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Largest inscribed rectangles in convex polygons

2012
*
Journal of Discrete Algorithms
*

We consider approximation algorithms for the problem of computing an

doi:10.1016/j.jda.2012.01.002
fatcat:xx342ul3wbcdlit4gvtolshuyq
*inscribed**rectangle*having*largest*area*in*a*convex**polygon*on n vertices. ... If the order of the vertices of the*polygon*is given, we present a randomized algorithm that computes an*inscribed**rectangle*with area at least (1 − ) times the optimum with probability t*in*time O ( 1 ... Given a*convex**polygon*P with n vertices, we want to compute a*largest**inscribed**rectangle**in*P . ...##
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Largest Inscribed Rectangles in Geometric Convex Sets
[article]

2021
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arXiv
*
pre-print

Finally, a parametrized optimization approach is developed to find the

arXiv:1905.13246v2
fatcat:xl3krdctjzdrdbcffg453e4eb4
*largest*(axis-aligned)*inscribed**rectangles**in*two-dimensional space. ... To find the*largest*axis-aligned*inscribed**rectangles**in*the higher dimensions, an interior-point method algorithm is presented and analyzed. ... higher dimensions, we begin with the geometric properties of the traditional*largest**inscribed**rectangles**in*a*convex**polygon**in*2D. ...##
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Finding the Largest Volume Parallelepipedon of Arbitrary Orientation in a Solid

2021
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IEEE Access
*

There are no other approximation algorithms for finding the

doi:10.1109/access.2021.3098234
fatcat:gyd7ivjm75conaz2cbunldpu3m
*largest*volume parallelepipedon of arbitrary orientation*inscribed**in*a closed 3D contour with a computational cost better than the algorithm ... However,*in*many cases the objects are available as irregular shapes with many vertices, and*in*order to apply algorithms effectively, it is essential to compute the*largest*volume parallelepipedon contained ... [27] , [28] considered approximation algorithms to calculate the*rectangle*with the*largest*area of arbitrary orientation*in*a*convex**polygon*with n vertices*in*O( 1 ε log 1 ε log n) for simple*polygons*...##
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Approximation of convex figures by pairs of rectangles

1998
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Computational geometry
*

If the n vertices of a

doi:10.1016/s0925-7721(96)00019-3
fatcat:pl7yk2imw5ccrl6w6renpx4l4a
*convex**polygon*C are given as a sorted array, such an approximating pair of*rectangles*can be computed*in*time O(log 2 n). ... We consider the problem of approximating a*convex*figure*in*the plane by a pair (r, R) of homothetic (that is, similar and parallel)*rectangles*with r C_ C C_ R. ... They compute the*largest*-area or the*largest*-perimeter*rectangle*with a given orientation contained*in*a*polygon*with n vertices*in*time O(log n). ...##
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Approximation of convex figures by pairs of rectangles
[chapter]

1990
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Lecture Notes in Computer Science
*

If the n vertices of a

doi:10.1007/3-540-52282-4_47
fatcat:xq5g37gyu5gv3lge5kvdhtaapi
*convex**polygon*C are given as a sorted array, such an approximating pair of*rectangles*can be computed*in*time O(log 2 n). ... We consider the problem of approximating a*convex*gure*in*the plane by a pair (r; R ) of homothetic (that is, similar and parallel)*rectangles*with r C R. ... They compute the*largest*-area or the*largest*-perimeter*rectangle*with a given orientation contained*in*a*polygon*with n vertices*in*time O(logn). ...##
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Largest triangles in a polygon
[article]

2020
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arXiv
*
pre-print

We study the problem of finding maximum-area triangles that can be

arXiv:2007.12330v1
fatcat:bzxfoca55ng2fkaithvudamagq
*inscribed**in*a*polygon**in*the plane. ...*In*the case with reorientations for*convex**polygons*with n vertices, we also present (1-ε)-approximation algorithms. ... [5] presented an algorithm of computing a*largest*axis-aligned*rectangle*that can be*inscribed**in*a*convex**polygon*. We follow their approach with some modification. ...##
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Maximum-Area Triangle in a Convex Polygon, Revisited
[article]

2017
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arXiv
*
pre-print

We revisit the following problem: Given a

arXiv:1705.11035v2
fatcat:2axjswqvujbhbhricckfxhtq6i
*convex**polygon*P, find the*largest*-area*inscribed*triangle. ... Also we show by example that the algorithm presented*in*1979 by Dobkin and Snyder for finding the*largest*-area k-gon that is*inscribed**in*a*convex**polygon*fails to find the optimal solution for k=4. ... Acknowledgments The authors would like to thank everybody who has discussed this discovery and its implications with them over the past months,*in*particular Bahareh Banyassady, Ahmad Biniaz, Prosenjit ...##
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Linear programming in R3 and the skeleton and largest incircle of a convex polygon

1987
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Computers and Mathematics with Applications
*

Rodin Almtraet--

doi:10.1016/0898-1221(87)90008-3
fatcat:tbolv5ejhzghtfl6oq5d7p6lgi
*In*this paper the geometrical problem of constructing the*largest*circle*inscribed**in*a (given)*convex**polygon*is solved*in*0(n) time. ... This problem is related to the construction of the skeleton of the*polygon*, which construction is shown to be accomplishable*in*0(n log n) time. ... Smit of the Computer Science Division of NRIMS for presenting them with the problem of*inscribing*a circle*in*a*polygon*. The authors would also like to thank Dr D. H. ...##
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Inscribing an axially symmetric polygon and other approximation algorithms for planar convex sets

2006
*
Computational geometry
*

Given a planar

doi:10.1016/j.comgeo.2005.06.001
fatcat:gulq3wgimbg5jex4nv2fl4cdea
*convex*set C, we give sublinear approximation algorithms to determine approximations of the*largest*axially symmetric*convex*set S contained*in*C, and the smallest such set S that contains ... More precisely, for any ε > 0, we find an axially symmetric*convex**polygon*Q ⊂ C with area |Q| > (1 − ε)|S| and we find an axially symmetric*convex**polygon*Q containing C with area |Q | < (1 + ε)|S |. ... Acknowledgement We are grateful to an anonymous referee for a very careful proof-reading of our manuscript, and*in*particular suggesting the idea behind the linear-time algorithm of Lemma 15. ...##
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Finding the Maximum Area Parallelogram in a Convex Polygon

2011
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Canadian Conference on Computational Geometry
*

We consider the problem of finding the maximum area parallelogram (MAP) inside a given

dblp:conf/cccg/JinM11
fatcat:sdhtncacfncwvhyq2b3megket4
*convex**polygon*. Our main result is an algorithm for computing the MAP*in*an n-sided*polygon**in*O(n 2 ) time. ... We also discuss applications of our result to the problem of computing the maximum area centrallysymmetric*convex*body (MAC) inside a given*convex**polygon*, and to a "fault tolerant area maximization" problem ... The authors would also like to thank Xiaoming Sun, Tiancheng Lou, and Zhiyi Huang for taking part*in*fruitful discussions. ...##
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Convexity Problems on Meshes with Multiple Broadcasting

1995
*
Journal of Parallel and Distributed Computing
*

, and the

doi:10.1006/jpdc.1995.1078
fatcat:addyhjklpnedzmssj2ht6frcii
*largest*-area*inscribed*triangle of a*convex*n-gon. ... Finally, we show that for two separable*convex*n-gons P and Q, the task of computing the minimum distance between P and Q can be performed*in*O(1) time on a mesh with multiple broadcasting of size n n. ... Their constructive criticism and comments have resulted*in*a much improved presentation. We wish to thank Professor Sahni for his timely and professional handling of our submission. ...##
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Planar Rectangular Sets and Steiner Symmetrization

1998
*
Elemente der Mathematik
*

Paul Scott has worked

doi:10.1007/s000170050030
fatcat:phlvprb3t5eyxltqx25f5jaxaa
*in*the Department of Pure Mathematics at the University Adelaide for the past 30 years. His research interests are*in**convex*sets and the geometry of numbers. ... He is also interested*in*mathematics education, and has edited and typeset 'The Australian Mathematics Teacher' for the past seven years. ... Final Comment The class of rectangular sets appears naturally here*in*terms of successive orthogonal symmetrizations; to my knowledge, this class does not occur elsewhere*in*the literature. ...##
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A Novel Method for Recognizing Sketched Objects by Learning Their Geometrical Features

2020
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jecet
*

This is currently important, particularly because of recent advances

doi:10.24214/jecet.b.9.2.21423
fatcat:qwxeurjzmrhnbccyvxdfdvcur4
*in*human computer interactions via portable devices. ...*In*this paper, we present and explain a novel method for recognizing sketched object by learning a specific set of geometrical features, and creating a classification for these objects. ...*polygons*: The*largest*area triangles that fits inside the*convex*hull. The*largest*area enclosing*rectangles*. ...##
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Large Area Convex Holes in Random Point Sets

2016
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SIAM Journal on Discrete Mathematics
*

We also consider the problems of estimating the

doi:10.1137/15m1024184
fatcat:7y7cchkvkrdklaxjgrz3swosnq
*largest*area*convex*hole, and the*largest*area of a*convex**polygonal*hole with vertices*in*Kn. ... Let K, L be*convex*sets*in*the plane. For normalization purposes, suppose that the area of K is 1. ... )*convex*hole; and let PolyMax(K n ) denote the random variable that measures the*largest*(*in*terms of area)*convex**polygon*with vertices*in*K n . ...##
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Large area convex holes in random point sets
[article]

2015
*
arXiv
*
pre-print

We also consider the problems of estimating the

arXiv:1506.04307v1
fatcat:k3ae7eauird2tdvwpnj7yqthyq
*largest*area*convex*hole, and the*largest*area of a*convex**polygonal*hole with vertices*in*K_n. ... Let K, L be*convex*sets*in*the plane. For normalization purposes, suppose that the area of K is 1. ... )*convex*hole; and let PolyMax(K n ) denote the random variable that measures the*largest*(*in*terms of area)*convex**polygon*with vertices*in*K n . ...
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