Intersections and circuits in sets of line segments
Journal of Combinatorial Optimization
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.
National Science Foundation
Cactus graph, Circuits, Halin graph, Intersection points, Maximal planar graph, Triangle-free planar graph
Mathematics and Statistics
Boris Brimkov, Jesse Geneson, Alathea Jensen, Jordan Broussard, and Pouria Salehi Nowbandegani. "Intersections and circuits in sets of line segments" Journal of Combinatorial Optimization (2022): 2302-2323. https://doi.org/10.1007/s10878-021-00731-3