Showing papers on "Polygon published in 2022"
14 citations
TL;DR: A polynomial exact algorithm is formulated that makes use of a triangular decomposition of the incremental Voronoi diagram and the first order optimality conditions to solve facility location problems where n facilities are present in a convex polygon in the rectilinear plane.
5 citations
TL;DR: In this article, the authors consider a mathematical model for skin contraction, which is based on solving a momentum balance under the assumptions of isotropy, homogeneity, Hooke's Law, infinitesimal strain theory and point forces exerted by cells.
2 citations
TL;DR: It is shown that it is NP -hard to minimize the area of the bounding box of an orthogonal drawing of a given planar graph, and that realizing a polyline within a bounding boxes of minimum area or within a fixed given rectangle isNP -hard.
Abstract: A rectilinear polygon is a simple polygon whose edges are axis-aligned. Walking counterclockwise on the boundary of such a polygon yields a sequence of left turns and right turns. The number of left turns always equals the number of right turns plus four. It is known that any such sequence can be realized by a rectilinear polygon. In this paper, we consider the problem of finding realizations that minimize the perimeter or the area of the polygon or the area of the bounding box of the polygon. We show that all three problems are NP -hard in general. This answers an open question of Patrignani (2001) [13] , who showed that it is NP -hard to minimize the area of the bounding box of an orthogonal drawing of a given planar graph. We also show that realizing a polyline within a bounding box of minimum area (or within a fixed given rectangle) is NP -hard. Then we consider the special cases of x-monotone and xy-monotone rectilinear polygons. For these, we can optimize the three objectives efficiently.
1 citations
01 Jan 2022
TL;DR: In this paper, a suboptimal deterministic algorithm, as well as an adapted differential evolution algorithm for tackling sensor placement is proposed. But the algorithm is not suitable for the case of large number of sensors.
Abstract: It is well known that determining visual sensors in 2D space can be often modeled as an Art Gallery problem. Tasks such as surveillance dictate the coverage of the interior of a non-convex polygon with the optimal number of sensors. The optimal sensor placement is a difficult combinatorial optimization problem, and it can be formulated as seeking the smallest number of sensors obliged to cover every point in a heterogeneous setting. In this article, we propose a suboptimal deterministic algorithm, as well as an adapted differential evolution algorithm for tackling sensor placement. Both versions of novel algorithms have been implemented and tested over hundreds of random polygons. According to the outcomes presented in the experimental analysis, it can be noticed that the approach based on differential evolution beats the deterministic technique as well as other stochastic optimization algorithms for practically all instances.
DOI•
01 Jan 2022TL;DR: In this paper, the authors proposed a method of finding the corner points and point cloud distortion in the point cloud map based on the Graham-scan algorithm, which can effectively identify the inflection point of the point clouds and correct the map.
Abstract: For the problem of finding the corner points and point cloud distortion in the point cloud map, this paper proposes a method of corner point recognition and point cloud correction based on the Graham-scan algorithm. The minimum convex hull polygon of the point cloud map is obtained through the Graham-scan algorithm. Then the corner points of the point cloud map are filtered out by setting the threshold, and the two-dimensional point cloud map is corrected based on the found corner points and the information collected by the IMU. Experiments show that this method has achieved good results, and can effectively identify the inflection point of the point cloud map and correct the point cloud map.