Simple floating-point filters for the two-dimensional orientation problem
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This paper is concerned with floating-point filters for a two dimensional orientation problem which is a basic problem in the field of computational geometry. If this problem is only approximately solved by floating-point arithmetic, then an incorrect result may be obtained due to accumulation of rounding errors. A floating-point filter can quickly guarantee the correctness of the computed result if the problem is well-conditioned. In this paper, a simple semi-static floating-point filter which handles floating-point exceptions such as overflow and underflow by only one branch is developed. In addition, an improved fully-static filter is developed.
KeywordsFloating-point arithmetic Floating-point filter Computational geometry
Mathematics Subject Classification65G50 68U05
The authors wishes to thank the anonymous referee for constructive and valuable comments. This research was partially supported by the CREST program, Japan Science and Technology Agency (JST).
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