Ozaki, KatsuhisaKatsuhisaOzakiOgita, TakeshiTakeshiOgitaRump, Siegfried M.Siegfried M.RumpOishi, Shin’ichiShin’ichiOishi2021-01-252021-01-252009-10Japan Journal of Industrial and Applied Mathematics 2/3 (26): 215-231 (2009)http://hdl.handle.net/11420/8559This 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.en1868-937X20092/3215231Springer Nature2D orientation problemAccurate algorithmFloating-point arithmeticRobust geometric predicateInformatikMathematikJournal Article10.1007/BF03186532Other