A modified Graham’s convex hull algorithm for finding the connected orthogonal convex hull of a finite planar point set

An, Phan Thanh; Huyen, Phong Thi Thu; Le, Nguyen Thi

doi:10.1016/j.amc.2020.125889

Cited by 14 publications

(12 citation statements)

References 17 publications

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“…In R 1 , an ortho-convex set and a convex set are the same, which is a connected set (an empty set, a point, or a single interval). In R 2 , a set is ortho-convex if its intersection with any horizontal or vertical line is connected (see [7,25]). Fig.…”

Section: Preliminarymentioning

confidence: 99%

“…After that, the notion of ortho-convexity is extended to higher dimensional spaces [10]. Researchers have studied and given some properties of ortho-convex sets along with developing results similar to that of traditional convex sets [7,1,11,23]. However, most of these results are obtained in the plane.…”

Section: Introductionmentioning

confidence: 99%

“…However, most of these results are obtained in the plane. Some algorithms for finding the orthogonally convex hull of a set of finite points or of x-y polygons are found in [7,2,12,14,17,19], where an x-y polygon is a simple polygon with horizontal and vertical edges.…”

Section: Introductionmentioning

confidence: 99%

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Blaschke, Separation Theorems and some Topological Properties for Orthogonally Convex Sets

An¹,

Le²

2022

Preprint

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In this paper, we deal with analytic and geometric properties of orthogonally convex sets. We establish a Blaschke-type theorem for pathconnected and orthogonally convex sets in the plane using othogonally convex paths. The separation of these sets is established using suitable grids. Consequently, a closed and orthogonally convex set is represented by the intersection of staircase-halfplanes in the plane. Some topological properties of orthogonally convex sets in dimensional spaces are also given.

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Section: Preliminarymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Blaschke, Separation Theorems and some Topological Properties for Orthogonally Convex Sets

An¹,

Le²

2022

Preprint

Self Cite

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“…Reasonable and accurate delineation of the flight-restricted area is essential to reduce these adverse effects. In this study, we mainly used the monitored radar echo data to filter and divide the data in order to determine the initial range of the flightrestricted area [22]. The Graham algorithm was then used for the dynamic prediction of the flight-restricted area.…”

Section: Delineation Of Flight-restricted Areas In Hazardous Weathermentioning

confidence: 99%

Improved F-RRT $^{*}$ Algorithm for Flight-Path Optimization in Hazardous Weather

Qiu

Jin

et al. 2022

International Journal of Aerospace Engineering

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Hazardous weather has become a major cause of flight delays in recent years. With the development of satellite navigation systems, the study of flight-path optimization under hazardous weather conditions has become especially important. In this study, radar data were used as the basis for the initial flight-restricted area under hazardous weather conditions, and the Graham algorithm was used to delineate the dynamic flight-restricted area by comprehensively considering the hazardous weather boundary changes along with the speed and direction. Then, under the grid environment model, the range of influence, size, and distribution characteristics of the flight-restricted area was examined, and the path optimization model was created according to constraints related to the path distance, corner size, and number of turning points. An improved F-RRT ∗ algorithm was developed to solve the model. The algorithm can overcome the problems of traditional path planning algorithms, such as strong randomness, poor guidance, slow convergence speed, unsmooth paths, and poor tracing smoothness. Finally, a simulation analysis was conducted on the Guiyang–Guangzhou route in China as an example. This study can address the drawbacks of existing research on route change and provide sufficient theoretical support and reference for the implementation of specific route change plans in the future.

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“…In fact, it is to sort the polar angles and then 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]. Nguyen designed a faster convex hull algorithm for disks [9].…”

Section: Introductionmentioning

confidence: 99%

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

Han

Zhang²,

Chen³

et al. 2021

Scientific Programming

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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.

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A modified Graham’s convex hull algorithm for finding the connected orthogonal convex hull of a finite planar point set

Cited by 14 publications

References 17 publications

Blaschke, Separation Theorems and some Topological Properties for Orthogonally Convex Sets

Blaschke, Separation Theorems and some Topological Properties for Orthogonally Convex Sets

Improved F-RRT $^{*}$ Algorithm for Flight-Path Optimization in Hazardous Weather

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

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A modified Graham’s convex hull algorithm for finding the connected orthogonal convex hull of a finite planar point set

Cited by 14 publications

References 17 publications

Blaschke, Separation Theorems and some Topological Properties for Orthogonally Convex Sets

Blaschke, Separation Theorems and some Topological Properties for Orthogonally Convex Sets

Improved F-RRT ∗ Algorithm for Flight-Path Optimization in Hazardous Weather

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

Contact Info

Product

Resources

About

Improved F-RRT $^{*}$ Algorithm for Flight-Path Optimization in Hazardous Weather