Robustness problems and verified computations for computational geometry

Katsuhisa Ozaki, Takeshi Ogita, Shinichi Oishi

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    This paper is concerned with robustness problems in computational geometry. To solve geometric problems, numerical computations by floating-point arithmetic are preferred in terms of computational performance. However, when the rounding errors of floating-point computations accumulate, meaningless results of the problems may be obtained. It is called robustness problem in computational geometry. Recently, several verified algorithms for a two-dimensional orientation problem have been developed. By applying these algorithms, we develop an algorithm which overcomes this problem. Finally, we present numerical examples for a convex hull for a set of points on two-dimensional spaces to illustrate an efficiency of the proposed algorithm.

    Original languageEnglish
    Title of host publicationAsia Simulation Conference 2009, JSST 2009
    PublisherJapan Society for Simulation Technology, JSST
    Publication statusPublished - 2009
    EventAsia Simulation Conference 2009, JSST 2009 - Shiga
    Duration: 2009 Oct 72009 Oct 9

    Other

    OtherAsia Simulation Conference 2009, JSST 2009
    CityShiga
    Period09/10/709/10/9

    Fingerprint

    Computational geometry
    Computational Geometry
    Robustness
    Digital arithmetic
    Floating-point Arithmetic
    Rounding error
    Floating point
    Accumulate
    Convex Hull
    Numerical Computation
    Set of points
    Numerical Examples

    Keywords

    • Accurate numerical computation
    • Computational geometry

    ASJC Scopus subject areas

    • Modelling and Simulation

    Cite this

    Ozaki, K., Ogita, T., & Oishi, S. (2009). Robustness problems and verified computations for computational geometry. In Asia Simulation Conference 2009, JSST 2009 Japan Society for Simulation Technology, JSST.

    Robustness problems and verified computations for computational geometry. / Ozaki, Katsuhisa; Ogita, Takeshi; Oishi, Shinichi.

    Asia Simulation Conference 2009, JSST 2009. Japan Society for Simulation Technology, JSST, 2009.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Ozaki, K, Ogita, T & Oishi, S 2009, Robustness problems and verified computations for computational geometry. in Asia Simulation Conference 2009, JSST 2009. Japan Society for Simulation Technology, JSST, Asia Simulation Conference 2009, JSST 2009, Shiga, 09/10/7.
    Ozaki K, Ogita T, Oishi S. Robustness problems and verified computations for computational geometry. In Asia Simulation Conference 2009, JSST 2009. Japan Society for Simulation Technology, JSST. 2009
    Ozaki, Katsuhisa ; Ogita, Takeshi ; Oishi, Shinichi. / Robustness problems and verified computations for computational geometry. Asia Simulation Conference 2009, JSST 2009. Japan Society for Simulation Technology, JSST, 2009.
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