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### Incremental Convex Hull as an Orientation to Solving theShortest Path Problem

Phan An
2012 International Journal of Information and Electronics Engineering
We find the Euclidean shortest path in the polygon between a and b. In this paper, an efficient algorithm based on incremental convex hulls is presented.  ...  The following problem is very classical in motion planning: Let a and b be two vertices of a polygon and P (Q, respectively) be the polyline formed by vertices of the polygon from a to b (from b to a,  ...  Then 1) u* is an extreme vertex of the convex hull of {u*}Y**. 2) The first edge (if viewed from u*) of the clock-wise convex hull of {u*}Y** is a link to X and Y.  ...

### A Hybrid Convex Hull Algorithm for Fingertips Detection

Guat Yew Tan, Bo Shen Woun, Ya Ping Wong
2016 Indian Journal of Science and Technology
Novelty/Improvement: The hybrid convex hull algorithm offers a direct way to detect the convex hull of the original image without edge detection process.  ...  Methodology: In this paper, we suggest to reduce the computational resources by leveraging on two proven algorithms and techniques in order to extract the convex hull vertices directly from a binary image  ...  As p 0 is the rightmost top vertex of the convex hull, let l be a point on L, ∀l∈L, l ≠ p 0 , p 0x <l x ≤ M x and l y = M y , l∉S. Thus, L is the exterior line of the convex polygon.  ...

### A Syudy on Applications of Convex Hull Algorithm in the SPH SPH에서의 Convex Hull 알고리즘 적용연구

Jin-Sung Lee, Young-Shin Lee
2011 Journal of the Korea Institute of Military Science and Technology
In this study, convex hull algorithm is presented as an improved method to eliminate this artifact. A convex hull is the smallest convex set that contains a certain set of points or a polygon.  ...  The selected candidate neighbours set are mapped into the new space by an inverse square mapping, and extract a convex hull. The neighbours are selected from the shell of the convex hull.  ...  구간별 particle set 가) A 구간 A 구간의 구성 particle은 Fig. 3에서 Ymax를 가진 P1 particle의 X data 이상의 X 값을 가지고, Xmax를 갖는 P2 particle의 Y 값을 초과하는 Y 값을 가지는 particle 집합으로 이루어진다.  ...

### On a partition into convex polygons

Masatsugu Urabe
1996 Discrete Applied Mathematics
In this paper we study the problem of partitioning point sets in the plane so that each equivalence class is a convex polygon with some conditions on the intersection properties of such sets.  ...  We also estimate the maximum of the minimum number of sets in a partition into empty convex polygons, over all sets of n points.  ...  Acknowledgements The author would like to thank Professor David Avis for his valuable suggestions and the referee for his helpful comments.  ...

### Optimum harvesting area of convex and concave polygon field for path planning of robot combine harvester

Md. Mostafizar Rahman, Kazunobu Ishii, Noboru Noguchi
2019 Intelligent Service Robotics
This paper presents an optimum harvesting area of a convex and concave polygon for the path planning of a robot combine harvester.  ...  Therefore, a suitable N-polygon algorithm and split of convex hull and cross-point method for determining the optimum harvesting area for path planning are proposed, which reduce the crop losses in the  ...  X H Y H cos π 2 − ϕ − sin π 2 − ϕ sin π 2 − ϕ cos π 2 − ϕ a b + X i Y i (1) Incremental convex hull algorithm The convex hull of a set of points Q is defined as the smallest convex polygon P that contains  ...

### A Moment-Based Shape Similarity Measurement for Areal Entities in Geographical Vector Data

Zhongliang Fu, Liang Fan, Zhiqiang Yu, Kaichun Zhou
2018 ISPRS International Journal of Geo-Information
Combined with convex hull and local moment invariants, polygons can be represented by convex hull moment invariant curves.  ...  The shape context descriptor extracts a global feature for each point on the boundary of polygons.  ...  If X is convex hull of polygon C, it can be represented as a set of vertices {P 1 , P 2 , . . . P n }.  ...

### PLANAR STRONG VISIBILITY

EUGENE FINK, DERICK WOOD
2003 International journal of computational geometry and applications
Testing the strong visibility of two points in a polygon. 2. Finding the strong convex hull of a point set or polygon. 3. Constructing the strong kernel of a polygon. 4.  ...  Strong visibility is a generalization of standard visibility, defined with respect to a fixed set of line orientations.  ...  On the other hand, since S-hull(P ) is convex, and Q is the minimal convex set containing P , we have Q ⊆ S-hull(P ); hence, S-hull(Q) ⊆ S-hull(P ).  ...

### Covering Polygons by Min-Area Convex Polygons [article]

Elias Dahlhaus, Sariel Har-Peled, Alan L. Hu
2019 arXiv   pre-print
We show that this process has a unique output, which is a cover of the input polygons by a set of disjoint convex polygons, of total minimum area.  ...  Given a set of disjoint simple polygons σ_1, ..., σ_n, of total complexity N, consider a convexification process that repeatedly replaces a polygon by its convex hull, and any two (by now convex) polygons  ...  For a set of polygons U, let CH(U) = CH ∪ σ∈U σ be the combined convex hull of all the polygons of U. Basic properties of convex-hulls Lemma 3.1.  ...

### CudaChain: an alternative algorithm for finding 2D convex hulls on the GPU

Gang Mei
2016 SpringerPlus
We at last obtain the expected convex hull of the input points by calculating the convex hull of the simple polygon.  ...  The proposed algorithm consists of two stages: (1) two rounds of preprocessing performed on the GPU and (2) the finalization of calculating the expected convex hull on the CPU.  ...  The author is grateful to the anonymous referee for helpful comments that improve this paper, especially for pointing out the references Akl (1984) and Nakagawa et al. (2009) .  ...

### Creating Star Worlds – Modelling Concave Obstacles for Reactive Motion Planning [article]

Albin Dahlin, Yiannis Karayiannidis
2022 arXiv   pre-print
The algorithm is based on two novel concepts presented here, namely admissible kernel and starshaped hull with specified kernel, which are closely related to the notion of starshaped hull.  ...  The utilization of the proposed method is illustrated with examples of a robot operating in a 2D workspace using a harmonic potential field approach in combination with the developed algorithm.  ...  For a convex set, A conv , the extended region of the starshaped hull with specified kernel K is based on the convex hull of the kernel points and their corresponding points of tangency.  ...

### Convex Hulls on Cellular Spaces: Spatial Computing on Cellular Automata

Luidnel Maignan, Frederic Gruau
2011 2011 Fifth IEEE Conference on Self-Adaptive and Self-Organizing Systems Workshops
Taking a spatial computing point of view, we present a cellular automata rule that constructs the discrete convex hull of arbitrary set of seeds in infinite spaces.  ...  In the cellular automata domain, the discrete convex hull computation rules proposed until now only deal with a connected set of seeds in infinite space, or with distant set of seeds in finite space.  ...  Adamatzky who pointed us firstly to the convex hull problem, which was the starting point of this work, and secondly to Gabriel graphs, when we showed him our particular graph and its properties.  ...

### AN EFFICIENT ALGORITHM FOR THE CONVEX HULL OF PLANAR SCATTERED POINT SET

Z. Fu, Y. Lu
2012 The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences
Computing the convex hull of a point set is requirement in the GIS applications.  ...  This paper studies on the problem of minimum convex hull and presents an improved algorithm for the minimum convex hull of planar scattered point set.  ...  The convex hull of a set Q of points is the smallest convex polygon P for which each point in Q is either on the boundary of P or in its interior (Cormen et al., 2009) .  ...

### Reduction of metabolic models by polygons optimization method applied to Bioethanol production with co-substrates

C.E. Robles-Rodriguez, C. Bideaux, S. Gaucel, B. Laroche, N. Gorret, C.A. Aceves-Lara
2014 IFAC Proceedings Volumes
Different polygons are tested to conjointly minimize the squared error (convex hull -experimental data) and maximize the convex hull area in order to reduce the set of metabolic reactions involved in the  ...  This paper proposes a new methodology for the reduction of metabolic networks based on the concept of convex hull by optimization methods.  ...  YA implies the reduction of convex hull by (i) selecting the active modes (AMs) that form the greatest triangle and (ii) increasing the area of the convex hull by adding one vertex (AMs) at a time to achieve  ...

### Minimum convex partition of a constrained point set

Thomas Fevens, Henk Meijer, David Rappaport
2001 Discrete Applied Mathematics
A convex partition with respect to a point set S is a planar subdivision whose vertices are the points of S, where the boundary of the unbounded outer face is the boundary of the convex hull of S, and  ...  In this paper, we will present a polynomial time algorithm to ÿnd a minimum convex partition with respect to a point set S where S is constrained to lie on the boundaries of a ÿxed number of nested convex  ...  Acknowledgements The authors wish to thank the anonymous referees for their suggestions and corrections to this paper.  ...

### Finding the convex hull of a simple polygon

Ronald L Graham, F Frances Yao
1983 Journal of Algorithms
It is well known that the convex hull of a set of n points in the plane can be found by an algorithm having worst-case complexity O(nlog n).  ...  A short linear-time algorithm for finding the convex hull when the points form the (ordered) vertices of a simple (i.e., non-self-intersecting) polygon is given.  ...  ACKNOWLEDGMENTS We are grateful to Joseph G'Rourke and Godftied Toussaint whose careful reading of an earlier draft uncovered an error in our paper.  ...
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