Speeding up the incremental construction of the union of geometric objects in practice

Eti Ezra, Dan Halperin, Micha Sharir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


We present a new incremental algorithm for constructing the union of n triangles in the plane. In our experiments, the new algorithm, which we call the Disjoint-Cover (DC) algorithm, performs significantly better than the standard randomized incremental construction (RIC) of the union. Our algorithm is rather hard to analyze rigorously, but we provide an initial such analysis, which yields an upper bound on its performance that is expressed in terms of the expected cost of the RIC algorithm. Our approach and analysis generalize verbatim to the construction of the union of other objects in the plane, and, with slight modifications, to three dimensions. We present experiments with a software implementation of our algorithm using the Cgal library of geometric algorithms.

Original languageEnglish
Title of host publicationAlgorithms - ESA 2002 - 10th Annual European Symposium, Proceedings
EditorsRolf Möhring, Rajeev Raman
PublisherSpringer Verlag
Number of pages12
ISBN (Electronic)3540441808, 9783540441809
StatePublished - 2002
Externally publishedYes
Event10th Annual European Symposium on Algorithms, ESA 2002 - Rome, Italy
Duration: 17 Sep 200221 Sep 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference10th Annual European Symposium on Algorithms, ESA 2002

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.


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