# An optimal algorithm for finding segments intersections

@inproceedings{Balaban1995AnOA, title={An optimal algorithm for finding segments intersections}, author={Ivan J. Balaban}, booktitle={SCG '95}, year={1995} }

This paper deals with a new deterministic algorithm for finding intersecting pairs from a given set of N segments in the plane. The algorithm is asymptotically optimal and has time and space complexity O(AJ log N+ K) and 0( IV ) respectively, where K is the number of intersecting pairs. The algorithm may be used for finding intersections not only line segments but also curve segments.

## 202 Citations

An algorithm for counting line segments intersections using planar partitions

- Mathematics, Computer Science2014 6th International Symposium on Communications, Control and Signal Processing (ISCCSP)
- 2014

The authors' algorithm divide given line segments into groups using Morton code and l quadtree levels and is effective as brute force algorithm when the number of intersections is large.

A Space-Efficient Algorithm for Segment Intersection

- Computer Science, MathematicsCCCG
- 2003

The space requirement for the classic linesegment intersection problem is examined, and so-called implicit data structures are used to make the standard sweep-line algorithm run in O((n + k) log n) time with only O(log 2 n) extra space.

On Sets of Line Segments Featuring a Cactus Structure

- Mathematics, Computer ScienceIWCIA
- 2017

Sharp upper and lower bounds are derived on the number of intersections and closed regions that can occur in a set of line segments whose underlying planar graph is a cactus graph, used to evaluate the complexity of certain algorithms for problems defined on sets of segments in terms of the cardinality of the segment sets.

Line-segment intersection made in-place

- Computer Science, MathematicsComput. Geom.
- 2007

We present a space-efficient algorithm for reporting all k intersections induced by a set of n line segments in the plane. Our algorithm is an in-place variant of Balaban's algorithm and, in the…

Implementatations of Algorithms For Line-Segment Intersection

- 2003

In this paper, I analyze the constant factors for implementations of line segment intersection algorithms. I explore how these algorithms could be applied to stochastic local search algorithms to…

An elementary algorithm for reporting intersections of red/blue curve segments

- Computer Science, MathematicsComput. Geom.
- 2002

A new sweep-line algorithm is given that reports the k intersecting pairs of segments of E that uses only three simple predicates that allow to decide if two segments intersect, if a point is left or right to another point, and if a points is above, below or on a segment.

Line-Segment Intersection Made In-Place

- Mathematics, Computer ScienceWADS
- 2005

This work presents a space-efficient algorithm for reporting all k intersections induced by a set of n line segments in the place that runs in $\mathcal{O}(n log^2_2 n + k)$ time using extra words of memory over and above the space used for the input to the algorithm.

Intersecting Red and Blue Line Segments in Optimal Time and Precision

- Computer ScienceJCDCG
- 2000

A sweep algorithm is given that uses the minimum arithmetic precision and runs in optimal O(n log n + k) time and O( n) space to output an arrangement with k vertices, or O(N log n) time to determine k.

Computing faces in segment and simplex arrangements

- Computer ScienceSTOC '95
- 1995

This work gives the first work-optimal deterministic parallel algorithm for constructing a set of m = O(nd 1 logc n+k) cells of constant descriptive complexity that covers their arrangement, and describes a sequential algorithm for computing a single face in an arrangement of n line segments that improves on a previous O(n log n) time algorithm.

Polygon Detection from a Set of Lines

- Mathematics
- 2021

Detecting polygons defined by a set of line segments in a plane is an important step in the analysis of vectorial drawings. This paper presents an approach that combines several algorithms to detect…

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