Point triangulation using Graham’s scan

Tereshchenko, Vasyl; Tereshchenko, Yaroslav; Kotsur, Dmytro

doi:10.1109/intech.2015.7173370

Cited by 11 publications

(5 citation statements)

References 6 publications

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“…Time complexity Brute force method [14] O(N^4) Ear clipping method [17] O(N^2) Seidel's method [11] O(N log N) Tarjan's method [7] O(N log log N) Chazelle's method [14] O(N)…”

Section: Methodsmentioning

confidence: 99%

“…One feature of the proposed algorithm is a very simple implementation, and the elements (triangles) of the resulting triangulation can be presented in the form of simple and fast data structure: a tree of triangles [17]. This makes the algorithm convenient for solving a wide range of applied and research problems, in particular, those referring to computational geometry and computer graphics, meshing and rendering [18], pattern recognition and image segmentation [19,20], approximation and 2D (3D) simulation.…”

Section: Methodsmentioning

confidence: 99%

“…An efficient triangulating algorithm is received. The proposed algorithm is characterized by a very simple implementation, and the elements (triangles) of the resulting triangulation can be presented in the form of simple and fast data structure: a tree of triangles [17].…”

mentioning

confidence: 99%

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Triangulating a Region Between Arbitrary Polygons

Tereshchenko¹,

Tereshchenko²

2017

IJC

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The paper presents an optimal algorithm for triangulating a region between arbitrary polygons on the plane with time complexity O(N log⁡N ). An efficient algorithm is received by reducing the problem to the triangulation of simple polygons with holes. A simple polygon with holes is triangulated using the method of monotone chains and keeping overall design of the algorithm simple. The problem is solved in two stages. In the first stage a convex hull for m polygons is constructed by Graham’s method. As a result, a simple polygon with holes is received. Thus, the problem of triangulating a region between arbitrary polygons is reduced to the triangulation of a simple polygon with holes. In the next stage the simple polygon with holes is triangulated using an approach based on procedure of splitting polygon onto monotone polygons using the method of chains [15]. An efficient triangulating algorithm is received. The proposed algorithm is characterized by a very simple implementation, and the elements (triangles) of the resulting triangulation can be presented in the form of simple and fast data structure: a tree of triangles [17].

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“…Time complexity Brute force method [14] O(N^4) Ear clipping method [17] O(N^2) Seidel's method [11] O(N log N) Tarjan's method [7] O(N log log N) Chazelle's method [14] O(N)…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Triangulating a Region Between Arbitrary Polygons

Tereshchenko¹,

Tereshchenko²

2017

IJC

Self Cite

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“…The foot outline projection in the X-Y plane (Fig. 11) consists of bumps extracted by using the Graham algorithm 58 . P2 is the point with the maximum absolute X value when the Y (1) P8 and P9 are the points with the maximum and minimum X values along the X-axis with a 14-20% FL.…”

Section: Foot Anthropometric Measurementsmentioning

confidence: 99%

An exploratory study of dynamic foot shape measurements with 4D scanning system

Zhang

Yick

Yue

et al. 2023

Sci Rep

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Accurate and reliable foot measurements at different stances offer comprehensive geometrical information on foot, thus enabling a more comfortable insole/footwear for practical use and daily activities. However, there lacks investigations on continuous deformation of foot shape during the roll-over process. This study analyses the foot deformation of 19 female diabetic patients during half weight bearing standing and self-selected walking speed by using a novel 4D foot scanning system. The scanning system has good repeatability and accuracy in both static and dynamic scanning situations. Point cloud registration for scanned image reorientation and algorithms to automatically extract foot measurements is developed. During the foot roll-over process, maximum deformation of length and girth dimensions are found at first toe contact. Width dimensions have maximum deformation at heel take off. The findings provide a new understanding of foot shape changes in dynamic situations, thus providing an optimal solution for foot comfort, function and protection.

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“…Step 2. Generate the minimum convex hull using the Graham scan algorithm [19], [31], [32], which is an efficient algorithm for finding the convex hull with time complexity O(nlgn). Fig.…”

Section: Development Of the Probability Mapmentioning

confidence: 99%

A Time Domain-Based Iterative Method for Helicopter Maritime Search Area Planning and Construction of the Simulation Environment

et al. 2020

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Helicopters are widely used in maritime search and rescue (SAR) missions. To improve the probability of success (POS) of SAR missions, search areas should be carefully planned. However, the search area is usually determined based on the survivors' probable locations at a given moment by existing planning methods, while the effects of the relative motion between the helicopter and the search objects are ignored, possibly leading to a significant decrease in the POS. To minimize the impact of search object motion, a time domain-based iterative planning (TIP) method is proposed in this paper to obtain the optimal search areas. The survivors' probable locations and mean drift direction are updated iteratively, while the probability map is developed by taking survivors' mean drift direction as a reference. Then, the optimal search area is determined by an iterative search method starting from the cell with the highest probability of containment. To evaluate the effectiveness of a search plan, an agent-based simulation environment of a maritime search mission is constructed based on the AnyLogic simulation platform. Taking a capsizing case as an example, the simulation results show that the novel TIP method minimizes the impact of search object motion on the search effectiveness and obtains higher POS values than those obtained by other methods.

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Point triangulation using Graham’s scan

Cited by 11 publications

References 6 publications

Triangulating a Region Between Arbitrary Polygons

Triangulating a Region Between Arbitrary Polygons

An exploratory study of dynamic foot shape measurements with 4D scanning system

A Time Domain-Based Iterative Method for Helicopter Maritime Search Area Planning and Construction of the Simulation Environment

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