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On the time complexity for circumscribing a convex polygon

1985
*
Computer Vision Graphics and Image Processing
*

In this paper,

doi:10.1016/0734-189x(85)90166-5
fatcat:vlp5pepsdja5hodrx7755dp3ee
*the**time**complexity**on**circumscribing*an n-gon by an m-gon, where m < n, is analyzed to be O(n lg n). ...*A*recent article "*Circumscribing**a**Convex**Polygon*by*a**Polygon*of Fewer Sides with Minimal Area Addition" by Dori and Ben-Bassat, Comput. Vision Graph. ... This is*a*note*on**the**time**complexity*analysis*for**circumscribing*an n-sided*convex**polygon*by an m-sided*polygon*with minimum area addition, where m < n. ...##
###
Hamiltonian triangulations and circumscribing polygons of disjoint line segments

1992
*
Computational geometry
*

Mirzaian,

doi:10.1016/0925-7721(92)90018-n
fatcat:oswj7nzim5dhjiuuns7dbwnql4
*A*., Hamiltonian triangulations and*circumscribing**polygons*of disjoint line seg- ... Acknowledgment*The*author would like to thank Michael B. Dillencourt*for*some helpful comments*on*an earlier draft of this paper. Note Added in Print. ... We have learned that Urabe and Watanabe have recently found*a*counter-example to Conjecture 0 which appears in this volume*on*pages 51-53. ...##
###
General method of Complex Polynomial for determining the radius of the circle circumscribed to a cyclic polygon an arbitrary number of sides, and some important consequences
[article]

2015
*
arXiv
*
pre-print

This paper presents

arXiv:1512.06183v1
fatcat:tdojrbkx5rhb3jvm7mo2mx4sta
*a*general method*for*obtaining radius of*the*corresponding circumference to*a*cyclical*polygon*n sides given*the*lengths of said sides, using*the*notion of*complex*number. ... Are also given like elements regarding non*convex**polygons*cyclic, although in this respect it deepens less and is not considered, course,*the*calculation of areas. ... calculation of areas of*convex**polygons*As it is known,*the*center of*the**circumscribed*circle to*a*cyclic*polygon*can be found, depending*on**the*lengths of*the*sides, within*the*area bounded by said ...##
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Erased arrangements of lines and convex decompositions of polyhedra

1998
*
Computational geometry
*

Chazelle proposed

doi:10.1016/s0925-7721(97)00024-2
fatcat:faanom4j4jhfpk65jlv7sv7rm4
*a*notch-cutting procedure*for*decomposing*a*non-*convex*polyhedron into*convex*pieces. ... Given*a*polyhedron P with n faces and r reflex edges, what is*the**complexity*of Chazelle's decomposition into*convex*pieces? ...*The*total*time*spent marking is bounded by*the*size of*the*arrangement: O(nr + r3). [] Conclusions We have given tight combinatorial bounds*for**the**complexity*of m*convex**polygons*defined by n lines ...##
###
Efficient nesting of congruent convex figures

1984
*
Communications of the ACM
*

We first show that

doi:10.1145/357994.358022
fatcat:26lr37lpajhffpljbqiynupz4i
*the*original problem can be decomposed into two subproblems--*one*consisting of finding all*convex*paver*polygons*and*the*other of optimal (minimal waste) circumscription of*the*original ... Optimal nesting is*the*arrangement of twodimensional*polygons*within*a*rectangular board so that waste is minimized. ... Second, we*circumscribe**the**convex**polygon*P, by another*polygon*that can pave*the*plane. ...##
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An Implementation of a linear time algorithm for computing the minimum perimeter triangle enclosing a convex polygon

2003
*
Canadian Conference on Computational Geometry
*

In this paper, we discuss an efficient and robust implementation of

dblp:conf/cccg/MedvedevaM03
fatcat:jkolqkjrsvehtcx4jmcdfp7yxq
*a*linear*time*algorithm due to [1]*for*computing*the*minimum perimeter triangle that*circumscribes**a**convex*n-gon. ...*The*proposed implementation is efficient in*the*sense that it complies with*the*algorithm's linear*time**complexity*while achieving*a*small constant factor. ... Overview of*the*Algorithm It was established in [6] that*a*minimum perimeter triangle that*circumscribes**a**convex**polygon*(*polygon*,*for*short) is flush with at least*one*of its edges. ...##
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Page 3506 of Mathematical Reviews Vol. , Issue 94f
[page]

1994
*
Mathematical Reviews
*

In particular,

*for*Minkowski addition in*a*fixed dimension d, they find*a*polynomial*time*algorithm*for*adding k*convex*d-polytopes with up to n vertices. ... This paper relates*a*problem from computational*convexity*to*one*in computer algebra. ...##
###
PolyMorph-2D: An Open-Source GIS Plug-in for Morphometric Analysis of Vector-based 2D Polygon Features Help File and User Guide
[article]

2021
*
Zenodo
*

Written in Java™ programming language,

doi:10.5281/zenodo.4726659
fatcat:jeqkxbyd75h4lpnmhshfep6hc4
*the*PolyMorph-2D plug-in can be used*for*morphometric analysis of vector-based two dimensional (2D)*polygon*features in OpenJUMP GIS software environment. ... PolyMorph-2D plug-in allows researchers from various earth and spatial science-related disciplines to compute morphometric parameters of 2D input vector features forming*a**polygon*(i.e.,*a*closed curve ... We also utilized an OpenJUMP script named MICGIS.jar (see Beyhan et al., 2020) to calculate*the*parameters related to Maximum Inscribed Circle (MIC) that can be drawn inside individual*polygon*features ...##
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A Decision Support System for Managing the Water Space

2019
*
IEEE Access
*

Given

doi:10.1109/access.2018.2885651
fatcat:ujxoaqqzejdy7d6kpnurnj7d2e
*a*specified spatio-temporal region*for*each*polygonal*or ellipsoidal object,*the*objective is to identify interference, defined as overlap, among*the*assigned regions. ...*The*challenge is to fuse information*on*bathymetry, obstacles, and planned spatial assignments to identify conflicts among any combination of*polygons*or ellipses. ... Avvari was with*the*University of Connecticut, Storrs, CT 06269-4157, USA. ...##
###
Page 6950 of Mathematical Reviews Vol. , Issue 93m
[page]

1993
*
Mathematical Reviews
*

*time*are presented

*for*

*the*case in which there is only

*one*movable obstacle in

*a*

*polygonal*environment with n corners and

*the*object to be moved and

*the*obstacle are

*convex*

*polygons*of constant

*complexity*... We present

*a*parallel algorithm

*for*

*the*

*polygon*sepa- ration problem.

*The*algorithm runs in O(logn)

*time*

*on*

*a*CREW PRAM with n processors, where n is

*the*number of points in

*the*two given sets. ...

##
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Trajectory Optimization for Curvature Bounded Non-Holonomic Vehicles: Application to Autonomous Driving
[article]

2018
*
arXiv
*
pre-print

We use

arXiv:1712.04978v2
fatcat:j4lvxrj45vaqnejucyoiqksarq
*the*proposed trajectory optimization as*the*basis*for*constructing*a*Model Predictive Control framework*for*navigating an autonomous car in*complex*scenarios like overtaking, lane changing and merging ... This leads to*a*less conservative approximation as compared to that obtained by approximating each*polygon*individually through its*circumscribing*circle. ... COLLISION AVOIDANCE BETWEEN*CONVEX**POLYGONS**The*proposed modeling approach*for*collision avoidance between*convex**polygons*hinges*on*two basic ingredients namely Minkowski sum and*circumscribing*circle ...##
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On solving geometric optimization problems using shortest paths

1990
*
Proceedings of the sixth annual symposium on Computational geometry - SCG '90
*

*On*S o l v i n g G e o m e t r i c O p t i m i z

*a*t i o n P r o b l e m s U s i n g S h o r t e s t P

*a*t h s * ...

*circumscribing*k-gon of

*a*

*convex*ngon [4] ,and an O(nlogn) algorithm

*for*finding

*the*minimum perimeter triangle

*circumscribing*

*a*

*convex*n-gon [4] . ... Note that any

*convex*/~-gon

*circumscribing*

*a*simple

*polygon*P also

*circumscribes*

*the*

*convex*hull of P. Many researchers have studied inclusion problems (e.g. [5] , [11] , [11] , [9] , [15] ). ...

##
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Page 80 of American Society of Civil Engineers. Collected Journals Vol. 129, Issue 2
[page]

2003
*
American Society of Civil Engineers. Collected Journals
*

Faces, edges, and points together are enclosed by

*the**convex*hull, consisting of edges and points*on**the*bound- ary of*the**polygon*.*The**convex**polygon*and*the*outer region fill*the*entire plane. ... ,*for**a*reference*on**the*subject). ...##
###
Shortest Paths Help Solve Geometric Optimization Problems in Planar Regions

1992
*
SIAM journal on computing (Print)
*

*The*structure

*for*our algorithms is as follows:

*a*) decompose

*the*initial problem into

*a*low-degree polynomial number of optimization problems; b) solve each individual subproblem in constant

*time*using ... To do this, we rst develop

*a*decomposition technique

*for*curved

*polygons*which we substitute

*for*triangulation in creating equally e cient curved versions of

*the*algorithms

*for*

*the*shortest-path tree, ... Ackowledgements

*The*authors gratefully acknowledge

*the*careful reading of

*the*two anonymous referees and their many suggestions

*for*improving

*the*readability of

*the*paper. ...

##
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Constrained Construction of Planar Delaunay Triangulations without Flipping

2018
*
Structural Mechanics of Engineering Constructions and Buildings
*

*A*novel method of construction is proposed, which is based directly

*on*

*the*empty circle property of Delaunay.

*The*geometry of

*the*steps of

*the*algorithm is simple and can be grasped intuitively. ...

*A*data structure

*for*triangulations of concave and multiply-connected domains is presented which permits convenient specification of

*the*constraints and

*the*triangulation. ...

*The*

*time*required

*for*

*the*triangulation and its graphical presentation

*on*

*a*conventional laptop computer is hardly noticeable. ...

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