On Intersecting a Set of Isothetic Line Segments with a Convex Polygon of Minimum Area

A convex grid drawing of a plane graph G is a drawing of G on the plane such that all vertices of G are put on grid points, all edges are drawn as straight-line segments without any edge-intersection, and every face boundary is a convex polygon. In this paper we give a linear-time algorithm for finding a convex grid drawing of every 4-connected plane graph G with four or more vertices on the outer face. The size of the drawing satisfies W + H ≤ n - 1, where n is the number of vertices of G, W is the width and H is the height of the grid drawing. Thus the area W · H is at most ⌈(n - 1)/2⌉ · ⌊(n - 1)/2⌋. Our bounds on the sizes are optimal in a sense that there exist an infinite number of 4-connected plane graphs whose convex drawings need grids such that W + H = n - 1 and W · H = ⌈(n - 1)/2⌉ · ⌊(n - 1)/2⌋.

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Revisit of Minimum-area Enclosing Rectangle of a Convex Polygon

2018 5th International Conference on Control, Decision and Information Technologies (CoDIT) ◽

10.1109/codit.2018.8394943 ◽

2018 ◽

Cited By ~ 1

Author(s):

Yin-Ting Lin ◽

Jing-Sin Liu

Keyword(s):

Convex Polygon ◽

Minimum Area

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A PRIORI FILTRATION OF POINTS FOR FINDING CONVEX HULL

Technological and Economic Development of Economy ◽

10.3846/13928619.2006.9637764 ◽

2006 ◽

Vol 12 (4) ◽

pp. 341-346 ◽

Cited By ~ 2

Author(s):

Laura Vyšniauskaitė ◽

Vydūnas Šaltenis

Keyword(s):

Convex Hull ◽

Convex Polygon ◽

A Priori ◽

Divide And Conquer ◽

Brute Force ◽

Experiment Research ◽

Main Attention ◽

Minimum Area ◽

Good Efficiency ◽

New Algorithms

Convex hull is the minimum area convex polygon containing the planar set. By now there are quite many convex hull algorithms (Graham Scan, Jarvis March, QuickHull, Incremental, Divide‐and‐Conquer, Marriage‐before‐Conquest, Monotone Chain, Brute Force). The main attention while choosing the algorithm is paid to the running time. In order to raise the efficiency of all the algorithms an idea of a priori filtration of points is given in this article. Besides, two new algorithms have been created and presented. The experiment research has shown a very good efficiency of these algorithms.

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APPROXIMATION OF POLYGONAL CURVES WITH MINIMUM NUMBER OF LINE SEGMENTS OR MINIMUM ERROR

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195996000058 ◽

1996 ◽

Vol 06 (01) ◽

pp. 59-77 ◽

Cited By ~ 77

Author(s):

W.S. CHAN ◽

F. CHIN

Keyword(s):

Time Complexity ◽

Convex Polygon ◽

Line Segments ◽

Minimum Error ◽

Curve Approximation ◽

Polygonal Curve ◽

Minimum Number ◽

Polygonal Curves ◽

Approximation Problems

We improve the time complexities for solving the polygonal curve approximation problems formulated by Imai and Iri. The time complexity for approximating any polygonal curve of n vertices with minimum number of line segments can be improved from O(n2 log n) to O(n2). The time complexity for approximating any polygonal curve with minimum error can also be improved from O(n2 log 2n) to O(n2 log n). We further show that if the curve to be approximated forms part of a convex polygon, the two problems can be solved in O(n) and O(n2) time respectively for both open and closed polygonal curves.

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COMPUTING THE CENTER OF AREA OF A CONVEX POLYGON

International Journal of Computational Geometry & Applications ◽

10.1142/s021819590300127x ◽

2003 ◽

Vol 13 (05) ◽

pp. 439-445 ◽

Cited By ~ 4

Author(s):

PETER BRAß ◽

LAURA HEINRICH-LITAN ◽

PAT MORIN

Keyword(s):

Convex Polygon ◽

Linear Time ◽

Time Algorithm ◽

Linear Time Algorithm ◽

Minimum Area

The center of area of a convex planar set X is the point p for which the minimum area of X intersected by any halfplane containing p is maximized. We describe a simple randomized linear-time algorithm for computing the center of area of a convex n-gon.

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