Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
Interval arithmetic yields efficient dynamic filters for computational geometry
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
SIAM Journal on Scientific Computing
Classroom examples of robustness problems in geometric computations
Computational Geometry: Theory and Applications
Safe and effective determinant evaluation
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Accurate Floating-Point Summation Part I: Faithful Rounding
SIAM Journal on Scientific Computing
Accurate Floating-Point Summation Part II: Sign, $K$-Fold Faithful and Rounding to Nearest
SIAM Journal on Scientific Computing
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
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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.