Robustness problems and verified computations for computational geometry

Katsuhisa Ozaki, Takeshi Ogita, Shin'ichi 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
Externally publishedYes
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
Digital arithmetic

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, Shin'ichi.

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, Shin'ichi. / 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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