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 Grid Partition Variable Step Alpha Shapes Algorithm

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Zhenxiu Liao ◽  
Jun Liu ◽  
Guodong Shi ◽  
Junxia Meng
Keyword(s):  
Average Distance ◽  
Discrete Point ◽  
Boundary Extraction ◽  
Grid Partition ◽  
Alpha Shapes ◽  
Extraction Algorithm ◽  
Variable Step ◽  
Point Set ◽  
Index Table ◽  
Previous Step

On the basis of Alpha Shapes boundary extraction algorithm for discrete point set, a grid partition variable step Alpha Shapes algorithm is proposed to deal with the shortcomings of the original Alpha Shapes algorithm in the processing of nonuniform distributed point set and multiconcave point set. Firstly, the grid partition and row-column index table are established for the point set, and the point set of boundary grid partition is quickly extracted. Then, the average distance of the k -nearest neighbors of the point is calculated as the value of α . For the point set of boundary grid partition extracted in the previous step, Alpha Shapes algorithm is used to quickly construct the point set boundary. The proposed algorithm is verified by experiments of simulated point set and measured point set, and it has high execution efficiency. Compared with similar algorithms, the larger the number of point sets is, the more obvious the execution efficiency is.

BASELINE BOUNDED HALF-PLANE VORONOI DIAGRAM

2013 ◽  
Vol 05 (03) ◽  
pp. 1350021 ◽  
Author(s):  
BING SU ◽  
YINFENG XU ◽  
BINHAI ZHU
Keyword(s):  
Voronoi Diagram ◽  
Half Plane ◽  
Line Segment ◽  
Euclidean Plane ◽  
Voronoi Region ◽  
Point Set ◽  
Set Of Points

Given a set of points P = {p1, p2, …, pn} in the Euclidean plane, with each point piassociated with a given direction vi∈ V. P(pi, vi) defines a half-plane and L(pi, vi) denotes the baseline that is perpendicular to viand passing through pi. Define a region dominated by piand vias a Baseline Bounded Half-Plane Voronoi Region, denoted as V or(pi, vi), if a point x ∈ V or(pi, vi), then (1) x ∈ P(pi, vi); (2) the line segment l(x, pi) does not cross any baseline; (3) if there is a point pj, such that x ∈ P(pj, vj), and the line segment l(x, pj) does not cross any baseline then d(x, pi) ≤ d(x, pj), j ≠ i. The Baseline Bounded Half-Plane Voronoi Diagram, denoted as V or(P, V), is the union of all V or(pi, vi). We show that V or(pi, vi) and V or(P, V) can be computed in O(n log n) and O(n2log n) time, respectively. For the heterogeneous point set, the same problem is also considered.

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.

4H-SiC Epi-Ready Substrate Qualification by Using Mirror Electron Microscope Inspection System

2020 ◽  
Vol 1004 ◽  
pp. 369-375
Author(s):  
Masaki Hasegawa ◽  
Kentaro Ohira ◽  
Noriyuki Kaneoka ◽  
Tomohiko Ogata ◽  
Katsunori Onuki ◽  
...  
Keyword(s):  
Electron Microscope ◽  
Epitaxial Layer ◽  
Basal Plane ◽  
Mechanical Polishing ◽  
Inspection System ◽  
Layer Surface ◽  
Discrete Point ◽  
Surface Polishing ◽  
Point Set ◽  
Crystal Damage

Crystal damage beneath the surface remaining after chemo-mechanical polishing (CMP) and basal plane dislocations (BPDs) of 4H-SiC epi-ready substrates have been inspected by using a mirror electron microscope inspection system non-destructively. Distributions of crystal damage and BPDs as well as their average densities are estimated by acquiring 80-μm square mirror electron images at positions distributed with an equal pitch over a substrate (“Discrete point set inspection”). Although the total inspected area is less than 1% of the entire substrate area, the inspection results for nine commercially available wafers reveal that there are large differences in surface polishing quality and BPD density between them. Evaluation on an epitaxial layer with a thickness of 10 μm grown on one of the inspected substrates indicated that correlation between distribution of the crystal damages on the substrate and that of bunched steps on the epitaxial layer surface.

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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