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A linear algorithm for finding the convex hull of a simple polygon

1979
*
Information Processing Letters
*

AcknowIedgment

doi:10.1016/0020-0190(79)90069-3
fatcat:k52cfefwkjhepfxsqpv56bcfh4
*The*authors gratefully acknowledge*the*help and encouragement*of*God.fried Toussaint during*the*course*of*this research. ... Once discarded,*a*point is never reconsidered and so*the**algorithm*runs in*linear*time. Conclusion We have exhibited an O(n)*algorithm**for**finding**the**convex**hull**of**a**simple**polygon*. ... Under*the**linear*decision tree model, Avis [ 11 has found an*a*(n log n) lower bound*for**the*general problem*of**finding**the**convex**hull**of**a*set*of*points in*the*plane. ...##
###
Recursive Calculation of Relative Convex Hulls
[chapter]

2011
*
Lecture Notes in Computer Science
*

*The*relative

*convex*

*hull*

*of*

*a*

*simple*

*polygon*

*A*, contained in

*a*second

*simple*

*polygon*B, is known to be

*the*minimum perimeter

*polygon*(MPP). ...

*The*paper recalls properties and

*algorithms*related to

*the*relative

*convex*

*hull*, and proposes

*a*(recursive)

*algorithm*

*for*calculating

*the*relative

*convex*

*hull*. ...

*Algorithms*

*for*Calculating Relative

*Convex*

*Hulls*Computing

*the*relative

*convex*

*hull*

*of*one

*simple*

*polygon*with respect to another

*simple*

*polygon*can be done in nearly (see below)

*linear*time. ...

##
###
Finding the convex hull of a simple polygon

1983
*
Journal of Algorithms
*

*A*short

*linear*-time

*algorithm*

*for*

*finding*

*the*

*convex*

*hull*when

*the*points form

*the*(ordered) vertices

*of*

*a*

*simple*(i.e., non-self-intersecting)

*polygon*is given. ... It is well known that

*the*

*convex*

*hull*

*of*

*a*set

*of*n points in

*the*plane can be found by an

*algorithm*having worst-case complexity O(nlog n). ... We should also point out that our

*algorithm*is similar in spirit to an unpublished

*algorithm*independently discovered by D. T. Lee. ...

##
###
Page 1178 of Mathematical Reviews Vol. , Issue 85c
[page]

1985
*
Mathematical Reviews
*

“In this paper, we describe

*a**simple**linear*time*algorithm**for*obtaining*the**convex**hull**of**a**simple**polygon*and establish its correctness. ... K. (6-TIFR)*A**linear*time*algorithm**for*obtaining*the**convex**hull**of**a**simple**polygon*. Pattern Recognition 16 (1983), no. 6, 587-592. ...##
###
Three problems about simple polygons

2006
*
Computational geometry
*

As

doi:10.1016/j.comgeo.2005.11.002
fatcat:bskyne4cfrgndahd73j3mhap64
*a*subroutine*for**the*above result, we show how to*find**the**convex**hull**of*any given subset*of**the*vertices*of*P in*linear*worst-case time. 3. ... We give three related*algorithmic*results concerning*a**simple**polygon*P : 1. ... Acknowledgements I thank Ralph Boland*for*helpful discussions on some*of*these problems. ...##
###
A linear-time algorithm for computing the voronoi diagram of a convex polygon

1989
*
Discrete & Computational Geometry
*

We present an

doi:10.1007/bf02187749
fatcat:imdybpi2lfh65izvvqu5woeneu
*algorithm**for*computing certain kinds*of*threedimensional*convex**hulls*in*linear*time. ... Our techniques can also be used to obtain*linear*-time*algorithms**for*computing*the*furthest-site Voronoi diagram and*the*medial axis*of**a**convex**polygon*and*for*deleting*a*site from*a*general planar Voronoi ... Acknowledgments*The*authors would like to thank William Thurston, Jorge Stolfi, and Steve Fortune*for*helpful discussions; and*the*referees*for*several helpful suggestions. 604*A*. Aggarwal, L. J. ...##
###
Constructing A Simple Polygonalizations

2011
*
Zenodo
*

We consider

doi:10.5281/zenodo.1060925
fatcat:4x45yvtudzfapmdbwxl3qmjjaa
*the*methods*of*construction*simple**polygons**for**a*set S*of*n points and applying them*for*searching*the*minimal area*polygon*. ... In this paper we propose*the*approximate*algorithm*, which generates*the**simple**polygonalizations**of**a*fixed set*of*points and*finds**the*minimal area*polygon*, in O (n3) time and using O(n2) memory. ... In [6, 7]*the*authors introduce "α-shape" -notion*for**the*generalization*of**a**convex**hull*that allows to develop methods*of*constructing*the**simple**polygons*with using Voronoi diagram. ...##
###
A simple linear algorithm for intersecting convex polygons

1985
*
The Visual Computer
*

*Finding*

*the*

*convex*

*hull*

*of*two intersecting

*convex*

*polygons*in step 1 can be done in O(m+n) time with several

*algorithms*[7], [10], [11] . ... This theorem leads Meisters to propose an O(n 3 )

*algorithm*

*for*triangulating

*simple*

*polygons*by

*finding*ears and "cutting them off". ... Unlike previous

*algorithms*,

*the*new

*algorithm*consists

*of*

*a*two-step combination

*of*two

*simple*

*algorithms*

*for*

*finding*

*convex*

*hulls*and triangulations

*of*

*polygons*. ...

##
###
Convex Traversal In Polygon With Segment Stabbing

2016
*
Zenodo
*

Given

doi:10.5281/zenodo.47698
fatcat:j3gkzx3fdvdjfdlxfoejz5of2q
*a*set S*of*disjoint*simple**polygons*on*a*bounded 2D-Plane, we studied*the*problem*of**finding**a*set*of**polygon*P, such that stabbing S by segment stabbing region in optimal way. ... We present*a*novel approach*for*solving*the**convex*traversing method in PTIME.*Convex*traversing is*a*mechanism*of*layering continues*convex**hull*extracted from points P. ... I wish to thank*for*his exemplary guidance and valuable feedbacks*for*helpful discussions. ...##
###
Incremental Convex Hull as an Orientation to Solving theShortest Path Problem

2012
*
International Journal of Information and Electronics Engineering
*

We

doi:10.7763/ijiee.2012.v2.181
fatcat:otjhzqktfjgn3djoqp3urloj6m
*find**the*Euclidean shortest path in*the**polygon*between*a*and b. In this paper, an efficient*algorithm*based on incremental*convex**hulls*is presented. ... Each such*convex**hull*is delivered from*the*incremental*convex**hull**algorithm**for**a*subpolyline*of*P (Q, respectively) just before reaching Q (P, respectively). ... Mitchell in [3] : "Can one devise*a**simple*O(n) time*algorithm**for*computing*the*shortest path between two points in*a**simple**polygon*(with n vertices), without resorting to*a*(complicated)*linear*-time ...##
###
On separating two simple polygons by a single translation

1989
*
Discrete & Computational Geometry
*

*The*

*algorithm*runs in time O(t(n)) where t(n) is

*the*time needed to triangulate an n-sided

*polygon*. ... Let P and Q be two disjoint

*simple*

*polygons*having n sides each. ...

*of*this problem. ...

##
###
Rapid preconditioning of data for accelerating convex hull computations

2014
*
Electronics Letters
*

*Linear*complexity (O(n)) methods, such as

*the*one due to Melkman [3], do exist but require

*a*set

*of*points that are ordered in some way,

*for*example, [3] requires an order where

*the*points form

*a*

*simple*...

*The*method is O(n). It helps any

*convex*

*hull*

*algorithm*run faster. ... As steps 1-3 are O(n), any 2D

*convex*

*hull*

*algorithm*, including

*linear*ones, can be used as

*a*final step 4 to build

*a*

*convex*

*hull*

*for*accelerated computations. ...

##
###
Covering Polygons by Min-Area Convex Polygons
[article]

2019
*
arXiv
*
pre-print

Furthermore, we present

arXiv:1912.03429v2
fatcat:qhx7yi6ebbcmdc7clbeu3oxkhq
*a*near*linear*time*algorithm**for*computing this partition. ... Given*a*set*of*disjoint*simple**polygons*σ_1, ..., σ_n,*of*total complexity N, consider*a*convexification process that repeatedly replaces*a**polygon*by its*convex**hull*, and any two (by now*convex*)*polygons*... Figure 6 . 3 : 63 Illustration*of**the**algorithm**for*computing*the**convex*-*hull**of*two*convex**polygons*. ...##
###
Finding the convex hull of a simple polygon in linear time

1986
*
Pattern Recognition
*

Though

doi:10.1016/0031-3203(86)90043-9
fatcat:kx36uotymrentnl76nn6hx6bpq
*linear**algorithms**for**finding**the**convex**hull**of**a*simply-connected*polygon*have been reported, not all are short and correct. ...*A*compact version based on Sklansky's original idea ~:~ and Bykat's counter-example qs~ is given. Its complexity and correctness are also shown.*Convex**hull**Linear**algorithm*Computational geometry ... INTRODUCTION There have been many reports on*a**linear**algorithm**for**finding**the**convex**hull**of**a**simple**polygon*. Certain versions were prone to counter-examples. ...##
###
Cartographic line simplification and polygon CSG formulæ in O(n log∗ n) time

1998
*
Computational geometry
*

By using

doi:10.1016/s0925-7721(98)00027-3
fatcat:a7zcfoyavrcsbavprijzxijuvy
*a*data structure that maintains*convex**hulls**of**polygonal*lines under splits, both were known to have O(n logn) time solutions in*the*worst-case. ...*A*constructive solid geometry (CSG) conversion*for**a**polygon*takes*a*list*of*vertices and produces*a*formula representing*the**polygon*as an intersection and union*of*primitive halfspaces. ... Acknowledgements We thank*the*referees*for*their careful reading and constructive comments that have improved*the*presentation*of*this paper. ...
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