Intersections and circuits in sets of line segments

Boris Brimkov (), Jesse Geneson (), Alathea Jensen (), Jordan Broussard () and Pouria Salehi Nowbandegani ()
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Boris Brimkov: Slippery Rock University
Jesse Geneson: San Jose State University
Alathea Jensen: Susquehanna University
Jordan Broussard: Washington State University
Pouria Salehi Nowbandegani: Broad Institute of MIT and Harvard

Journal of Combinatorial Optimization, 2022, vol. 44, issue 4, No 9, 2302-2323

Abstract: Abstract Sets of straight line segments with special structures and properties appear in various applications of geometric modeling, such as scientific visualization, computer-aided design, and medical image processing. In this paper, we derive sharp upper and lower bounds on the number of intersection points and closed regions that can occur in sets of line segments with certain structure, in terms of the number of segments. In particular, we consider sets of segments whose underlying planar graphs are Halin graphs, cactus graphs, maximal planar graphs, and triangle-free planar graphs, as well as randomly produced segment sets.

Keywords: Intersection points; Circuits; Halin graph; Cactus graph; Maximal planar graph; Triangle-free planar graph (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10878-021-00731-3

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