We consider stabbing regions for a set S of n line segments in the plane, that is, regions in the plane that contain exactly one endpoint of each segment of S. Concretely, we provide efficient algorithms for reporting all combinatorially different stabbing regions for S for regions that can be described as the intersection of axis-parallel halfplanes; these are halfplanes, strips, quadrants, 3-sided rectangles, and rectangles. The running times are O(n) (for the halfplane case), O(n log n) (for strips, quadrants, and 3-sided rectangles), and O(n2 log n) (for rectangles).
CITATION STYLE
Claverol, M., Garijo, D., Korman, M., Seara, C., & Silveira, R. I. (2015). Stabbing segments with rectilinear objects. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9210, pp. 53–64). Springer Verlag. https://doi.org/10.1007/978-3-319-22177-9_5
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