Edelsbrunner, HerbertIST Austria ; Maurer, Hermann A ; Preparata, Franco P ; Rosenberg, Arnold L ; Welzl, Emo ; Wood, Derick
An algorithm for the geometric problem of determining a line (called a stabbing line) which intersects each ofn given line segments in the plane is presented. As a matter of fact, the algorithm computes a description of all stabbing lines. A purely geometric fact is proved which infers that this description requiresO(n) space to be specified. Our algorithm computes it inO(n logn) time which is optimal in the worst case. Using the description of the stabbing lines, we are able to decide inO(logn) time whether or not a specified line is a stabbing line. Finally, the problem of maintaining the description of all stabbing lines while inserting and deleting line segments is addressed.
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Edelsbrunner H, Maurer H, Preparata F, Rosenberg A, Welzl E, Wood D. Stabbing line segments. Bit. 1982;22(3):274-281. doi:10.1007/BF01934440
Edelsbrunner, H., Maurer, H., Preparata, F., Rosenberg, A., Welzl, E., & Wood, D. (1982). Stabbing line segments. Bit, 22(3), 274–281. https://doi.org/10.1007/BF01934440
Edelsbrunner, Herbert, Hermann Maurer, Franco Preparata, Arnold Rosenberg, Emo Welzl, and Derick Wood. “Stabbing Line Segments.” Bit 22, no. 3 (1982): 274–81. https://doi.org/10.1007/BF01934440.
H. Edelsbrunner, H. Maurer, F. Preparata, A. Rosenberg, E. Welzl, and D. Wood, “Stabbing line segments,” Bit, vol. 22, no. 3, pp. 274–281, 1982.
Edelsbrunner H, Maurer H, Preparata F, Rosenberg A, Welzl E, Wood D. 1982. Stabbing line segments. Bit. 22(3), 274–281.
Edelsbrunner, Herbert, et al. “Stabbing Line Segments.” Bit, vol. 22, no. 3, Springer, 1982, pp. 274–81, doi:10.1007/BF01934440.