Open Access
October 2009 Adaptive and Efficient Algorithm for 2D Orientation Problem
Katsuhisa Ozaki, Takeshi Ogita, Siegfried M. Rump, Shin'ichi Oishi
Japan J. Indust. Appl. Math. 26(2-3): 215-231 (October 2009).


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 $3\times 3$ matrix. Numerical results illustrate that our algorithm works fairly faster than the state-of-the-art algorithm in various cases.


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Katsuhisa Ozaki. Takeshi Ogita. Siegfried M. Rump. Shin'ichi Oishi. "Adaptive and Efficient Algorithm for 2D Orientation Problem." Japan J. Indust. Appl. Math. 26 (2-3) 215 - 231, October 2009.


Published: October 2009
First available in Project Euclid: 1 February 2010

zbMATH: 1185.65037
MathSciNet: MR2589473

Keywords: 2D orientation problem , accurate algorithm , floating-point arithmetic , robust geometric predicate

Rights: Copyright © 2009 The Japan Society for Industrial and Applied Mathematics

Vol.26 • No. 2-3 • October 2009
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