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

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.