# An Elementary Algorithm for Reporting Intersections of Red/Blue Curve Segments

1 PRISME - Geometry, Algorithms and Robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Let E_r and E_b be two sets of x-monotone and non-intersecting curve segments, E=E_r \cup E_b and |E|=n. We give a new sweep-line algorithm that reports the $k$ intersecting pairs of segments of E. Our algorithm 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 point is above, below or on a segment. These three predicates seem to be the simplest predicates that lead to subquadratic algorithms. Our algorithm is almost optimal in this restricted model of computation. Its time complexity is \$O((n+k)\logn) and it requires O(n) space. The same algoritm has been described in our previous report [5]. That report presented also an algoritm for the general case but its analysis was not not correct.
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Type de document :
Rapport
[Research Report] RR-3999, INRIA. 2000, pp.13
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Littérature citée [1 références]

https://hal.inria.fr/inria-00072646
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 10:29:31
Dernière modification le : jeudi 11 janvier 2018 - 16:24:46
Document(s) archivé(s) le : dimanche 4 avril 2010 - 21:00:11

### Identifiants

• HAL Id : inria-00072646, version 1

### Citation

Jean-Daniel Boissonnat, Antoine Vigneron. An Elementary Algorithm for Reporting Intersections of Red/Blue Curve Segments. [Research Report] RR-3999, INRIA. 2000, pp.13. 〈inria-00072646〉

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