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

Duncan McCallum, David Avis
1979 Information Processing Letters
AcknowIedgment 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]

Gisela Klette
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

Ronald L Graham, F Frances Yao
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  We should also point out that our algorithm is similar in spirit to an unpublished algorithm independently discovered by D. T. Lee.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

Timothy M. Chan
2006 Computational geometry
As 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

Alok Aggarwal, Leonidas J. Guibas, James Saxe, Peter W. Shor
1989 Discrete & Computational Geometry
We present an 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

V. Tereshchenko, V. Muravitskiy
2011 Zenodo
We consider 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

Godfried T. Toussaint
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 , ,  .  ...  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

B. Usha Rani, Elango S.
2016 Zenodo
Given 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

Phan An
2012 International Journal of Information and Electronics Engineering
We 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  : "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

G. Toussaint
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 , do exist but require a set of points that are ordered in some way, for example,  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]

Elias Dahlhaus, Sariel Har-Peled, Alan L. Hu
2019 arXiv   pre-print
Furthermore, we present 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

S.Y. Shin, T.C. Woo
1986 Pattern Recognition
Though 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

John Hershberger, Jack Snoeyink
1998 Computational geometry
By using 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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