006
*
Lecture Notes in Computer Science
*

This paper presents a new framework for drawing graphs

doi:10.1007/11618058_49
fatcat:4753aqzzsvdmpm6k7633ovzjk4
*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. ...##
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On growing connected β -skeletons

2013
*
Computational geometry
*

A β-

doi:10.1016/j.comgeo.2012.11.009
fatcat:i67bu7573jcb7iemizm7mqyqnm
*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 ...##
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A Multi-Object Feature Selection Based Text Detection and Extraction Using Skeletonized Region Optical Character Recognition in-Text Images

2018
*
International Journal of Engineering & Technology
*

This contributes the intra

doi:10.14419/ijet.v7i3.6.16009
fatcat:lqaenfdnbnfpnmxp6xkoy6xjgu
*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*. ...##
###
Contour interpolation by straight skeletons

2004
*
Graphical Models
*

Then, the straight

doi:10.1016/j.gmod.2004.05.001
fatcat:5m6h6egi3vbkpid5tho5gl7hki
*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. ...##
###
Motorcycle Graphs and Straight Skeletons

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*...

##
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Straight Skeletons and Mitered Offsets of Nonconvex Polytopes

2016
*
Discrete & Computational Geometry
*

We give a concise definition of mitered offset surfaces for nonconvex polytopes

doi:10.1007/s00454-016-9811-5
pmid:32355389
pmcid:PMC7175731
fatcat:nn3ljw7aejaktpdzibhckxe7me
*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*...##
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Structural stabilities and electronic properties for planar Si compounds

2006
*
e-Journal of Surface Science and Nanotechnology
*

We have investigated atomic

doi:10.1380/ejssnt.2006.528
fatcat:dv7bo2atcnetpcgxhncwutkhgi
*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, ...##
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Adaptive Remeshing of Non-Manifold Surfaces
[article]

2008
*
Eurographics State of the Art Reports
*

We present a unified approach for consistent remeshing of arbitrary non-manifold triangle meshes

doi:10.2312/egs.20081013
fatcat:4g6amv3ypnga5pz3cp7ecnxpda
*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) . ...##
###
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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