English
Related papers

Related papers: Polygon Detection from a Set of Lines

200 papers

While well-known methods to list the intersections of either a list of segments or a complex polygon aim at achieving optimal time-complexity they often do so at the cost of memory comsumption and complex code. Real-life software…

Computational Geometry · Computer Science 2013-05-28 Jean Souviron

In this paper, we discuss the algorithm engineering aspects of an O(n^2)-time algorithm [6] for computing a minimum-area convex polygon that intersects a set of n isothetic line segments.

Computational Geometry · Computer Science 2016-09-07 Xin Wu , Xijie Zeng , Bryan St. Amour , Asish Mukhopadhyay

An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding lo single-valued, continuous functions which are defined over rectangular domains. The algorithm…

Graphics · Computer Science 2011-07-29 Ignacio Vega-Paez , Jose Angel Ortega , Georgina G. Pulido

We present an $O(n\log n)$-time algorithm that determines whether a given planar $n$-gon is weakly simple. This improves upon an $O(n^2\log n)$-time algorithm by Chang, Erickson, and Xu (2015). Weakly simple polygons are required as input…

Computational Geometry · Computer Science 2017-08-01 Hugo Akitaya , Greg Aloupis , Jeff Erickson , Csaba D. Tóth

We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and…

Computational Geometry · Computer Science 2025-01-08 David Eppstein

A polynomial time algorithm which detects all paths and cycles of all lengths in form of vertex pairs (start, finish).

Discrete Mathematics · Computer Science 2007-09-10 Sergey Gubin

This paper proposed a method to judge whether the point is inside or outside of the simple convex polygon by the intersection of the vertical line. It determined the point to an area enclosed by two straight lines, then convert the problem…

Computational Geometry · Computer Science 2022-06-07 Sun Yixuan , Zhu Zhehao

We formulate the task of detecting lines and paragraphs in a document into a unified two-level clustering problem. Given a set of text detection boxes that roughly correspond to words, a text line is a cluster of boxes and a paragraph is a…

Computer Vision and Pattern Recognition · Computer Science 2022-03-21 Shuang Liu , Renshen Wang , Michalis Raptis , Yasuhisa Fujii

We introduce a computational origami problem which we call the segment folding problem: given a set of $n$ line-segments in the plane the aim is to make creases along all segments in the minimum number of folding steps. Note that a folding…

Computational Geometry · Computer Science 2022-01-17 Takashi Horiyama , Fabian Klute , Matias Korman , Irene Parada , Ryuhei Uehara , Katsuhisa Yamanaka

Given a set of objects $O$ in the plane, the corresponding intersection graph is defined as follows. Each object defines a vertex and an edge joins two vertices whenever the corresponding objects intersect. We study here the case of unit…

Computational Geometry · Computer Science 2025-12-09 Michael Hoffmann , Tillmann Miltzow , Simon Weber , Lasse Wulf

We propose an algorithm based on Newton's method and subdivision for finding all zeros of a polynomial system in a bounded region of the plane. This algorithm can be used to find the intersections between a line and a surface, which has…

Numerical Analysis · Mathematics 2025-10-20 Gun Srijuntongsiri , Stephen A. Vavasis

Determining if a point is in a polygon or not is used by a lot of applications in computer graphics, computer games and geoinformatics. Implementing this check is error-prone since there are many special cases to be considered. This holds…

Computational Geometry · Computer Science 2017-07-25 Michael Galetzka , Patrick O. Glauner

Suppose that a polygon $P$ is given as an array containing the vertices in counterclockwise order. We analyze how many vertices (including the index of each of these vertices) we need to know before we can bound $P$, i.e., report a bounded…

Computational Geometry · Computer Science 2025-09-05 Mikkel Abrahamsen , Jack Stade , Shuyi Yan , Hanwen Zhang

We derive a mixed integer nonlinear programming formulation for the problem of finding a convex polygon with a given number of vertices that is small (diameter at most one) and has maximum perimeter. The formulation is based on a geometric…

Optimization and Control · Mathematics 2024-04-03 Bernd Mulansky , Andreas Potschka

We introduce the \emph{visibility center} of a set of points inside a polygon -- a point $c_V$ such that the maximum geodesic distance from $c_V$ to see any point in the set is minimized. For a simple polygon of $n$ vertices and a set of…

Computational Geometry · Computer Science 2022-12-06 Anna Lubiw , Anurag Murty Naredla

We describe an algorithm for computing the separating common tangents of two simple polygons using linear time and only constant workspace. A tangent of a polygon is a line touching the polygon such that all of the polygon lies to the same…

Computational Geometry · Computer Science 2015-11-13 Mikkel Abrahamsen

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…

Computational Geometry · Computer Science 2020-07-24 Jeremy Castagno , Ella Atkins

Deciding whether a family of disjoint axis-parallel line segments in the plane can be linked into a simple polygon (or a simple polygonal chain) by adding segments between their endpoints is NP-hard.

Computational Geometry · Computer Science 2021-09-07 Rain Jiang , Kai Jiang , Minghui Jiang

A polygon C is an intersecting polygon for a set O of objects in the plane if C intersects each object in O, where the polygon includes its interior. We study the problem of computing the minimum-perimeter intersecting polygon and the…

Computational Geometry · Computer Science 2022-08-17 Antonios Antoniadis , Mark de Berg , Sándor Kisfaludi-Bak , Antonis Skarlatos

Lane detection is to detect lanes on the road and provide the accurate location and shape of each lane. It severs as one of the key techniques to enable modern assisted and autonomous driving systems. However, several unique properties of…

Computer Vision and Pattern Recognition · Computer Science 2018-07-06 Ze Wang , Weiqiang Ren , Qiang Qiu