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Line Segment Intersection Testing

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Abstract

A method for accurately determining whether two given line segments intersect is presented. This method uses the standard floating-point arithmetic that conforms to IEEE 754 standard. If three or four ending points of the two given line segments are on a same vertical or horizontal line, the intersection testing result is obtained directly. Otherwise, the ending points and their connections are mapped onto a 3×3 grid, and the intersection testing falls into one of the five testing classes. The intersection testing method is based on our method for floating-point dot product summation, whose error bound is 1ulp. Our method does not have the limitation in the method of Gavrilova and Rokne (2000) that the product of two floating-point numbers is calculated by a twice higher precision floating-point arithmetic than that of the multipliers. Furthermore, this method requires less than one-fifth of the running time used by the method of Gavrilova and Rokne (2000), and our new method for calculating the sign of a sum of n floating-point numbers requires less than one-fifteenth of the running time used by ESSA.

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Authors and Affiliations

  1. School of Software, Tsinghua University, Beijing, 100084, China

    Y.-K. Zhu, J.-H. Yong & G.-Q. Zheng

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  1. Y.-K. Zhu
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  2. J.-H. Yong
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  3. G.-Q. Zheng
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Correspondence to Y.-K. Zhu.

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Zhu, YK., Yong, JH. & Zheng, GQ. Line Segment Intersection Testing. Computing 75, 337–357 (2005). https://doi.org/10.1007/s00607-005-0120-8

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  • DOI: https://doi.org/10.1007/s00607-005-0120-8

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