A robust algorithm for geometric predicate by error-free determinant transformation

Katsuhisa Ozaki, Takeshi Ogita, Shinichi Oishi

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    This paper concerns a robust algorithm for the 2D orientation problem which is one of the basic tasks in computational geometry. Recently, a fast and accurate floating-point summation algorithm is investigated by Rump, Ogita and Oishi in [S.M. Rump, T. Ogita, S. Oishi, Accurate floating-point summation. Part I: Faithful rounding, SIAM J. Sci. Comput. 31 (1) (2008) 189-224], in which a new kind of an error-free transformation of floating-point numbers is used. Based on it, a new algorithm of error-free determinant transformation for the 2D orientation problem is proposed, which gives a correct result. Numerical results are presented for illustrating that the proposed algorithm has some advantage over preceding algorithms in terms of measured computing time.

    Original languageEnglish
    Pages (from-to)3-13
    Number of pages11
    JournalInformation and Computation
    Volume216
    DOIs
    Publication statusPublished - 2012 Jul

    Fingerprint

    Robust Algorithm
    Predicate
    Determinant
    Floating point
    Summation
    Rounding
    Computational Geometry
    Computational geometry
    Faithful
    Numerical Results
    Computing

    Keywords

    • Computational geometry
    • Error-free determinant transformation
    • Verified numerical computation

    ASJC Scopus subject areas

    • Information Systems
    • Computational Theory and Mathematics
    • Theoretical Computer Science
    • Computer Science Applications

    Cite this

    A robust algorithm for geometric predicate by error-free determinant transformation. / Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shinichi.

    In: Information and Computation, Vol. 216, 07.2012, p. 3-13.

    Research output: Contribution to journalArticle

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