Topic
Line segment intersection
About: Line segment intersection is a research topic. Over the lifetime, 411 publications have been published within this topic receiving 7993 citations.
Papers published on a yearly basis
Papers
TL;DR: Algorithms that count the number of pairwise intersections among a set of N objects in the plane and algorithms that report all such intersections are given.
Abstract: An interesting class of "geometric intersection problems" calls for dealing with the pairwise intersections among a set of N objects in the plane, These problems arise in many applications such as printed circuit design, architectural data bases, and computer graphics. Shamos and Hoey have described a number of algorithms for detecting whether any two objects in a planar set intersect. In this paper we extend their work by giving algorithms that count the number of such intersections and algorithms that report all such intersections.
1,136 citations
25 Oct 1976
TL;DR: An O(N log N) algorithm is given to determine whether any two intersect and use it to detect whether two simple plane polygons intersect and to show that the Simplex method is not optimal.
Abstract: We develop optimal algorithms for forming the intersection of geometric objects in the plane and apply them to such diverse problems as linear programming, hidden-line elimination, and wire layout. Given N line segments in the plane, finding all intersecting pairs requires O(N2) time. We give an O(N log N) algorithm to determine whether any two intersect and use it to detect whether two simple plane polygons intersect. We employ an O(N log N) algorithm for finding the common intersection of N half-planes to show that the Simplex method is not optimal. The emphasis throughout is on obtaining upper and lower bounds and relating these results to other problems in computational geometry.
514 citations
TL;DR: An algorithm to test whether their intersection is empty, and if so to find a separating plane, and to construct their intersection polyhedron is developed, which runs in timeO (n log n), where n is the sum of the numbers of vertices of the two polyhedra.
351 citations
TL;DR: The development and implementation of a line segment-based token tracker that combines prediction and matching steps and is illustrated in several experiments that have been carried out considering noisy synthetic data and real scenes obtained from the INRIA mobile robot.
341 citations
24 Oct 1988
TL;DR: The authors present the first optimal algorithm for the following problem: given n line segments in the plane, compute all k pairwise intersections in O(n log n+k) time.
Abstract: The authors present the first optimal algorithm for the following problem: given n line segments in the plane, compute all k pairwise intersections in O(n log n+k) time. Within the same asymptotic cost the algorithm will also compute the adjacencies of the planar subdivision induced by the segments, which is a useful data structure for contour-filling on raster devices. >
292 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2020 | 4 |
| 2019 | 5 |
| 2018 | 3 |
| 2017 | 8 |
| 2016 | 8 |