Cross Product and Partitioned Filtering-Based Graham Convex Hull for Buoy Drifting Area Demarcating

Han Xue,Weicheng Zhang,Chao Ni,Xiping Lu,Shah Nazir

doi:10.1155/2021/7713884

Abstract

An improved Graham scan convex hull algorithm is designed using the convex hull region shrinkage algorithm and the sample selection decision algorithm. In the sorting of Graham scan convex hull algorithm, the cross-multiplication method is used instead of the operation of finding the polar angle, which avoids the high computational complexity of finding the inverse trigonometric function. When the polar angles are the same, that is, the two points are collinear, the points close to each other are deleted directly. Select the maximal horizontal ordinate point, minimal horizontal ordinate point, maximal longitudinal coordinate point, and minimal longitudinal coordinate point. Connect these points and obtain lines. The whole plane is divided into different regions. The points that are not on the convex hull are deleted, and the redundant points are removed. This can speed up the calculation of approximate convex hull boundary and shorten the time of convex hull calculation. The proposed algorithm is used for buoy drifting area demarcating. The offsets of the geometric center of the high-frequency position point and the distance from geometric center of high-frequency position of buoy to sinking stone are calculated. The experimental results show that the new algorithm can effectively accelerate the convex hull calculation. We use the convex hull process to compute the area of the drifting buoy position and discover that the drift area of the port hand buoy is similar. The drift area of the port hand buoys is similar. The drift area of the port hand buoy is greater than that of the port hand buoy.

Highlights

A buoy is a kind of artificial mark used to mark warning and channel boundary, which can guide ships to navigate, locate, and avoid obstacles [1,2,3,4]
Select the maximal longitudinal coordinate point Qe and minimal longitudinal coordinate point Qw. Connect these points and obtain lines. e whole plane is divided into different regions. e points that are not on the convex hull are deleted, and the redundant points are removed. is can speed up the calculation of approximate convex hull boundary and shorten the time of convex hull calculation
Most vertices that are not on the convex hull are deleted, which reduces the calculation scale. e inverse trigonometric function is replaced by cross multiplication

Summary

Introduction

A buoy is a kind of artificial mark used to mark warning and channel boundary, which can guide ships to navigate, locate, and avoid obstacles [1,2,3,4]. E idea of Graham’s scanning is to find a point on the convex hull first and start from that point to find the points on the convex hull one by one in a counterclockwise direction. It is to sort the polar angles and use them to query. A modified Graham’s convex hull algorithm is proposed for finding the connected orthogonal convex hull of a finite planar point set [8]. Wu et al designed an improved Graham algorithm for determining the convex hull of planar points’ set [12]

Results

Discussion

Conclusion