BIT Numerical Mathematics

, Volume 56, Issue 2, pp 729–749 | Cite as

Simple floating-point filters for the two-dimensional orientation problem

  • Katsuhisa Ozaki
  • Florian Bünger
  • Takeshi Ogita
  • Shin’ichi Oishi
  • Siegfried M. Rump


This paper is concerned with floating-point filters for a two dimensional orientation problem which is a basic problem in the field of computational geometry. If this problem is only approximately solved by floating-point arithmetic, then an incorrect result may be obtained due to accumulation of rounding errors. A floating-point filter can quickly guarantee the correctness of the computed result if the problem is well-conditioned. In this paper, a simple semi-static floating-point filter which handles floating-point exceptions such as overflow and underflow by only one branch is developed. In addition, an improved fully-static filter is developed.


Floating-point arithmetic Floating-point filter  Computational geometry 

Mathematics Subject Classification

65G50 68U05 



The authors wishes to thank the anonymous referee for constructive and valuable comments. This research was partially supported by the CREST program, Japan Science and Technology Agency (JST).


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Katsuhisa Ozaki
    • 1
  • Florian Bünger
    • 2
  • Takeshi Ogita
    • 3
  • Shin’ichi Oishi
    • 4
  • Siegfried M. Rump
    • 2
  1. 1.College of Systems Engineering and ScienceShibaura Institute of TechnologySaitama-shiJapan
  2. 2.Institute for Reliable ComputingHamburg University of TechnologyHamburgGermany
  3. 3.School of Arts and SciencesTokyo Woman’s Christian UniversitySuginami-kuJapan
  4. 4.Faculty of Science and EngineeringWaseda UniversityShinjyuku-kuJapan

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