A robust algorithm for geometric predicate by error-free determinant transformation

Katsuhisa Ozaki; Takeshi Ogita; Shinichi Oishi

doi:10.1016/j.ic.2011.09.007

A robust algorithm for geometric predicate by error-free determinant transformation

Katsuhisa Ozaki, Takeshi Ogita, Shinichi Oishi

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

2 Citations (Scopus)

Abstract

This paper concerns a robust algorithm for the 2D orientation problem which is one of the basic tasks in computational geometry. Recently, a fast and accurate floating-point summation algorithm is investigated by Rump, Ogita and Oishi in [S.M. Rump, T. Ogita, S. Oishi, Accurate floating-point summation. Part I: Faithful rounding, SIAM J. Sci. Comput. 31 (1) (2008) 189-224], in which a new kind of an error-free transformation of floating-point numbers is used. Based on it, a new algorithm of error-free determinant transformation for the 2D orientation problem is proposed, which gives a correct result. Numerical results are presented for illustrating that the proposed algorithm has some advantage over preceding algorithms in terms of measured computing time.

Original language	English
Pages (from-to)	3-13
Number of pages	11
Journal	Information and Computation
Volume	216
DOIs	https://doi.org/10.1016/j.ic.2011.09.007
Publication status	Published - 2012 Jul

Keywords

Computational geometry
Error-free determinant transformation
Verified numerical computation

ASJC Scopus subject areas

Theoretical Computer Science
Information Systems
Computer Science Applications
Computational Theory and Mathematics

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10.1016/j.ic.2011.09.007

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abstract = "This paper concerns a robust algorithm for the 2D orientation problem which is one of the basic tasks in computational geometry. Recently, a fast and accurate floating-point summation algorithm is investigated by Rump, Ogita and Oishi in [S.M. Rump, T. Ogita, S. Oishi, Accurate floating-point summation. Part I: Faithful rounding, SIAM J. Sci. Comput. 31 (1) (2008) 189-224], in which a new kind of an error-free transformation of floating-point numbers is used. Based on it, a new algorithm of error-free determinant transformation for the 2D orientation problem is proposed, which gives a correct result. Numerical results are presented for illustrating that the proposed algorithm has some advantage over preceding algorithms in terms of measured computing time.",

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AU - Oishi, Shinichi

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AB - This paper concerns a robust algorithm for the 2D orientation problem which is one of the basic tasks in computational geometry. Recently, a fast and accurate floating-point summation algorithm is investigated by Rump, Ogita and Oishi in [S.M. Rump, T. Ogita, S. Oishi, Accurate floating-point summation. Part I: Faithful rounding, SIAM J. Sci. Comput. 31 (1) (2008) 189-224], in which a new kind of an error-free transformation of floating-point numbers is used. Based on it, a new algorithm of error-free determinant transformation for the 2D orientation problem is proposed, which gives a correct result. Numerical results are presented for illustrating that the proposed algorithm has some advantage over preceding algorithms in terms of measured computing time.

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A robust algorithm for geometric predicate by error-free determinant transformation

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