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How beta-skeletons lose their edges
[article]
2013
arXiv
pre-print
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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
2014
Information Sciences
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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
2013
Proceedings of the Sixth ACM SIGSPATIAL International Workshop on Computational Transportation Science - IWCTS '13
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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]
2014
arXiv
pre-print
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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
2016
International journal of computational geometry and applications
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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]
2014
Lecture Notes in Computer Science
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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]
2006
Lecture Notes in Computer Science
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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
2013
Computational geometry
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2013 pre-print arXiv:1304.1986v1 fatcat:ajfy3bvsxfaxjbpd7mdbfz7cim
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
2018
International Journal of Engineering & Technology
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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
2004
Graphical Models
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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
2007
Algorithmica
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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
2016
Discrete & Computational Geometry
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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
2006
e-Journal of Surface Science and Nanotechnology
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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]
2008
Eurographics State of the Art Reports
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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
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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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