Adaptive and efficient algorithm for 2D orientation problem

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

doi:10.1007/BF03186532

Adaptive and efficient algorithm for 2D orientation problem

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

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	215-231
Number of pages	17
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	26
Issue number	2-3
DOIs	https://doi.org/10.1007/BF03186532
Publication status	Published - 2009 Oct

Keywords

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

ASJC Scopus subject areas

Engineering(all)
Applied Mathematics

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10.1007/BF03186532

Cite this

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title = "Adaptive and efficient algorithm for 2D orientation problem",

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.",

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author = "Katsuhisa Ozaki and Takeshi Ogita and Rump, {Siegfried M.} and Shin'ichi Oishi",

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AU - Ozaki, Katsuhisa

AU - Ogita, Takeshi

AU - Rump, Siegfried M.

AU - Oishi, Shin'ichi

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Y1 - 2009/10

N2 - 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.

AB - 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.

KW - 2D orientation problem

KW - Accurate algorithm

KW - Floating-point arithmetic

KW - Robust geometric predicate

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JO - Japan Journal of Industrial and Applied Mathematics

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Adaptive and efficient algorithm for 2D orientation problem

Abstract

Keywords

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