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

Katsuhisa Ozaki, Takeshi Ogita, Shinichi Oishi

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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
Publication statusPublished - 2012 Jul


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

ASJC Scopus subject areas

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


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