An Efficient Approach of Convex Hull Triangulation Based on Monotonic Chain

2012 ◽  
Vol 263-266 ◽  
pp. 1605-1608
Author(s):  
Yu Ping Zhang ◽  
Zhao Ri Deng ◽  
Rui Qi Zhang
Keyword(s):  
Convex Hull ◽  
Convex Polygon ◽  
Efficient Approach ◽  
Point Set ◽  
Delaunay Algorithm ◽  
Better Than

The triangulation of convex hull has the characteristics of point-set and polygon triangulation. According to some relative definitions, this paper proposed a triangulation of convex hull based on a monotonic chain. This method is better than Delaunay algorithm and is more efficient than other convex polygon algorithms. It is a good algorithm.

Sphericity Evaluation Based on Minimum Circumscribed Sphere Method

2012 ◽  
Vol 433-440 ◽  
pp. 3146-3151 ◽  
Author(s):  
Fan Wu Meng ◽  
Chun Guang Xu ◽  
Juan Hao ◽  
Ding Guo Xiao
Keyword(s):  
Convex Hull ◽  
Early Stage ◽  
Measured Data ◽  
Efficient Approach ◽  
Critical Data ◽  
Material Condition ◽  
Data Points ◽  
Point Set ◽  
Data Point

The search of sphericity evaluation is a time-consuming work. The minimum circumscribed sphere (MCS) is suitable for the sphere with the maximum material condition. An algorithm of sphericity evaluation based on the MCS is introduced. The MCS of a measured data point set is determined by a small number of critical data points according to geometric criteria. The vertices of the convex hull are the candidates of these critical data points. Two theorems are developed to solve the sphericity evaluation problems. The validated results show that the proposed strategy offers an effective way to identify the critical data points at the early stage of computation and gives an efficient approach to solve the sphericity problems.

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.

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.

scholarly journals Exact Formulae for Variances of Functionals of Convex Hulls

2013 ◽  
Vol 45 (04) ◽  
pp. 917-924
Author(s):  
Christian Buchta
Keyword(s):  
Convex Hull ◽  
Asymptotic Distribution ◽  
Convex Polygon ◽  
Convex Hulls ◽  
Affine Invariance ◽  
Uniform Sample

The vertices of the convex hull of a uniform sample from the interior of a convex polygon are known to be concentrated close to the vertices of the polygon. Furthermore, the remaining area of the polygon outside of the convex hull is concentrated close to the vertices of the polygon. In order to see what happens in a corner of the polygon given by two adjacent edges, we consider—in view of affine invariance—n points P 1,…, P n distributed independently and uniformly in the interior of the triangle with vertices (0, 1), (0, 0), and (1, 0). The number of vertices of the convex hull, which are close to the origin (0, 0), is then given by the number Ñ n of points among P 1,…, P n , which are vertices of the convex hull of (0, 1), P 1,…, P n , and (1, 0). Correspondingly, D̃ n is defined as the remaining area of the triangle outside of this convex hull. We derive exact (nonasymptotic) formulae for var Ñ n and var . These formulae are in line with asymptotic distribution results in Groeneboom (1988), Nagaev and Khamdamov (1991), and Groeneboom (2012), as well as with recent results in Pardon (2011), (2012).

Strategy stability in complex randomly mating diploid populations

1982 ◽  
Vol 19 (03) ◽  
pp. 653-659 ◽  
Author(s):  
W. G. S. Hines
Keyword(s):  
Convex Hull ◽  
Lyapunov Functions ◽  
Evolutionarily Stable Strategy ◽  
Stable Strategy ◽  
Convergence In Mean ◽  
Evolutionarily Stable ◽  
Diploid Populations ◽  
Better Than

A class of Lyapunov functions is used to demonstrate that strategy stability occurs in complex randomly mating diploid populations. Strategies close to the evolutionarily stable strategy tend to fare better than more remote strategies. If convergence in mean strategy to an evolutionarily stable strategy is not possible, evolution will continue until all strategies in use lie on a unique face of the convex hull of available strategies. The results obtained are also relevant to the haploid parthenogenetic case.

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
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