scholarly journals An Efficient Algorithm of Convex Hull for Very Large Planar Point Set

2013 ◽  
Author(s):  
Guangquan Fan ◽  
Liping Ma ◽  
Bingru Yang
Keyword(s):  
Convex Hull ◽  
Efficient Algorithm ◽  
Planar Point ◽  
Point Set

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.

CENTROID TRIANGULATIONS FROM k-SETS

2011 ◽  
Vol 21 (06) ◽  
pp. 635-659 ◽  
Author(s):  
WAEL EL ORAIBY ◽  
DOMINIQUE SCHMITT ◽  
JEAN-CLAUDE SPEHNER
Keyword(s):  
Convex Hull ◽  
Voronoi Diagram ◽  
Efficient Algorithm ◽  
Worst Case ◽  
Point Set

Given a set V of n points in the plane, no three of them being collinear, a convex inclusion chain of V is an ordering of the points of V such that no point belongs to the convex hull of the points preceding it in the ordering. We call k-set of the convex inclusion chain, every k-set of an initial subsequence of at least k points of the ordering. We show that the number of such k-sets (without multiplicity) is an invariant of V, that is, it does not depend on the choice of the convex inclusion chain. Moreover, this number is equal to the number of regions of the order-k Voronoi diagram of V (when no four points are cocircular). The dual of the order-k Voronoi diagram belongs to the set of so-called centroid triangulations that have been originally introduced to generate bivariate simplex spline spaces. We show that the centroids of the k-sets of a convex inclusion chain are the vertices of such a centroid triangulation. This leads to the currently most efficient algorithm to construct particular centroid triangulations of any given point set; it runs in O(n log n + k(n - k) log k) worst case time.

COMPUTING A DOUBLE-RAY CENTER FOR A PLANAR POINT SET

1999 ◽  
Vol 09 (02) ◽  
pp. 109-123 ◽  
Author(s):  
ALEX GLOZMAN ◽  
KLARA KEDEM ◽  
GREGORY SHPITALNIK
Keyword(s):  
Hausdorff Distance ◽  
Efficient Algorithm ◽  
Center Problem ◽  
Planar Point ◽  
Point Set

A double-ray configuration is a configuration in the plane consisting of two rays emanating from one point. Given a set S of n points in the plane, we want to find a double-ray configuration that minimizes the Hausdorff distance from S to this configuaration. We call this problem the double-ray center problem. We present an efficient algorithm for computing the double-ray center for set S of n points in the plane which runs in time O(n3α(n) log 2n).

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.

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