A new algorithm for computing the convex hull of a planar point set

2007 ◽  
Vol 8 (8) ◽  
pp. 1210-1217 ◽  
Author(s):  
Guang-hui Liu ◽  
Chuan-bo Chen
Keyword(s):  
Convex Hull ◽  
Planar Point ◽  
Point Set

A Fast Convex Hull Algorithm of Planar Point Set

2013 ◽  
Vol 706-708 ◽  
pp. 1852-1855
Author(s):  
Hong Fei Jiang
Keyword(s):  
Convex Hull ◽  
Planar Point ◽  
Point Set ◽  
Convex Hull Algorithm

In this paper ,a new algorithm is proposed for improving speed of calculating convex hull of planar point set .The algorithm creates a square mesh to manage points ,when eliminating points which are obviously in convex hull ,selecting or eliminating of points can be converted to that of grid , work of calculation depends on points near edges of convex hull and density of grid but not the number of points ;at the meantime ,remainder points are sorted roughly .When calculating convex hull of remainder points ,a method is presented which can take advantage of order of remainder points ,it calculates boundaries of convex hull segment by segment ,then ,combines the boundaries to form convex hull.

An Efficient Convex Hull Algorithm Using Affine Transformation in Planar Point Set

2014 ◽  
Vol 39 (11) ◽  
pp. 7785-7793 ◽  
Author(s):  
Changyuan Xing ◽  
Zhongyang Xiong ◽  
Yufang Zhang ◽  
Xuegang Wu ◽  
Jingpei Dan ◽  
...  
Keyword(s):  
Convex Hull ◽  
Affine Transformation ◽  
Planar Point ◽  
Point Set ◽  
Convex Hull Algorithm

A FAST AND COMPLETE CONVEX-HULL ALGORITHM ARCHITECTURE BASED ON ELLIPSE AND ELASTIC ELLIPSE METHODS

2013 ◽  
Vol 27 (08) ◽  
pp. 1354008
Author(s):  
XUE GANG WU ◽  
BIN FANG ◽  
YUAN YAN TANG ◽  
PATRICK SHEN-PEI WANG
Keyword(s):  
Convex Hull ◽  
Affine Transformation ◽  
Circle Method ◽  
Extreme Points ◽  
Transformation Method ◽  
Data Sets ◽  
Planar Point ◽  
Point Set ◽  
Convex Hull Algorithm ◽  
Better Than

The number of inner points excluded in an initial convex hull (ICH) is vital to the efficiency getting the convex hull (CH) in a planar point set. The maximum inscribed circle method proposed recently is effective to remove inner points in ICH. However, limited by density distribution of a planar point set, it does not always work well. Although the affine transformation method can be used, it is still hard to have a better performance. Furthermore, the algorithm mentioned above fails to deal with the exceptional distribution: the gravity centroid (GC) of a planar point set is outside or on the edge formed by the extreme points in ICH. This paper considers how to remove more inner points in ICH when GC is inside of ICH and completely process the case which mentioned above. Further, we presented a complete algorithm architecture: (1) using the ellipse and elasticity ellipse methods (EM and EEM) to remove more inner points in ICH and process the cases: GC is inside or outside of ICH. (2) Using the traditional methods to process the situation: the initial centroid is on the edge in ICH. It is adaptive to more data sets than other algorithms. The experiments under seven distributions show that the proposed method performs better than other traditional algorithms in saving time and space.

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

An Efficient Improved Algorithm of Convex Hull

2014 ◽  
Vol 602-605 ◽  
pp. 3104-3106
Author(s):  
Shao Hua Liu ◽  
Jia Hua Zhang
Keyword(s):  
Convex Hull ◽  
Line Segment ◽  
Main Idea ◽  
Discrete Point ◽  
Directed Line ◽  
Generation Algorithm ◽  
Simple Program ◽  
Point Set ◽  
High Computational Efficiency ◽  
Improved Algorithm

This paper introduced points and directed line segment relation judgment method, the characteristics of generation and Graham method using the original convex hull generation algorithm of convex hull discrete points of the convex hull, an improved algorithm for planar discrete point set is proposed. The main idea is to use quadrilateral to divide planar discrete point set into five blocks, and then by judgment in addition to the four district quadrilateral internally within the point is in a convex edge. The result shows that the method is relatively simple program, high computational efficiency.

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