Adaptive and efficient algorithm for 2D orientation problem

Katsuhisa Ozaki, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi

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1 Citation (Scopus)

Abstract

This paper is concerned with a robust geometric predicate for the 2D orientation problem. Recently, a fast and accurate floating-point summation algorithm is investigated by Rump, Ogita and Oishi, which provably outputs a result faithfully rounded from the exact value of the summation of floating-point numbers. We optimize their algorithm for applying it to the 2D orientation problem which requires only a correct sign of a determinant of a 3×3 matrix. Numerical results illustrate that our algorithm works fairly faster than the state-of-the-art algorithm in various cases.

Original languageEnglish
Pages (from-to)215-231
Number of pages17
JournalJapan Journal of Industrial and Applied Mathematics
Volume26
Issue number2-3
Publication statusPublished - 2009 Oct
Externally publishedYes

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Keywords

  • 2D orientation problem
  • Accurate algorithm
  • Floating-point arithmetic
  • Robust geometric predicate

ASJC Scopus subject areas

  • Applied Mathematics
  • Engineering(all)

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