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

中文翻译：

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二维方向问题的自适应高效算法

本文关注的是二维方向问题的鲁棒几何谓词。最近，Rump、Ogita 和 Oishi 研究了一种快速准确的浮点求和算法，该算法可证明输出忠实地从浮点数总和的精确值四舍五入的结果。我们优化了他们的算法，将其应用于 2D 方向问题，该问题只需要 3 × 3 矩阵行列式的正确符号。数值结果表明，在各种情况下，我们的算法比最先进的算法运行得更快。