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### On the time complexity for circumscribing a convex polygon

Tony C Wood, Hyun-Chan Lee
1985 Computer Vision Graphics and Image Processing
In this paper, 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

Andranik Mirzaian
1992 Computational geometry
Mirzaian, 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]

Denis Martínez Tápanes, J. Enrique Martínez Serra, L. Osiel Rodríguez Cañizarez
2015 arXiv   pre-print
This paper presents 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  ...

### Erased arrangements of lines and convex decompositions of polyhedra

J.E. Hershberger, J.S. Snoeyink
1998 Computational geometry
Chazelle proposed 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

Dov Dori, Moshe Ben-Bassat
1984 Communications of the ACM
We first show that 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.  ...

### 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 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.  ...

### 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]

Cüneyt Güler, Burak Beyhan, Hidayet Tağa
2021 Zenodo
Written in Java™ programming language, 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  ...

### A Decision Support System for Managing the Water Space

Donald Mcmenemy, Gopi Vinod Avvari, David Sidoti, Adam Bienkowski, Krishna R. Pattipati
2019 IEEE Access
Given 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.  ...

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

Mithun Babu, Yash Oza, C. A. Balaji, Arun Kumar Singh, Bharath Gopakarishnan, K. Madhava Kirshna
2018 arXiv   pre-print
We use 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  ...

### On solving geometric optimization problems using shortest paths

Elefterios A. Melissaratos, Diane L. Souvaine
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] ).  ...

### 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

Elefterios A. Melissaratos, Diane L. Souvaine
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.  ...

### Constrained Construction of Planar Delaunay Triangulations without Flipping

V.V. Galishnikova, P.J. Pahl
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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