Convex polygon ≈ Convex polygon
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Origamizer: A Practical Algorithm for Folding Any Polyhedron Open
It was established at SoCG'99 that every polyhedral complex can be folded from a sufficiently large square of paper, but the known algorithms are extremely impractical, wasting most of the material and making folds through many layers of p…
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Convex Decomposition for a Coverage Path Planning for Autonomous Vehicles: Interior Extension of Edges Open
To cover an area of interest by an autonomous vehicle, such as an Unmanned Aerial Vehicle (UAV), planning a coverage path which guides the unit to cover the area is an essential process. However, coverage path planning is often problematic…
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Exhaustive search of convex pentagons which tile the plane Open
We present an exhaustive search of all families of convex pentagons which tile the plane. This research shows that there are no more than the already 15 known families. In particular, this implies that there is no convex polygon which allo…
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A new path planning method based on concave polygon convex decomposition and artificial bee colony algorithm Open
Free space algorithms are kind of graphics-based methods for path planning. With previously known map information, graphics-based methods have high computational efficiency in providing a feasible path. However, the existing free space alg…
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Complete coverage path planning for pests-ridden in precision agriculture using UAV Open
International audience
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Flight planning in multi-unmanned aerial vehicle systems: Nonconvex polygon area decomposition and trajectory assignment Open
Nowadays, it is quite common to have one unmanned aerial vehicle (UAV) working on a task but having a team of UAVs is still rare. One of the problems that prevent us from using teams of UAVs more frequently is flight planning. In this work…
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Mining Convex Polygon Patterns with Formal Concept Analysis Open
Pattern mining is an important task in AI for eliciting hypotheses from the data. When it comes to spatial data, the geo-coordinates are often considered independently as two different attributes. Consequently, rectangular patterns are sea…
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An enlarged polygon method without binary variables for obstacle avoidance trajectory optimization Open
In this article, an Enlarged Polygon/Polyhedron (ELP) method without binary variables is proposed to represent the Convex Polygonal/Polyhedral Obstacle Avoidance (CPOA) constraints in trajectory optimization. First, the equivalent conditio…
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Route-Planning Method for Plant Protection Rotor Drones in Convex Polygon Regions Open
Aiming at the problem of low operating efficiency due to the poor endurance of plant protection rotor drones and the small volume of pesticide carried, this paper proposes a route-planning algorithm for convex polygon regions based on the …
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Point-in-convex polygon and point-in-convex polyhedron algorithms with O(1) complexity using space subdivision Open
There are many space subdivision and space partitioning techniques used in\nmany algorithms to speed up computations. They mostly rely on orthogonal space\nsubdivision, resp. using hierarchical data structures, e.g. BSP trees,\nquadtrees, …
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A Practical Interlacing-Based Coverage Path Planning Method for Fixed-Wing UAV Photogrammetry in Convex Polygon Regions Open
This paper investigates the coverage path planning problem for a fixed-wing UAV in convex polygon regions with several practical task requirements in photogrammetry considered. A typical camera model pointing forward-down for photogrammetr…
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Deterministic Linear Time Constrained Triangulation using Simplified Earcut Open
Triangulation algorithms that conform to a set of non-intersecting input segments typically proceed in an incremental fashion, by inserting points first, and then segments. Inserting a segment amounts to: (1) deleting all the triangles it …
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Polygon Containment and Translational Min-Hausdorff-Distance between Segment Sets are 3SUM-Hard Open
The 3SUM problem represents a class of problems conjectured to require $Ω(n^2)$ time to solve, where $n$ is the size of the input. Given two polygons $P$ and $Q$ in the plane, we show that some variants of the decision problem, whether the…
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Convex Polygon Packing Based Meshing Algorithm for Modeling of Rock and Porous Media Open
In this work, we propose new packing algorithm designed for the generation of polygon meshes to be used for modeling of rock and porous media based on the virtual element method. The packing problem to be solved corresponds to a two-dimens…
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Metric Dimension of Irregular Convex Triangular Networks Open
Irregular convex triangular networks consist of the interior of a 6-sided convex polygon drawn on the infinite triangular network. Formal description of these applicable networks is provided. In the main result it is proved that the metric…
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A linear-time algorithm for the maximum-area inscribed triangle in a convex polygon Open
Given the n vertices of a convex polygon in cyclic order, can the triangle of maximum area inscribed in P be determined by an algorithm with O(n) time complexity? A purported linear-time algorithm by Dobkin and Snyder from 1979 has recentl…
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Subdivisions of rotationally symmetric planar convex bodies minimizing the maximum relative diameter Open
In this work we study subdivisions of k-rotationally symmetric\n\t\t\t\t planar convex bodies that minimize the maximum relative diameter\n\t\t\t\t functional. For some particular subdivisions called k-partitions, consisting\n\t\t\t\t of k…
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Polylidar - Polygons From Triangular Meshes Open
This paper presents Polylidar, an efficient algorithm to extract non-convex polygons from 2D point sets, including interior holes. Plane segmented point clouds can be input into Polylidar to extract their polygonal counterpart, thereby red…
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Edge-Unfolding Nearly Flat Convex Caps Open
The main result of this paper is a proof that a nearly flat, acutely triangulated convex cap C in R^3 has an edge-unfolding to a non-overlapping polygon in the plane. A convex cap is the intersection of the surface of a convex polyhedron a…
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Tilings with noncongruent triangles Open
We solve a problem of R. Nandakumar by proving that there is no tiling of the plane with pairwise noncongruent triangles of equal area and equal perimeter. We also show that any tiling of a convex polygon with more than three sides with fi…
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Multi-Robot Workspace Division Based on Compact Polygon Decomposition Open
In this work, we tackle the problem of multi-robot convex workspace division. We present an algorithm to split a convex area among several robots into the corresponding number of parts based on the area requirements for each part. The core…
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Computational Design of Iris Folding Patterns Open
Iris folding is a motif consisting of layered strips of paper, forming a spiral pattern behind an aperture, which can be used to make cards and gift tags. This paper describes an interactive computational tool to assist in the design and c…
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The pentagram map, Poncelet polygons, and commuting difference operators Open
The pentagram map takes a planar polygon $P$ to a polygon $P'$ whose vertices are the intersection points of consecutive shortest diagonals of $P$ . This map is known to interact nicely with Poncelet polygons, that is, polygons which are s…
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Convex Drawings of Hierarchical Graphs in Linear Time, with Applications to Planar Graph Morphing Open
A hierarchical plane st-graph H can be thought of as a combinatorial description of a planar drawing Γ of a 2-connected graph G in which each edge is a y-monotone curve and each face encloses a y-monotone region (that is, a region whose in…
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Covering Polygons is Even Harder Open
In the MINIMUM CONVEX COVER (MCC) problem, we are given a simple polygon $\mathcal P$ and an integer $k$, and the question is if there exist $k$ convex polygons whose union is $\mathcal P$. It is known that MCC is $\mathsf{NP}$-hard [Culbe…
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VARIOUS CENTROIDS OF POLYGONS AND SOME CHARACTERIZATIONS OF RHOMBI Open
For a polygon P, we consider the centroid $G_0$ of the vertices of P, the centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P. When P is a triangle, (1) we always have $G_0=G_2$ and (2) P satisfies $G_1=G_2$ if and…
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Tight Two-Dimensional Outer-Approximations of Feasible Sets in Wireless Sensor Networks Open
Finding a tight ellipsoid that contains the intersection of a finite number of ellipsoids is of interest in positioning applications for wireless sensor networks (WSNs). To this end, we propose a novel geometrical method in 2-dimensional (…
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Convex hull as a heuristic Open
Recent studies in the field of numerical cognition quantify the impact of physical properties of an array on its enumeration, demonstrating that enumeration relies on the perception of these properties. This paper marks a shift in reasonin…
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On the number of lattice convex chains Open
An asymptotic formula is presented for the number of planar lattice convex\npolygonal lines joining the origin to a distant point of the diagonal. The\nformula involves the non-trivial zeros of the zeta function and leads to a\nnecessary a…
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A high-frequency boundary element method for scattering by a class of multiple obstacles Open
We propose a boundary element method for problems of time-harmonic acoustic scattering by multiple obstacles in two dimensions, at least one of which is a convex polygon. By combining a hybrid numerical-asymptotic (HNA) approximation space…